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<body>
<div>*** START OF THE PROJECT GUTENBERG EBOOK 48871 ***</div>

<div class="front">
<div class="div1 cover">
<div class="divBody">
<p class="par first"></p>
<div class="figure xd21e115width"><img src="images/new-cover.jpg" alt=
"Newly Designed Front Cover." width="480" height="720"></div>
<p class="par"></p>
</div>
</div>
<div class="div1 titlepage">
<div class="divBody">
<p class="par first"></p>
<div class="figure xd21e121width"><img src="images/titlepage.png" alt=
"Original Title Page." width="440" height="720"></div>
<p class="par"></p>
</div>
</div>
<div class="titlePage">
<div class="docTitle">
<div class="mainTitle">MANUAL FOR THE SOLUTION OF MILITARY
CIPHERS</div>
</div>
<div class="byline">BY<br>
<span class="docAuthor">PARKER HITT</span><br>
<i>Captain of Infantry, U. S. A.</i></div>
<div class="docImprint">PRESS OF<br>
THE ARMY SERVICE SCHOOLS<br>
Fort Leavenworth, Kansas<br>
<span class="docDate">1916</span></div>
</div>
<p><span class="pagenum">[<a id="xd21e150" href="#xd21e150" name=
"xd21e150">v</a>]</span></p>
<div class="div1 head">
<div class="divBody">
<p class="par first xd21e152">MANUAL FOR THE SOLUTION<br>
OF MILITARY CIPHERS</p>
<p class="par xd21e152">BY<br>
PARKER HITT<br>
Captain of Infantry, United States Army</p>
</div>
</div>
<div class="div1 introduction">
<div class="divHead">
<h2 class="main">Introduction</h2>
</div>
<div class="divBody">
<p class="par xd21e165"><span class="xd21e165init">T</span>he history
of war teems with occasions where the interception of dispatches and
orders written in plain language has resulted in defeat and disaster
for the force whose intentions thus became known at once to the enemy.
For this reason, prudent generals have used cipher and code messages
from time immemorial. The necessity for exact expression of ideas
practically excludes the use of codes for military work although it is
possible that a special tactical code might be useful for preparation
of tactical orders.</p>
<p class="par">It is necessary therefore to fall back on ciphers for
general military work if secrecy of communication is to be fairly well
assured. It may as well be stated here that no practicable military
cipher is mathematically indecipherable if intercepted; the most that
can be expected is to delay for a longer or shorter time the
deciphering of the message by the interceptor.</p>
<p class="par">The capture of messengers is no longer the only means
available to the enemy for gaining information as to the plans of a
commander. All radio messages sent out can be copied at hostile
stations within radio range. If the enemy can get a fine wire within
one hundred feet of a buzzer line or within thirty feet of a telegraph
line, the message can be copied by induction. Messages passing over
commercial telegraph lines, and even over military lines, can be copied
by spies in the offices. On telegraph lines of a permanent nature it is
possible to install high speed automatic sending and receiving machines
and thus prevent surreptitious copying of messages, but nothing but a
secure cipher will serve with other means of communication.
<span class="pagenum">[<a id="xd21e171" href="#xd21e171" name=
"xd21e171">vi</a>]</span></p>
<p class="par">It is not alone the body of the message which should be
in cipher. It is equally important that, during transmission, the
preamble, place from, date, address and signature be enciphered; but
this should be done by the sending operator and these parts must, of
course, be deciphered by the receiving operator before delivery. A
special operators&rsquo; cipher should be used for this purpose but it
is difficult to prescribe one that would be simple enough for the
average operator, fast and yet reasonably safe. Some form of rotary
cipher machine would seem to be best suited for this special
purpose.</p>
<p class="par">It is unnecessary to point out that a cipher which can
be deciphered by the enemy in a few hours is worse than useless. It
requires a surprisingly long time to encipher and decipher a message,
using even the simplest kind of cipher, and errors in transmission of
cipher matter by wire or radio are unfortunately too common.</p>
<p class="par">Kerckhoffs has stated that a military cipher should
fulfill the following requirements:</p>
<ul>
<li>1st. The system should be materially, if not mathematically,
indecipherable.</li>
<li>2d. It should cause no inconvenience if the apparatus and methods
fall into the hands of the enemy.</li>
<li>3d. The key should be such that it could be communicated and
remembered without the necessity of written notes and should be
changeable at the will of the correspondents.</li>
<li>4th. The system should be applicable to telegraphic
correspondence.</li>
<li>5th. The apparatus should be easily carried and a single person
should be able to operate it.</li>
<li>6th. Finally, in view of the circumstances under which it must be
used, the system should be an easy one to operate, demanding neither
mental strain nor knowledge of a long series of rules.</li>
</ul>
<p class="par"></p>
<p class="par">A brief consideration of these six conditions must lead
to the conclusion that there is no perfect military cipher. The first
requirement is the one most often overlooked by those prescribing the
use of any given cipher and, even if not overlooked, the
indecipherability of any cipher likely to be used for military purposes
is usually vastly overestimated by those prescribing the use of it.</p>
<p class="par">If this were not true, there would have been neither
material for, nor purpose in, the preparation of these notes. Of the
hundreds of actual cipher messages examined by the writer, at least
nine-tenths have been solved by the methods to be set forth. These
messages were prepared by the methods in use by the United States Army,
the various Mexican <span class="pagenum">[<a id="xd21e196" href=
"#xd21e196" name="xd21e196">vii</a>]</span>armies and their secret
agents, and by other methods in common use. The usual failure has been
with very short messages. Foreign works consulted lead to the belief
that many European powers have used, for military purposes, cipher
methods which vary from an extreme simplicity to a complexity which is
more apparent than real. What effect recent events have had on this
matter remains to be seen. It is enough that the cipher experts of
practically every European country have appealed to the military
authorities of their respective countries time and again to do away
with these useless ciphers and to adopt something which offers more
security, even at the expense of other considerations.</p>
<p class="par">The cipher of the amateur, or of the non-expert who
makes one up for some special purpose, is almost sure to fall into one
of the classes whose solution is an easy matter. The human mind works
along the same lines, in spite of an attempt at originality on the part
of the individual, and this is particularly true of cipher work because
there are so few sources of information available. In other words, the
average man, when he sits down to evolve a cipher, has nothing to
improve upon; he invents and there is no one to tell him that his
invention is, in principle, hundreds of years old. The ciphers of the
Abb&eacute; Tritheme, 1499, are the basis of most of the modern
substitution ciphers.</p>
<p class="par">In view of these facts, no message should be considered
indecipherable. Very short messages are often very difficult and may
easily be entirely beyond the possibility of analysis and solution, but
it is surprising what can be done, at times, with a message of only a
few words.</p>
<p class="par">In the event of active operations, cipher experts will
be in demand at once. Like all other experts, the cipher expert is not
born or made in a day; and it is only constant work with ciphers,
combined with a thorough knowledge of their underlying principles, that
will make one worthy of the name. <span class="pagenum">[<a id="pb1"
href="#pb1" name="pb1">1</a>]</span></p>
</div>
</div>
</div>
<div class="body">
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter I</h2>
<h2 class="main">Equipment for Cipher Work</h2>
</div>
<div class="divBody">
<p class="par xd21e212"><span class="xd21e212init">S</span>uccess in
dealing with unknown ciphers is measured by these four things in the
order named; perseverance, careful methods of analysis, intuition,
luck. The ability at least to read the language of the original text is
very desirable but not essential.</p>
<p class="par">Cipher work will have little permanent attraction for
one who expects results at once, without labor, for there is a vast
amount of purely routine labor in the preparation of frequency tables,
the rearrangement of ciphers for examination, and the trial and fitting
of letter to letter before the message begins to appear.</p>
<p class="par">The methods of analysis given in these notes cover only
the simpler varieties of cipher and it is, of course, impossible to
enumerate all the varieties of these. It is believed that the methods
laid down are sound and several years of successful work along this
line would seem to confirm this belief. For more advanced work there is
no recourse but to study the European authorities whose writings are
mostly in French, German, and Italian and, unfortunately, are rarely
available in English translations.</p>
<p class="par">Under intuition must be included a knowledge of the
general situation and, if possible, the special situation which led to
the sending of the cipher message. The knowledge or guess that a
certain cipher <span class="corr" id="xd21e220" title=
"Source: messages">message</span> contains a particular word, often
leads to its solution. <span class="pagenum">[<a id="pb2" href="#pb2"
name="pb2">2</a>]</span></p>
<p class="par">As to luck, there is the old miner&rsquo;s proverb:
&ldquo;Gold is where you find it.&rdquo;</p>
<p class="par">The equipment for an office, where much cipher work is
handled, will now be considered. The casual worker with ciphers can get
along with much less, but the methods of filing and keeping a record of
all messages studied should be followed wherever possible. The
interchange of results between individuals and between offices should
be encouraged and, in time of active operations, should be mandatory.
An enemy may be using the same cipher in widely separated parts of the
zone of operations and it is useless labor to have many cipher offices
working on intercepted messages, all in the same cipher, when one
office may have the solution that will apply to all of them.</p>
<p class="par">Cipher work requires concentration and quiet and often
must proceed without regard to hours. The office should be chosen with
these points in mind. A clerical force is desirable and even necessary
if there is much work to do. The clerk or clerks can soon be trained to
do the routine part of the analysis.</p>
<p class="par">It is believed that each Field Army should have such an
office where all ciphers intercepted by forces under command of the
Field Army Commander should be sent at once for examination. This work
naturally falls to the Intelligence section of the General Staff at
this headquarters. A special radio station, with receiving instruments
only, should be an adjunct to this office and its function should be to
copy all hostile radio messages whether in cipher or plain text. Such a
radio station requires but a small antenna; one of the pack set type or
any amateur&rsquo;s antenna is sufficient, and the station instruments
can be easily carried in a suit case. Three thoroughly competent
operators should be <span class="pagenum">[<a id="pb3" href="#pb3"
name="pb3">3</a>]</span>provided, so that the station can be
&ldquo;listening in&rdquo; during the entire twenty-four hours.</p>
<p class="par">The office should be provided with tables of frequency
of the language of the enemy, covering single letters and digraphs; a
dictionary and grammar of that language; copies of the War Department
Code, Western Union Code and any other available ones; types of
apparatus or, at least, data on apparatus and cipher methods in use by
the enemy; and a safe filing cabinet and card index for filing messages
examined. A typewriter is also desirable.</p>
<p class="par">The office work on a cipher under examination should be
done on paper of a standard and uniform size. Printed forms containing
twenty-six ruled lines and a vertical alphabet are convenient and save
time in preparation of frequency tables. Any new cipher methods which
are found to be in use by the enemy should, when solved, be
communicated to all similar offices in the Army for their
information.</p>
<p class="par">Unless an enemy were exceedingly vigilant and changed
keys and methods frequently, such an office would, in a few days, be in
a position to disclose completely all intercepted cipher communications
of the enemy with practically no delay. <span class="pagenum">[<a id=
"pb4" href="#pb4" name="pb4">4</a>]</span></p>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter II</h2>
<h2 class="main">Principles of Mechanism of a Written Language</h2>
</div>
<div class="divBody">
<p class="par xd21e247"><span class="xd21e247init">W</span>ith a few
exceptions, notably Chinese, all modern languages are constructed of
words which in turn are formed from letters. In any given language the
number of letters, and their conventional order is fixed. Thus English
is written with 26 letters and their conventional order is <span class=
"tt">A</span>, <span class="tt">B</span>, <span class="tt">C</span>,
<span class="tt">D</span>, <span class="tt">E</span>, etc. Some letters
are used very frequently and others rarely. In fact, if ten thousand
consecutive letters of a text be counted and the frequency of
occurrence of each letter be noted, the numbers found will be
practically identical with those obtained from any other text of ten
thousand letters in the same language. The relative proportion of
occurrence of the various letters will also hold approximately for even
very short texts.</p>
<p class="par">Such a count of a large number of letters, when it is
put in the form of a table, is known as a frequency table. Every
language has its own distinctive frequency table and, for any given
language, the frequency table is almost as fixed as the alphabet. There
are minor differences in frequency tables prepared from texts on
special subjects. For example, if the text be newspaper matter, the
frequency table will differ slightly from one prepared from military
orders and will also differ slightly from one prepared from telegraph
messages. But these differences are very slight as compared with the
differences between the frequency tables of two different
languages.</p>
<p class="par">Again there is a fixed ratio of occurrence of
<span class="pagenum">[<a id="pb5" href="#pb5" name=
"pb5">5</a>]</span>every letter with every other for any language and
this, put in table form, constitutes a table of frequency of digraphs.
In the same way a table of trigraphs, showing the ratio of occurrence
of any three letters in sequence, could be prepared, but such a table
would be very extensive and a count of the more common three letter
combinations is usually used.</p>
<p class="par">Other tables, such as frequency of initial and final
letters of words, might be of value but the common practice is to put
cipher text into groups of five or ten letters each and eliminate word
forms. This is almost a necessity in telegraphic and radio
communication to enable the receiving operator to check correct receipt
of a message. He must get five letters, neither more nor less, per word
or he is sure a mistake has been made. There is little difficulty, as a
rule, in restoring word forms in the deciphered message.</p>
<p class="par">We will now take up, in order, the various frequency
tables and linguistic peculiarities of English and Spanish. Frequency
tables for French, German, and Italian for single letters will follow.
All frequency tables have been re-calculated from at least ten thousand
letters of text and compared with existing tables. No marked difference
has been found in any case between the re-calculated tables and those
already in use.</p>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Data for Solution of Ciphers in English</h3>
</div>
<div class="divBody">
<p class="par first"><span class="sc">Table I.</span>&mdash;Normal
frequency table. Frequency for ten thousand letters and for two hundred
letters. This latter is put in graphic form and is necessarily an
approximation. Taken from military orders and reports, English text.
<span class="pagenum">[<a id="pb6" href="#pb6" name=
"pb6">6</a>]</span></p>
<div class="table">
<table class="xd21e283">
<thead>
<tr class="label">
<td class="xd21e284 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e285 cellHeadTop cellHeadBottom">10,000 Letters</td>
<td colspan="2" class=
"xd21e285 cellHeadRight cellHeadTop cellHeadBottom">200 Letters</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e284 cellLeft">A</td>
<td class="xd21e285">778</td>
<td class="xd21e285">16</td>
<td class="xd21e287 cellRight">1111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">B</td>
<td class="xd21e285">141</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">C</td>
<td class="xd21e285">296</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">D</td>
<td class="xd21e285">402</td>
<td class="xd21e285">8</td>
<td class="xd21e287 cellRight">11111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">E</td>
<td class="xd21e285">1277</td>
<td class="xd21e285">26</td>
<td class="xd21e287 cellRight">11111111111111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">F</td>
<td class="xd21e285">197</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">G</td>
<td class="xd21e285">174</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">H</td>
<td class="xd21e285">595</td>
<td class="xd21e285">12</td>
<td class="xd21e287 cellRight">111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">I</td>
<td class="xd21e285">667</td>
<td class="xd21e285">13</td>
<td class="xd21e287 cellRight">1111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">J</td>
<td class="xd21e285">51</td>
<td class="xd21e285">1</td>
<td class="xd21e287 cellRight">1</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">K</td>
<td class="xd21e285">74</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">L</td>
<td class="xd21e285">372</td>
<td class="xd21e285">7</td>
<td class="xd21e287 cellRight">1111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">M</td>
<td class="xd21e285">288</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">N</td>
<td class="xd21e285">686</td>
<td class="xd21e285">14</td>
<td class="xd21e287 cellRight">11111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">O</td>
<td class="xd21e285">807</td>
<td class="xd21e285">16</td>
<td class="xd21e287 cellRight">1111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">P</td>
<td class="xd21e285">223</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Q</td>
<td class="xd21e285">8</td>
<td class="xd21e285"></td>
<td class="xd21e287 cellRight"></td>
</tr>
<tr>
<td class="xd21e284 cellLeft">R</td>
<td class="xd21e285">651</td>
<td class="xd21e285">13</td>
<td class="xd21e287 cellRight">1111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">S</td>
<td class="xd21e285">622</td>
<td class="xd21e285">12</td>
<td class="xd21e287 cellRight">111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">T</td>
<td class="xd21e285">855</td>
<td class="xd21e285">17</td>
<td class="xd21e287 cellRight">11111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">U</td>
<td class="xd21e285">308</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">V</td>
<td class="xd21e285">112</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">W</td>
<td class="xd21e285">176</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">X</td>
<td class="xd21e285">27</td>
<td class="xd21e285"></td>
<td class="xd21e287 cellRight"></td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Y</td>
<td class="xd21e285">196</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft cellBottom">Z</td>
<td class="xd21e285 cellBottom">17</td>
<td class="xd21e285 cellBottom"></td>
<td class="xd21e287 cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par xd21e529">Vowels <span class="tt">AEIOU</span> = 38.37%;
consonants <span class="tt">LNRST</span> = 31.86%; consonants
<span class="tt">JKQXZ</span> = 1.77%.</p>
<p class="par xd21e529">The vowels may be safely taken as 40%,
consonants <span class="tt">LNRST</span> as 30% and consonants
<span class="tt">JKQXZ</span> as 2%.</p>
<p class="par xd21e529">Order of letters: <span class="tt">E T O A N I
R S H D L U C M P F Y W G B V K J X Z Q</span>.</p>
<p class="par"><span class="sc">Table II.</span>&mdash;Frequency table
for telegraph messages, English text. This table varies slightly from
the standard frequency table because the common word &ldquo;the&rdquo;
is rarely used in telegrams and there is a tendency to use longer and
less common words in preparing telegraph messages. <span class=
"pagenum">[<a id="pb7" href="#pb7" name="pb7">7</a>]</span></p>
<div class="table">
<table class="xd21e283">
<thead>
<tr class="label">
<td class="xd21e284 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e285 cellHeadTop cellHeadBottom">10,000 Letters</td>
<td colspan="2" class=
"xd21e285 cellHeadRight cellHeadTop cellHeadBottom">200 Letters</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e284 cellLeft">A</td>
<td class="xd21e285">813</td>
<td class="xd21e285">16</td>
<td class="xd21e287 cellRight">1111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">B</td>
<td class="xd21e285">149</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">C</td>
<td class="xd21e285">306</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">D</td>
<td class="xd21e285">417</td>
<td class="xd21e285">8</td>
<td class="xd21e287 cellRight">11111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">E</td>
<td class="xd21e285">1319</td>
<td class="xd21e285">26</td>
<td class="xd21e287 cellRight">11111111111111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">F</td>
<td class="xd21e285">205</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">G</td>
<td class="xd21e285">201</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">H</td>
<td class="xd21e285">386</td>
<td class="xd21e285">8</td>
<td class="xd21e287 cellRight">11111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">I</td>
<td class="xd21e285">711</td>
<td class="xd21e285">14</td>
<td class="xd21e287 cellRight">11111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">J</td>
<td class="xd21e285">42</td>
<td class="xd21e285">1</td>
<td class="xd21e287 cellRight">1</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">K</td>
<td class="xd21e285">88</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">L</td>
<td class="xd21e285">392</td>
<td class="xd21e285">8</td>
<td class="xd21e287 cellRight">11111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">M</td>
<td class="xd21e285">273</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">N</td>
<td class="xd21e285">718</td>
<td class="xd21e285">14</td>
<td class="xd21e287 cellRight">11111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">O</td>
<td class="xd21e285">844</td>
<td class="xd21e285">17</td>
<td class="xd21e287 cellRight">11111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">P</td>
<td class="xd21e285">243</td>
<td class="xd21e285">5</td>
<td class="xd21e287 cellRight">11111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Q</td>
<td class="xd21e285">38</td>
<td class="xd21e285">1</td>
<td class="xd21e287 cellRight">1</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">R</td>
<td class="xd21e285">677</td>
<td class="xd21e285">14</td>
<td class="xd21e287 cellRight">11111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">S</td>
<td class="xd21e285">656</td>
<td class="xd21e285">13</td>
<td class="xd21e287 cellRight">1111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">T</td>
<td class="xd21e285">634</td>
<td class="xd21e285">13</td>
<td class="xd21e287 cellRight">1111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">U</td>
<td class="xd21e285">321</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">V</td>
<td class="xd21e285">136</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">W</td>
<td class="xd21e285">166</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">X</td>
<td class="xd21e285">51</td>
<td class="xd21e285">1</td>
<td class="xd21e287 cellRight">1</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Y</td>
<td class="xd21e285">208</td>
<td class="xd21e285">4</td>
<td class="xd21e287 cellRight">1111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft cellBottom">Z</td>
<td class="xd21e285 cellBottom">6</td>
<td class="xd21e285 cellBottom"></td>
<td class="xd21e287 cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par xd21e529">In this table the vowels <span class=
"tt">AEIOU</span> = 40.08%, consonants <span class="tt">LNRST</span> =
30.77% and consonants <span class="tt">JKQXZ</span> = 2.25%.</p>
<p class="par xd21e529">Orders of letters: <span class="tt">E O A N I R
S T D L H U C M P Y F G W B V K X J Q Z</span>.</p>
<p class="par"><span class="sc">Table III.</span>&mdash;Table of
frequency of digraphs, duals or pairs (English). This table was
prepared from 20,000 letters, but the figures shown are on the basis of
2,000 letters. For this reason they are, to a certain extent,
approximate; that is, merely because no figures are shown for certain
combinations, we should not assume that such combinations never occur
but rather that they are rare. The letters in the horizontal line at
the top and bottom are the leading letters; those in the vertical
columns at the sides are the following letters. Thus in two thousand
letters we may expect to find <span class="tt">AH</span> once and
<span class="tt">HA</span> twenty-six times. <span class=
"pagenum">[<a id="pb8" href="#pb8" name="pb8">8</a>]</span></p>
<div class="table">
<table class="borderAll xd21e835">
<thead>
<tr class="label">
<td class="xd21e836 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="cellHeadTop cellHeadBottom">A</td>
<td class="cellHeadTop cellHeadBottom">B</td>
<td class="cellHeadTop cellHeadBottom">C</td>
<td class="cellHeadTop cellHeadBottom">D</td>
<td class="cellHeadTop cellHeadBottom">E</td>
<td class="cellHeadTop cellHeadBottom">F</td>
<td class="cellHeadTop cellHeadBottom">G</td>
<td class="cellHeadTop cellHeadBottom">H</td>
<td class="cellHeadTop cellHeadBottom">I</td>
<td class="cellHeadTop cellHeadBottom">J</td>
<td class="cellHeadTop cellHeadBottom">K</td>
<td class="cellHeadTop cellHeadBottom">L</td>
<td class="cellHeadTop cellHeadBottom">M</td>
<td class="cellHeadTop cellHeadBottom">N</td>
<td class="cellHeadTop cellHeadBottom">O</td>
<td class="cellHeadTop cellHeadBottom">P</td>
<td class="cellHeadTop cellHeadBottom">Q</td>
<td class="cellHeadTop cellHeadBottom">R</td>
<td class="cellHeadTop cellHeadBottom">S</td>
<td class="cellHeadTop cellHeadBottom">T</td>
<td class="cellHeadTop cellHeadBottom">U</td>
<td class="cellHeadTop cellHeadBottom">V</td>
<td class="cellHeadTop cellHeadBottom">W</td>
<td class="cellHeadTop cellHeadBottom">X</td>
<td class="cellHeadTop cellHeadBottom">Y</td>
<td class="cellHeadRight cellHeadTop cellHeadBottom">Z</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e836 cellLeft">A</td>
<td></td>
<td>1</td>
<td>7</td>
<td>10</td>
<td>22</td>
<td>3</td>
<td>2</td>
<td>26</td>
<td>4</td>
<td>2</td>
<td>2</td>
<td>7</td>
<td>8</td>
<td>11</td>
<td>2</td>
<td>9</td>
<td></td>
<td>13</td>
<td>12</td>
<td>9</td>
<td></td>
<td>2</td>
<td>4</td>
<td>1</td>
<td>12</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">B</td>
<td>5</td>
<td></td>
<td></td>
<td>1</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td>1</td>
<td>1</td>
<td>1</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">C</td>
<td>6</td>
<td></td>
<td>1</td>
<td>1</td>
<td>14</td>
<td>2</td>
<td></td>
<td></td>
<td>11</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>11</td>
<td>3</td>
<td></td>
<td></td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>1</td>
<td></td>
<td>1</td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">D</td>
<td>6</td>
<td></td>
<td></td>
<td>12</td>
<td>30</td>
<td>1</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td>30</td>
<td>1</td>
<td></td>
<td></td>
<td>4</td>
<td>1</td>
<td>1</td>
<td>1</td>
<td></td>
<td>1</td>
<td></td>
<td>3</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">E</td>
<td></td>
<td>11</td>
<td>14</td>
<td>16</td>
<td>12</td>
<td>2</td>
<td>6</td>
<td>33</td>
<td>10</td>
<td>2</td>
<td>6</td>
<td>18</td>
<td>14</td>
<td>12</td>
<td>1</td>
<td>7</td>
<td></td>
<td>36</td>
<td>11</td>
<td>12</td>
<td>2</td>
<td>16</td>
<td>5</td>
<td></td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">F</td>
<td>3</td>
<td></td>
<td></td>
<td>2</td>
<td>8</td>
<td>2</td>
<td>1</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td>3</td>
<td>25</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">G</td>
<td>4</td>
<td></td>
<td></td>
<td>1</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>11</td>
<td>2</td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">H</td>
<td>1</td>
<td></td>
<td>11</td>
<td>2</td>
<td>4</td>
<td>1</td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>2</td>
<td>1</td>
<td>1</td>
<td></td>
<td>2</td>
<td>10</td>
<td>50</td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td>2</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">I</td>
<td>2</td>
<td>1</td>
<td>4</td>
<td>12</td>
<td>6</td>
<td>5</td>
<td>1</td>
<td>12</td>
<td>1</td>
<td></td>
<td>5</td>
<td>9</td>
<td>8</td>
<td>12</td>
<td>1</td>
<td>3</td>
<td></td>
<td>12</td>
<td>13</td>
<td>22</td>
<td>2</td>
<td>3</td>
<td>6</td>
<td></td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">J</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">K</td>
<td>1</td>
<td></td>
<td>1</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">L</td>
<td>14</td>
<td>6</td>
<td>2</td>
<td>1</td>
<td>6</td>
<td>1</td>
<td>1</td>
<td>1</td>
<td>6</td>
<td></td>
<td></td>
<td>9</td>
<td></td>
<td>3</td>
<td>6</td>
<td>3</td>
<td></td>
<td>3</td>
<td>2</td>
<td>3</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">M</td>
<td>7</td>
<td></td>
<td></td>
<td>3</td>
<td>13</td>
<td>2</td>
<td></td>
<td>2</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td>1</td>
<td>10</td>
<td></td>
<td></td>
<td>4</td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">N</td>
<td>38</td>
<td></td>
<td></td>
<td>3</td>
<td>25</td>
<td></td>
<td>2</td>
<td>1</td>
<td>31</td>
<td></td>
<td>3</td>
<td></td>
<td>2</td>
<td>2</td>
<td>39</td>
<td></td>
<td></td>
<td>4</td>
<td>3</td>
<td></td>
<td>11</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">O</td>
<td>1</td>
<td>1</td>
<td>12</td>
<td>4</td>
<td>8</td>
<td>8</td>
<td>3</td>
<td>12</td>
<td>18</td>
<td>2</td>
<td></td>
<td>4</td>
<td>7</td>
<td>8</td>
<td>3</td>
<td>7</td>
<td></td>
<td>13</td>
<td>15</td>
<td>22</td>
<td></td>
<td>2</td>
<td>6</td>
<td>1</td>
<td>5</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">P</td>
<td>2</td>
<td></td>
<td></td>
<td>1</td>
<td>8</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td>2</td>
<td>4</td>
<td>2</td>
<td>3</td>
<td>2</td>
<td></td>
<td>1</td>
<td>8</td>
<td>1</td>
<td>4</td>
<td></td>
<td></td>
<td>3</td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Q</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">R</td>
<td>16</td>
<td>1</td>
<td>3</td>
<td>3</td>
<td>40</td>
<td>3</td>
<td>6</td>
<td>2</td>
<td>6</td>
<td></td>
<td></td>
<td>1</td>
<td>2</td>
<td>1</td>
<td>25</td>
<td>8</td>
<td></td>
<td>2</td>
<td>2</td>
<td>8</td>
<td>11</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">S</td>
<td>16</td>
<td>1</td>
<td></td>
<td>3</td>
<td>25</td>
<td>1</td>
<td>2</td>
<td></td>
<td>17</td>
<td></td>
<td>1</td>
<td>2</td>
<td>1</td>
<td>12</td>
<td>7</td>
<td>2</td>
<td></td>
<td>9</td>
<td>11</td>
<td>6</td>
<td>11</td>
<td></td>
<td>1</td>
<td></td>
<td>6</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">T</td>
<td>25</td>
<td>1</td>
<td>3</td>
<td>12</td>
<td>13</td>
<td>5</td>
<td>2</td>
<td>3</td>
<td>20</td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td>24</td>
<td>8</td>
<td>2</td>
<td></td>
<td>16</td>
<td>20</td>
<td>11</td>
<td>6</td>
<td></td>
<td>2</td>
<td>2</td>
<td>7</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">U</td>
<td>1</td>
<td>2</td>
<td>1</td>
<td>6</td>
<td>1</td>
<td>3</td>
<td>2</td>
<td>2</td>
<td></td>
<td>3</td>
<td></td>
<td>3</td>
<td>1</td>
<td></td>
<td>17</td>
<td>1</td>
<td>5</td>
<td>3</td>
<td>5</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">V</td>
<td>3</td>
<td>1</td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">W</td>
<td>1</td>
<td></td>
<td></td>
<td>2</td>
<td>8</td>
<td></td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td>1</td>
<td>2</td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">X</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Y</td>
<td>3</td>
<td>2</td>
<td></td>
<td>2</td>
<td>4</td>
<td></td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>8</td>
<td>1</td>
<td>2</td>
<td></td>
<td>1</td>
<td></td>
<td>3</td>
<td>1</td>
<td>7</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Z</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e2354 xd21e836 cellLeft cellBottom"></td>
<td class="xd21e2354 cellBottom">A</td>
<td class="xd21e2354 cellBottom">B</td>
<td class="xd21e2354 cellBottom">C</td>
<td class="xd21e2354 cellBottom">D</td>
<td class="xd21e2354 cellBottom">E</td>
<td class="xd21e2354 cellBottom">F</td>
<td class="xd21e2354 cellBottom">G</td>
<td class="xd21e2354 cellBottom">H</td>
<td class="xd21e2354 cellBottom">I</td>
<td class="xd21e2354 cellBottom">J</td>
<td class="xd21e2354 cellBottom">K</td>
<td class="xd21e2354 cellBottom">L</td>
<td class="xd21e2354 cellBottom">M</td>
<td class="xd21e2354 cellBottom">N</td>
<td class="xd21e2354 cellBottom">O</td>
<td class="xd21e2354 cellBottom">P</td>
<td class="xd21e2354 cellBottom">Q</td>
<td class="xd21e2354 cellBottom">R</td>
<td class="xd21e2354 cellBottom">S</td>
<td class="xd21e2354 cellBottom">T</td>
<td class="xd21e2354 cellBottom">U</td>
<td class="xd21e2354 cellBottom">V</td>
<td class="xd21e2354 cellBottom">W</td>
<td class="xd21e2354 cellBottom">X</td>
<td class="xd21e2354 cellBottom">Y</td>
<td class="xd21e2354 cellRight cellBottom">Z</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par"><span class="sc">Table IV.</span>&mdash;Order of
frequency of common pairs to be expected in a count of 2,000 letters of
military or semi-military English text. (Based on a count of 20,000
letters).</p>
<div class="table">
<table class="xd21e2416">
<tr>
<td class="xd21e2417 cellLeft cellTop">TH</td>
<td class="xd21e2418 cellTop">50</td>
<td class="xd21e2417 cellTop">AT</td>
<td class="xd21e2418 cellTop">25</td>
<td class="xd21e2417 cellTop">ST</td>
<td class="xd21e2418 cellRight cellTop">20</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ER</td>
<td class="xd21e2418">40</td>
<td class="xd21e2417">EN</td>
<td class="xd21e2418">25</td>
<td class="xd21e2417">IO</td>
<td class="xd21e2418 cellRight">18</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ON</td>
<td class="xd21e2418">39</td>
<td class="xd21e2417">ES</td>
<td class="xd21e2418">25</td>
<td class="xd21e2417">LE</td>
<td class="xd21e2418 cellRight">18</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">AN</td>
<td class="xd21e2418">38</td>
<td class="xd21e2417">OF</td>
<td class="xd21e2418">25</td>
<td class="xd21e2417">IS</td>
<td class="xd21e2418 cellRight">17</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">RE</td>
<td class="xd21e2418">36</td>
<td class="xd21e2417">OR</td>
<td class="xd21e2418">25</td>
<td class="xd21e2417">OU</td>
<td class="xd21e2418 cellRight">17</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">HE</td>
<td class="xd21e2418">33</td>
<td class="xd21e2417">NT</td>
<td class="xd21e2418">24</td>
<td class="xd21e2417">AR</td>
<td class="xd21e2418 cellRight">16</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">IN</td>
<td class="xd21e2418">31</td>
<td class="xd21e2417">EA</td>
<td class="xd21e2418">22</td>
<td class="xd21e2417">AS</td>
<td class="xd21e2418 cellRight">16</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ED</td>
<td class="xd21e2418">30</td>
<td class="xd21e2417">TI</td>
<td class="xd21e2418">22</td>
<td class="xd21e2417">DE</td>
<td class="xd21e2418 cellRight">16</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ND</td>
<td class="xd21e2418">30</td>
<td class="xd21e2417">TO</td>
<td class="xd21e2418">22</td>
<td class="xd21e2417">RT</td>
<td class="xd21e2418 cellRight">16</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft cellBottom">HA</td>
<td class="xd21e2418 cellBottom">26</td>
<td class="xd21e2417 cellBottom">IT</td>
<td class="xd21e2418 cellBottom">20</td>
<td class="xd21e2417 cellBottom">VE</td>
<td class="xd21e2418 cellRight cellBottom">16</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par"><span class="sc">Table V.</span>&mdash;Table of
recurrence of groups of three letters to be expected in a count of
10,000 letters of English text.</p>
<div class="table">
<table class="xd21e2416">
<tr>
<td class="xd21e2417 cellLeft cellTop">THE</td>
<td class="xd21e2418 cellTop">89</td>
<td class="xd21e2417 cellTop">TIO</td>
<td class="xd21e2418 cellTop">33</td>
<td class="xd21e2417 cellTop">EDT</td>
<td class="xd21e2418 cellRight cellTop">27</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">AND</td>
<td class="xd21e2418">54</td>
<td class="xd21e2417">FOR</td>
<td class="xd21e2418">33</td>
<td class="xd21e2417">TIS</td>
<td class="xd21e2418 cellRight">25</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">THA</td>
<td class="xd21e2418">47</td>
<td class="xd21e2417">NDE</td>
<td class="xd21e2418">31</td>
<td class="xd21e2417">OFT</td>
<td class="xd21e2418 cellRight">23</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ENT</td>
<td class="xd21e2418">39</td>
<td class="xd21e2417">HAS</td>
<td class="xd21e2418">28</td>
<td class="xd21e2417">STH</td>
<td class="xd21e2418 cellRight">21</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft cellBottom">ION</td>
<td class="xd21e2418 cellBottom">36</td>
<td class="xd21e2417 cellBottom">NCE</td>
<td class="xd21e2418 cellBottom">27</td>
<td class="xd21e2417 cellBottom">MEN</td>
<td class="xd21e2418 cellRight cellBottom">20</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb9" href="#pb9" name=
"pb9">9</a>]</span></p>
<p class="par"><span class="sc">Table VI.</span>&mdash;Table of
frequency of occurrence of letters as initials and finals of English
words. Based on a count of 4,000 words; this table gives the figures
for an average 100 words and is necessarily an approximation, like
Table III. English words are derived from so many sources that it is
not impossible for any letter to occur as an initial or final of a
word, although <span class="tt">Q</span>, <span class="tt">X</span> and
<span class="tt">Z</span> are rare as initials and <span class=
"tt">B</span>, <span class="tt">I</span>, <span class="tt">J</span>,
<span class="tt">Q</span>, <span class="tt">V</span>, <span class=
"tt">X</span> and <span class="tt">Z</span> are rare as finals.</p>
<div class="table">
<table class="xd21e2669">
<tr>
<td class="xd21e2670 cellLeft cellTop">Letters</td>
<td class="cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">J</td>
<td class="cellTop">K</td>
<td class="cellTop">L</td>
<td class="cellTop">M</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">T</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">W</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="xd21e2670 cellLeft">Initial</td>
<td>9</td>
<td>6</td>
<td>6</td>
<td>5</td>
<td>2</td>
<td>4</td>
<td>2</td>
<td>3</td>
<td>3</td>
<td>1</td>
<td>1</td>
<td>2</td>
<td>4</td>
<td>2</td>
<td>10</td>
<td>2</td>
<td>-</td>
<td>4</td>
<td>5</td>
<td>17</td>
<td>2</td>
<td>-</td>
<td>7</td>
<td>-</td>
<td>3</td>
<td class="cellRight">-</td>
</tr>
<tr>
<td class="xd21e2670 cellLeft cellBottom">Final</td>
<td class="cellBottom">1</td>
<td class="cellBottom">-</td>
<td class="cellBottom">-</td>
<td class="cellBottom">10</td>
<td class="cellBottom">17</td>
<td class="cellBottom">6</td>
<td class="cellBottom">4</td>
<td class="cellBottom">2</td>
<td class="cellBottom">-</td>
<td class="cellBottom">-</td>
<td class="cellBottom">1</td>
<td class="cellBottom">6</td>
<td class="cellBottom">1</td>
<td class="cellBottom">9</td>
<td class="cellBottom">4</td>
<td class="cellBottom">1</td>
<td class="cellBottom">-</td>
<td class="cellBottom">8</td>
<td class="cellBottom">9</td>
<td class="cellBottom">11</td>
<td class="cellBottom">1</td>
<td class="cellBottom">-</td>
<td class="cellBottom">1</td>
<td class="cellBottom">-</td>
<td class="cellBottom">8</td>
<td class="cellRight cellBottom">-</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It is practically impossible to find five consecutive
letters in an English text without a vowel and we may expect from one
to three with two as the general average. In any twenty letters we may
expect to find from 6 to 9 vowels with 8 as an average. Among
themselves the relative frequency of occurrence of each of the vowels,
(including <span class="tt">Y</span> when a vowel) is as follows:</p>
<div class="table">
<table class="xd21e2416">
<tr>
<td class="xd21e2417 cellLeft cellTop">A,</td>
<td class="xd21e2418 cellTop">19.5%</td>
<td class="xd21e2417 cellTop">E,</td>
<td class="xd21e2418 cellTop">32.0%</td>
<td class="xd21e2417 cellTop">I,</td>
<td class="xd21e2418 cellRight cellTop">16.7%</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft cellBottom">O,</td>
<td class="xd21e2418 cellBottom">20.2%</td>
<td class="xd21e2417 cellBottom">U,</td>
<td class="xd21e2418 cellBottom">8.0%</td>
<td class="xd21e2417 cellBottom">Y,</td>
<td class="xd21e2418 cellRight cellBottom">3.6%</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The foregoing tables give all the essential facts about
the mechanism of the English language from the standpoint of the
solution of ciphers. The use to be made of these tables will be evident
when the solution of different types of ciphers is taken up.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Data for the Solution of Ciphers in Spanish</h3>
</div>
<div class="divBody">
<p class="par first">The Spanish language is written with the following
alphabet:</p>
<div class="blockquote">
<p class="par first xd21e152"><span class="tt">A B C CH D E F G H I J L
LL<br>
M N &Ntilde; O P Q R RR S T U V X Y Z</span></p>
</div>
<p class="par"></p>
<p class="par">while the exact sense often depends upon the use of
accents over the vowels. However, in cipher work it is exceedingly
inconvenient to use the permanent digraphs, <span class="tt">CH</span>,
<span class="tt">LL</span> and <span class="tt">RR</span> and they do
not appear as such in any specimens of Spanish or Mexican cipher
<span class="pagenum">[<a id="pb10" href="#pb10" name=
"pb10">10</a>]</span>examined. Accented vowels and <span class=
"tt">&Ntilde;</span> are also not found and we may, in general, say
that a cipher whose text is Spanish will be prepared with the following
alphabet:</p>
<div class="blockquote">
<p class="par first xd21e152"><span class="tt">A B C D E F G H I J L M
N O P Q R S T U V X Y Z</span></p>
</div>
<p class="par"></p>
<p class="par">and the receiver must supply the accents and the tilde
over the <span class="tt">N</span> to conform to the general sense.</p>
<p class="par">However, many Mexican cipher alphabets contain the
letters <span class="tt">K</span> and <span class="tt">W</span>. This
is particularly true of the ciphers in use by secret service agents who
must be prepared to handle words like <span class="tt">NEW YORK</span>,
<span class="tt">WILSON</span> and <span class="tt">WASHINGTON</span>.
The letters <span class="tt">K</span> and <span class="tt">W</span>
will, however, have a negligible frequency except in short messages
where words like these occur more than once.</p>
<p class="par">In this connection, if a cipher contains Mexican
geographical names like <span class="tt">CHIHUAHUA</span>, <span class=
"tt">MEXICO</span>, <span class="tt">MUZQUIZ</span>, the letters
<span class="tt">H</span>, <span class="tt">X</span> and <span class=
"tt">Z</span> will have a somewhat exaggerated frequency.</p>
<p class="par">In Spanish, the letter <span class="tt">Q</span> is
always followed by <span class="tt">U</span> and the <span class=
"tt">U</span> is always followed by one of the other vowels,
<span class="tt">A</span>, <span class="tt">E</span>, <span class=
"tt">I</span> or <span class="tt">O</span>. As <span class=
"tt">QUE</span> or <span class="tt">QUI</span> occurs not infrequently
in Spanish text, particularly in telegraphic correspondence, it is well
worth noting that, if a <span class="tt">Q</span> occurs in a
transposition cipher, we must connect it with <span class="tt">U</span>
and another vowel. The clue to several transposition ciphers has been
found from this simple relation.</p>
<p class="par"><span class="sc">Table VII.</span>&mdash;Normal
frequency table for military orders and reports, calculated on a basis
of 10,000 letters of Spanish text. The graphic form is on a basis of
200 letters. <span class="pagenum">[<a id="pb11" href="#pb11" name=
"pb11">11</a>]</span></p>
<div class="table">
<table class="xd21e3010">
<thead>
<tr class="label">
<td class="xd21e284 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e285 cellHeadTop cellHeadBottom">10,000 Letters</td>
<td colspan="2" class=
"xd21e285 cellHeadRight cellHeadTop cellHeadBottom">200 Letters</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e284 cellLeft">A</td>
<td class="xd21e285">1352</td>
<td class="xd21e285">27</td>
<td class="xd21e287 cellRight">111111111111111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">B</td>
<td class="xd21e285">102</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">C</td>
<td class="xd21e285">474</td>
<td class="xd21e285">9</td>
<td class="xd21e287 cellRight">111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">D</td>
<td class="xd21e285">524</td>
<td class="xd21e285">10</td>
<td class="xd21e287 cellRight">1111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">E</td>
<td class="xd21e285">1402</td>
<td class="xd21e285">28</td>
<td class="xd21e287 cellRight">1111111111111111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">F</td>
<td class="xd21e285">91</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">G</td>
<td class="xd21e285">137</td>
<td class="xd21e285">3</td>
<td class="xd21e287 cellRight">111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">H</td>
<td class="xd21e285">102</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">I</td>
<td class="xd21e285">606</td>
<td class="xd21e285">12</td>
<td class="xd21e287 cellRight">111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">J</td>
<td class="xd21e285">41</td>
<td class="xd21e285">1</td>
<td class="xd21e287 cellRight">1</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">L</td>
<td class="xd21e285">517</td>
<td class="xd21e285">10</td>
<td class="xd21e287 cellRight">1111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">M</td>
<td class="xd21e285">300</td>
<td class="xd21e285">6</td>
<td class="xd21e287 cellRight">111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">N</td>
<td class="xd21e285">619</td>
<td class="xd21e285">12</td>
<td class="xd21e287 cellRight">111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">O</td>
<td class="xd21e285">818</td>
<td class="xd21e285">16</td>
<td class="xd21e287 cellRight">1111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">P</td>
<td class="xd21e285">257</td>
<td class="xd21e285">5</td>
<td class="xd21e287 cellRight">11111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Q</td>
<td class="xd21e285">87</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">R</td>
<td class="xd21e285">751</td>
<td class="xd21e285">15</td>
<td class="xd21e287 cellRight">111111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">S</td>
<td class="xd21e285">724</td>
<td class="xd21e285">14</td>
<td class="xd21e287 cellRight">11111111111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">T</td>
<td class="xd21e285">422</td>
<td class="xd21e285">8</td>
<td class="xd21e287 cellRight">11111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">U</td>
<td class="xd21e285">387</td>
<td class="xd21e285">7</td>
<td class="xd21e287 cellRight">1111111</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">V</td>
<td class="xd21e285">85</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft">X</td>
<td class="xd21e285">6</td>
<td class="xd21e285"></td>
<td class="xd21e287 cellRight"></td>
</tr>
<tr>
<td class="xd21e284 cellLeft">Y</td>
<td class="xd21e285">103</td>
<td class="xd21e285">2</td>
<td class="xd21e287 cellRight">11</td>
</tr>
<tr>
<td class="xd21e284 cellLeft cellBottom">Z</td>
<td class="xd21e285 cellBottom">42</td>
<td class="xd21e285 cellBottom">1</td>
<td class="xd21e287 cellRight cellBottom">1</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par xd21e529">In this table the vowels <span class=
"tt">AEIOU</span> = 45.65%; consonants <span class="tt">LNRST</span> =
30.33%; consonants <span class="tt">JKQXZ</span> = 1.76%.</p>
<p class="par xd21e529">Order of letters:</p>
<p class="par xd21e3253"><span class="tt">E A O R S N I D L C T U M P G
Y (BH) F Q V Z J X</span>.</p>
<p class="par"><span class="sc">Table VIII.</span>&mdash;Table of
frequency of digraphs, duals or pairs, Spanish text. Like Table III,
this table is on the basis of 2,000 letters although prepared from a
count of 20,000 letters. For this reason it is, to a certain extent an
approximation; that is, merely because no figures are shown for certain
combinations, we should not assume that such combinations never occur
but rather that they are rare. The letters in the horizontal lines at
the top and bottom are the leading letters; those in the vertical
columns at the sides are the following letters. Thus, in two thousand
letters, we may expect to find <span class="tt">AI</span> twice and
<span class="tt">IA</span> twenty-three times. <span class=
"pagenum">[<a id="pb12" href="#pb12" name="pb12">12</a>]</span></p>
<div class="table">
<table class="borderAll xd21e835">
<thead>
<tr class="label">
<td class="xd21e836 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="cellHeadTop cellHeadBottom">A</td>
<td class="cellHeadTop cellHeadBottom">B</td>
<td class="cellHeadTop cellHeadBottom">C</td>
<td class="cellHeadTop cellHeadBottom">D</td>
<td class="cellHeadTop cellHeadBottom">E</td>
<td class="cellHeadTop cellHeadBottom">F</td>
<td class="cellHeadTop cellHeadBottom">G</td>
<td class="cellHeadTop cellHeadBottom">H</td>
<td class="cellHeadTop cellHeadBottom">I</td>
<td class="cellHeadTop cellHeadBottom">J</td>
<td class="cellHeadTop cellHeadBottom">L</td>
<td class="cellHeadTop cellHeadBottom">M</td>
<td class="cellHeadTop cellHeadBottom">N</td>
<td class="cellHeadTop cellHeadBottom">O</td>
<td class="cellHeadTop cellHeadBottom">P</td>
<td class="cellHeadTop cellHeadBottom">Q</td>
<td class="cellHeadTop cellHeadBottom">R</td>
<td class="cellHeadTop cellHeadBottom">S</td>
<td class="cellHeadTop cellHeadBottom">T</td>
<td class="cellHeadTop cellHeadBottom">U</td>
<td class="cellHeadTop cellHeadBottom">V</td>
<td class="cellHeadTop cellHeadBottom">X</td>
<td class="cellHeadTop cellHeadBottom">Y</td>
<td class="cellHeadTop cellHeadBottom">Z</td>
<td class="cellHeadRight cellHeadTop cellHeadBottom"></td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e836 cellLeft">A</td>
<td>9</td>
<td>4</td>
<td>19</td>
<td>11</td>
<td>5</td>
<td></td>
<td>6</td>
<td>17</td>
<td>23</td>
<td></td>
<td>54</td>
<td>18</td>
<td>9</td>
<td>3</td>
<td>20</td>
<td></td>
<td>29</td>
<td>11</td>
<td>21</td>
<td>8</td>
<td>6</td>
<td></td>
<td>2</td>
<td>5</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">B</td>
<td>6</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">C</td>
<td>24</td>
<td></td>
<td>6</td>
<td>6</td>
<td>24</td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td>3</td>
<td></td>
<td>8</td>
<td>8</td>
<td></td>
<td></td>
<td>9</td>
<td>5</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">D</td>
<td>31</td>
<td></td>
<td></td>
<td></td>
<td>29</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>19</td>
<td>13</td>
<td></td>
<td></td>
<td>10</td>
<td>9</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td class="cellRight">D</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">E</td>
<td>12</td>
<td>2</td>
<td>6</td>
<td>59</td>
<td>10</td>
<td></td>
<td>1</td>
<td>5</td>
<td>7</td>
<td>2</td>
<td>12</td>
<td>18</td>
<td>22</td>
<td>4</td>
<td>9</td>
<td></td>
<td>38</td>
<td>25</td>
<td>28</td>
<td>25</td>
<td>3</td>
<td></td>
<td>3</td>
<td></td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">F</td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight">F</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">G</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td>8</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">H</td>
<td>2</td>
<td></td>
<td>12</td>
<td></td>
<td>10</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight">H</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">I</td>
<td>2</td>
<td></td>
<td>23</td>
<td>16</td>
<td></td>
<td>5</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td>11</td>
<td>13</td>
<td></td>
<td></td>
<td></td>
<td>6</td>
<td>10</td>
<td>5</td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">J</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">J</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">L</td>
<td>21</td>
<td>3</td>
<td>6</td>
<td></td>
<td>39</td>
<td>3</td>
<td>3</td>
<td></td>
<td>7</td>
<td></td>
<td>21</td>
<td></td>
<td>5</td>
<td>6</td>
<td></td>
<td></td>
<td>12</td>
<td>2</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">M</td>
<td>12</td>
<td></td>
<td></td>
<td></td>
<td>6</td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td>1</td>
<td></td>
<td>6</td>
<td>15</td>
<td></td>
<td></td>
<td>7</td>
<td>2</td>
<td></td>
<td>6</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">N</td>
<td>32</td>
<td></td>
<td></td>
<td></td>
<td>46</td>
<td></td>
<td>2</td>
<td></td>
<td>8</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>32</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>12</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">O</td>
<td></td>
<td></td>
<td>26</td>
<td>22</td>
<td>2</td>
<td>6</td>
<td>3</td>
<td>4</td>
<td>9</td>
<td></td>
<td>16</td>
<td>2</td>
<td>8</td>
<td></td>
<td>20</td>
<td></td>
<td>15</td>
<td>7</td>
<td>11</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">P</td>
<td>13</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td>4</td>
<td>9</td>
<td>2</td>
<td>7</td>
<td></td>
<td></td>
<td>4</td>
<td>11</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">P</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Q</td>
<td>11</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">Q</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">R</td>
<td>40</td>
<td></td>
<td></td>
<td></td>
<td>27</td>
<td>2</td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td>36</td>
<td>3</td>
<td></td>
<td>11</td>
<td></td>
<td>17</td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">S</td>
<td>39</td>
<td></td>
<td></td>
<td></td>
<td>52</td>
<td></td>
<td></td>
<td></td>
<td>10</td>
<td></td>
<td></td>
<td></td>
<td>7</td>
<td>14</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>14</td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">T</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td>13</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td>4</td>
<td></td>
<td>18</td>
<td>5</td>
<td></td>
<td></td>
<td>6</td>
<td>30</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">U</td>
<td>2</td>
<td></td>
<td>4</td>
<td>2</td>
<td>6</td>
<td>3</td>
<td>4</td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td>2</td>
<td>6</td>
<td></td>
<td>4</td>
<td>17</td>
<td></td>
<td>15</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">V</td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td class="cellRight">V</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">X</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">X</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Y</td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td>6</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td class="cellRight">Y</td>
</tr>
<tr>
<td class="xd21e836 cellLeft">Z</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>4</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">Z</td>
</tr>
<tr>
<td class="xd21e2354 xd21e836 cellLeft cellBottom"></td>
<td class="xd21e2354 cellBottom">A</td>
<td class="xd21e2354 cellBottom">B</td>
<td class="xd21e2354 cellBottom">C</td>
<td class="xd21e2354 cellBottom">D</td>
<td class="xd21e2354 cellBottom">E</td>
<td class="xd21e2354 cellBottom">F</td>
<td class="xd21e2354 cellBottom">G</td>
<td class="xd21e2354 cellBottom">H</td>
<td class="xd21e2354 cellBottom">I</td>
<td class="xd21e2354 cellBottom">J</td>
<td class="xd21e2354 cellBottom">L</td>
<td class="xd21e2354 cellBottom">M</td>
<td class="xd21e2354 cellBottom">N</td>
<td class="xd21e2354 cellBottom">O</td>
<td class="xd21e2354 cellBottom">P</td>
<td class="xd21e2354 cellBottom">Q</td>
<td class="xd21e2354 cellBottom">R</td>
<td class="xd21e2354 cellBottom">S</td>
<td class="xd21e2354 cellBottom">T</td>
<td class="xd21e2354 cellBottom">U</td>
<td class="xd21e2354 cellBottom">V</td>
<td class="xd21e2354 cellBottom">X</td>
<td class="xd21e2354 cellBottom">Y</td>
<td class="xd21e2354 cellBottom">Z</td>
<td class="xd21e2354 cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par"><span class="sc">Table IX.</span>&mdash;Order of
frequency of common pairs to be expected in a count of 2,000 letters of
Spanish military orders and reports. Based on Table VIII.</p>
<div class="table">
<table class="xd21e2416">
<tr>
<td class="xd21e2417 cellLeft cellTop">DE</td>
<td class="xd21e2418 cellTop">59</td>
<td class="xd21e2417 cellTop">ON</td>
<td class="xd21e2418 cellTop">32</td>
<td class="xd21e2417 cellTop">AC</td>
<td class="xd21e2418 cellRight cellTop">24</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">LA</td>
<td class="xd21e2418">54</td>
<td class="xd21e2417">AD</td>
<td class="xd21e2418">31</td>
<td class="xd21e2417">EC</td>
<td class="xd21e2418 cellRight">24</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">ES</td>
<td class="xd21e2418">52</td>
<td class="xd21e2417">ST</td>
<td class="xd21e2418">30</td>
<td class="xd21e2417">CI</td>
<td class="xd21e2418 cellRight">23</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">EN</td>
<td class="xd21e2418">46</td>
<td class="xd21e2417">ED</td>
<td class="xd21e2418">29</td>
<td class="xd21e2417">IA</td>
<td class="xd21e2418 cellRight">23</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">AR</td>
<td class="xd21e2418">40</td>
<td class="xd21e2417">RA</td>
<td class="xd21e2418">29</td>
<td class="xd21e2417">DO</td>
<td class="xd21e2418 cellRight">22</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">AS</td>
<td class="xd21e2418">39</td>
<td class="xd21e2417">TE</td>
<td class="xd21e2418">28</td>
<td class="xd21e2417">NE</td>
<td class="xd21e2418 cellRight">22</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">EL</td>
<td class="xd21e2418">39</td>
<td class="xd21e2417">ER</td>
<td class="xd21e2418">27</td>
<td class="xd21e2417">AL</td>
<td class="xd21e2418 cellRight">21</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">RE</td>
<td class="xd21e2418">38</td>
<td class="xd21e2417">CO</td>
<td class="xd21e2418">26</td>
<td class="xd21e2417">LL</td>
<td class="xd21e2418 cellRight">21</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft">OR</td>
<td class="xd21e2418">36</td>
<td class="xd21e2417">SE</td>
<td class="xd21e2418">25</td>
<td class="xd21e2417">PA</td>
<td class="xd21e2418 cellRight">20</td>
</tr>
<tr>
<td class="xd21e2417 cellLeft cellBottom">AN</td>
<td class="xd21e2418 cellBottom">32</td>
<td class="xd21e2417 cellBottom">UE</td>
<td class="xd21e2418 cellBottom">25</td>
<td class="xd21e2417 cellBottom">PO</td>
<td class="xd21e2418 cellRight cellBottom">20</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb13" href="#pb13" name=
"pb13">13</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Alphabetic Frequency Tables</h3>
<h3 class="sub">(Truesdell)</h3>
</div>
<div class="divBody">
<p class="par first">Frequency of occurrence in 1,000 letters of
text:</p>
<div class="table">
<table class="xd21e4854">
<thead>
<tr class="label">
<td class="cellHeadLeft cellHeadTop cellHeadBottom">Letter</td>
<td class="cellHeadTop cellHeadBottom">French</td>
<td class="cellHeadTop cellHeadBottom">German</td>
<td class="cellHeadTop cellHeadBottom">Italian</td>
<td class="cellHeadRight cellHeadTop cellHeadBottom">Portuguese</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">A</td>
<td>80</td>
<td>52</td>
<td>117</td>
<td class="cellRight">140</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>6</td>
<td>18</td>
<td>6</td>
<td class="cellRight">6</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>33</td>
<td>31</td>
<td>45</td>
<td class="cellRight">34</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>40</td>
<td>51</td>
<td>31</td>
<td class="cellRight">40</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>197</td>
<td>173</td>
<td>126</td>
<td class="cellRight">142</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>9</td>
<td>21</td>
<td>10</td>
<td class="cellRight">12</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>7</td>
<td>42</td>
<td>17</td>
<td class="cellRight">10</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>6</td>
<td>41</td>
<td>6</td>
<td class="cellRight">10</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>65</td>
<td>81</td>
<td>114</td>
<td class="cellRight">59</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>3</td>
<td>1</td>
<td><a class="noteref" id="t11.asrc" href="#t11.a" name=
"t11.asrc">1</a></td>
<td class="cellRight">5</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td>10</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>49</td>
<td>28</td>
<td>72</td>
<td class="cellRight">32</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>31</td>
<td>20</td>
<td>30</td>
<td class="cellRight">46</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>79</td>
<td>120</td>
<td>66</td>
<td class="cellRight">48</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>57</td>
<td>28</td>
<td>93</td>
<td class="cellRight">110</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>32</td>
<td>8</td>
<td>30</td>
<td class="cellRight">28</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>12</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td>3</td>
<td class="cellRight">16</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>74</td>
<td>69</td>
<td>64</td>
<td class="cellRight">64</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>66</td>
<td>57</td>
<td>49</td>
<td class="cellRight">88</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>65</td>
<td>60</td>
<td>60</td>
<td class="cellRight">43</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>62</td>
<td>51</td>
<td>29</td>
<td class="cellRight">46</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>21</td>
<td>9</td>
<td>20</td>
<td class="cellRight">15</td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td>15</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>3</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>2</td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td><a class="pseudonoteref" href="#t11.a">1</a></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">1</td>
<td class="cellBottom">14</td>
<td class="cellBottom">12</td>
<td class="cellRight cellBottom">4</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Order of Frequency</h3>
</div>
<div class="divBody">
<p class="par first xd21e152"><i>French</i></p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">E</td>
<td class="cellTop">A</td>
<td class="cellTop">N</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">I</td>
<td class="cellTop">U</td>
<td class="cellTop">O</td>
<td class="cellTop">L</td>
<td class="cellTop">D</td>
<td class="cellTop">C</td>
<td class="cellTop">P</td>
<td class="cellTop">M</td>
<td class="cellTop">V</td>
<td class="cellTop">Q</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">B</td>
<td class="cellTop">J</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">T</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">H</td>
<td class="cellBottom">X</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e152"><i>German</i></p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">E</td>
<td class="cellTop">N</td>
<td class="cellTop">I</td>
<td class="cellTop">R</td>
<td class="cellTop">T</td>
<td class="cellTop">S</td>
<td class="cellTop">A</td>
<td class="cellTop">D</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">C</td>
<td class="cellTop">L</td>
<td class="cellTop">F</td>
<td class="cellTop">M</td>
<td class="cellTop">B</td>
<td class="cellTop">W</td>
<td class="cellTop">Z</td>
<td class="cellTop">K</td>
<td class="cellTop">V</td>
<td class="cellTop">P</td>
<td class="cellTop">J</td>
<td class="cellTop">Q</td>
<td class="cellTop">X</td>
<td class="cellRight cellTop">Y</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">U</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">O</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e152"><i>Italian</i></p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">E</td>
<td class="cellTop">A</td>
<td class="cellTop">I</td>
<td class="cellTop">O</td>
<td class="cellTop">L</td>
<td class="cellTop">N</td>
<td class="cellTop">R</td>
<td class="cellTop">T</td>
<td class="cellTop">S</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">M</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">G</td>
<td class="cellTop">Z</td>
<td class="cellTop">F</td>
<td class="cellTop">B</td>
<td class="cellRight cellTop">Q</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">P</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">H</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e152"><i>Portuguese</i></p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">E</td>
<td class="cellTop">A</td>
<td class="cellTop">O</td>
<td class="cellTop">S</td>
<td class="cellTop">R</td>
<td class="cellTop">I</td>
<td class="cellTop">N</td>
<td class="cellTop">M</td>
<td class="cellTop">T</td>
<td class="cellTop">D</td>
<td class="cellTop">C</td>
<td class="cellTop">L</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">V</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">B</td>
<td class="cellTop">J</td>
<td class="cellTop">Z</td>
<td class="cellTop">X</td>
<td class="cellRight cellTop">Y</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">U</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">H</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb14" href="#pb14" name=
"pb14">14</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Graphic Frequency Tables</h3>
</div>
<div class="divBody">
<p class="par first">Frequency of occurrence in 200 letters of
text.</p>
<p class="par xd21e152"><i>French</i></p>
<div class="table">
<table class="frequency">
<tr>
<td class="first cellLeft cellTop">A</td>
<td class="second cellTop">16</td>
<td class="cellRight cellTop">1111111111111111</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>39</td>
<td class="cellRight">111111111111111111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>16</td>
<td class="cellRight">1111111111111111</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>11</td>
<td class="cellRight">11111111111</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>15</td>
<td class="cellRight">111111111111111</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>12</td>
<td class="cellRight">111111111111</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>4</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e152"><i>Italian</i></p>
<div class="table">
<table class="frequency">
<tr>
<td class="first cellLeft cellTop">A</td>
<td class="second cellTop">23</td>
<td class="cellRight cellTop">11111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>9</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>25</td>
<td class="cellRight">1111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>3</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>23</td>
<td class="cellRight">11111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>14</td>
<td class="cellRight">11111111111111</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>19</td>
<td class="cellRight">1111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>12</td>
<td class="cellRight">111111111111</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>4</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">2</td>
<td class="cellRight cellBottom">11</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb15" href="#pb15" name=
"pb15">15</a>]</span></p>
<p class="par xd21e152"><i>German</i></p>
<div class="table">
<table class="frequency">
<tr>
<td class="first cellLeft cellTop">A</td>
<td class="second cellTop">10</td>
<td class="cellRight cellTop">1111111111</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>4</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>32</td>
<td class="cellRight">11111111111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>4</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>8</td>
<td class="cellRight">11111111</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>8</td>
<td class="cellRight">11111111</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>16</td>
<td class="cellRight">1111111111111111</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>4</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>24</td>
<td class="cellRight">111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>14</td>
<td class="cellRight">11111111111111</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>11</td>
<td class="cellRight">11111111111</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>12</td>
<td class="cellRight">111111111111</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td>3</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">3</td>
<td class="cellRight cellBottom">111</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e152"><i>Portuguese</i></p>
<div class="table">
<table class="frequency">
<tr>
<td class="first cellLeft cellTop">A</td>
<td class="second cellTop">28</td>
<td class="cellRight cellTop">1111111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>7</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>8</td>
<td class="cellRight">11111111</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>28</td>
<td class="cellRight">1111111111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>2</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>12</td>
<td class="cellRight">111111111111</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>1</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>9</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>10</td>
<td class="cellRight">1111111111</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>22</td>
<td class="cellRight">1111111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>6</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>3</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>13</td>
<td class="cellRight">1111111111111</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>18</td>
<td class="cellRight">111111111111111111</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>9</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>9</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>3</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">1</td>
<td class="cellRight cellBottom">1</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb16" href="#pb16" name=
"pb16">16</a>]</span></p>
</div>
</div>
</div>
<div class="footnotes">
<hr class="fnsep">
<p class="par footnote"><span class="label"><a class="noteref" id=
"t11.a" href="#t11.asrc" name="t11.a">1</a></span> Occurrence rare,
usually in proper names.&nbsp;<a class="fnarrow" href=
"#t11.asrc">&uarr;</a></p>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter III</h2>
<h2 class="main">Technique of Cipher Examination</h2>
</div>
<div class="divBody">
<p class="par xd21e6283"><span class="xd21e6283init">I</span>n time of
active operations it is important that captured or intercepted cipher
messages reach the examining office with the least possible delay. The
text of messages, captured at a distance from the examining office,
should be sent to the office by telegraph or telephone, the original
messages being forwarded to the office as soon thereafter as
possible.</p>
<p class="par">The preamble, &ldquo;place from,&rdquo; date, address
and signature, give most important clues as to the language of the
cipher, the cipher method probably used, and even the subject matter of
the message. If the whole of a telegraphic or radio message is in
cipher, it is highly probable that the preamble, &ldquo;place
from,&rdquo; etc., are in an operators&rsquo; cipher and are distinct
from the body of the message. As these operators&rsquo; ciphers are
necessarily simple, an attempt should always be made to discover, by
methods of analysis to be set forth later, the exact extent of the
operator&rsquo;s cipher and then to decipher the parts of the messages
enciphered with it.</p>
<p class="par">In military messages, we almost invariably find the
language of the text to be that of the nation to which the military
force belongs. The language of the text of the message of secret agents
is, however, another matter and, in dealing with such messages, we
should use all available evidence, both external and internal, before
deciding finally on the language used. Whenever a frequency table can
be prepared, <span class="pagenum">[<a id="pb17" href="#pb17" name=
"pb17">17</a>]</span>such a table will give the best evidence for this
purpose.</p>
<p class="par">All work in enciphering and deciphering messages and in
copying ciphers should be done with capital letters. There is much less
chance of error when working with capitals and, with little practice,
it is just about as fast. An additional safeguard is to use black ink
or pencil for the plain text and colored ink or pencil for the cipher.
A separate color may be used for the key when necessary.</p>
<p class="par">The following blank form is suggested as convenient for
keeping a record of a cipher under examination. It should accompany the
cipher through the examining process and should be filled in as the
facts are determined. This record, the original cipher and all notes of
work done during the examination, should be filed together when the
examination is completed, whether the cipher has been solved or not. It
may be that other ciphers solved later will give clues to the solution
of such unsolved ciphers.</p>
<p class="par">The first column of this blank should be filled out from
data furnished by the officer obtaining the cipher from the enemy. A
general order, emphasizing the importance of promptly forwarding
captured or intercepted ciphers to an examining office, could specify
that a brief report embodying this data should be forwarded with each
cipher.</p>
<p class="par">The second column of the blank should be filled out
progressively as the work proceeds. The office number should be a
serial one, the first cipher examined being No. 1. The date and hour of
receipt at examining office will be a check as to the time required to
transmit it from place of capture. The spaces &ldquo;From<span class=
"corr" id="xd21e6299" title="Not in source">,</span>&rdquo;
&ldquo;At,&rdquo; &ldquo;To,&rdquo; &ldquo;At,&rdquo;
&ldquo;Date,&rdquo; are for <span class="pagenum">[<a id="pb18" href=
"#pb18" name="pb18">18</a>]</span>the information concerning sender and
addressee of the cipher and are to be obtained from the message. In
case an operators&rsquo; cipher has been used, these parts of the
message will have to be deciphered before the blanks can be filled
in.</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td colspan="4" class="xd21e6306 cellLeft cellRight cellTop">
<b>Intelligence Section, General Staff</b></td>
</tr>
<tr>
<td colspan="4" class="xd21e6306 cellLeft cellRight"><b>1st Field
Army</b></td>
</tr>
<tr>
<td colspan="4" class="xd21e6316 cellLeft cellRight">
<div class="table">
<table class="xd21e6318">
<tr>
<td rowspan="2" class="xd21e6320 cellLeft cellTop"></td>
<td class="dashfill cellTop">-----------</td>
<td class="dashfill cellRight cellTop">-----------</td>
</tr>
<tr>
<td class="fieldannot cellLeft cellBottom">Place,</td>
<td class="fieldannot cellRight cellBottom">Date</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td colspan="4" class="xd21e6306 cellLeft cellRight"><i>Record of
Cipher Examination</i></td>
</tr>
<tr>
<td colspan="2" class="xd21e6336 cellLeft cellBottom">
<div class="table">
<table class="xd21e6318">
<tr>
<td colspan="3" class="cellLeft cellRight cellTop">This cipher obtained
by</td>
</tr>
<tr>
<td colspan="3" class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td colspan="3" class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td class="cellLeft">at</td>
<td class="dashfill">-----------</td>
<td class="dashfill cellRight">-----------</td>
</tr>
<tr>
<td class="cellLeft">on</td>
<td class="dashfill">-----------</td>
<td class="dashfill cellRight">-----------</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="fieldannot cellBottom">(date)</td>
<td class="fieldannot cellRight cellBottom">(hour)</td>
</tr>
</table>
</div>
<p class="par">How being transmitted when obtained. (Underscore means
used and enter data on sending and receiving stations).</p>
<div class="table">
<table class="xd21e6318">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">Sending Station</td>
<td class="cellRight cellTop">Receiving Station</td>
</tr>
<tr>
<td class="cellLeft">Radio</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Telephone</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Telegraph</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Buzzer</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Helio</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Lantern</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Flag</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Cyclist</td>
<td>from</td>
<td class="cellRight">to</td>
</tr>
<tr>
<td class="cellLeft">Foot Messenger</td>
<td>
<table class="ditto">
<tr class="s">
<td>from</td>
</tr>
<tr class="d">
<td>,,</td>
</tr>
</table>
</td>
<td class="cellRight">
<table class="ditto">
<tr class="s">
<td>to</td>
</tr>
<tr class="d">
<td>,,</td>
</tr>
</table>
</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Mtd. Messenger</td>
<td class="cellBottom">
<table class="ditto">
<tr class="s">
<td>from</td>
</tr>
<tr class="d">
<td>,,</td>
</tr>
</table>
</td>
<td class="cellRight cellBottom">
<table class="ditto">
<tr class="s">
<td>to</td>
</tr>
<tr class="d">
<td>,,</td>
</tr>
</table>
</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">How obtained. (Underscore means used). Captured before
delivery to addressee. Captured after delivery to addressee.
Intercepted, not received by addressee. Copied, but received by
addressee.</p>
<p class="par"><span class="sc">Remarks</span>:</p>
</td>
<td colspan="2" class="xd21e6336 cellRight cellBottom">
<div class="table">
<table class="xd21e6318">
<tr>
<td colspan="3" class="cellLeft cellRight cellTop"><span class=
"fieldlabel">Office No.</span> <span class=
"dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight">
<div class="table">
<table class="xd21e6318">
<tr>
<td class="cellLeft cellTop">Received</td>
<td class="dashfill cellTop">-----------</td>
<td class="dashfill cellRight cellTop">-----------</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="fieldannot cellBottom">(Date)</td>
<td class="fieldannot cellRight cellBottom">(Hour)</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">From</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">At</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">To</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">At</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">Date</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">Probable language of text</span> <span class=
"dashfill">-----------</span>
<div class="table">
<table class="xd21e6318">
<tr>
<td rowspan="4" class="xd21e6545 cellLeft cellTop">Class</td>
<td rowspan="4" class="xd21e6547 cellTop"><img src="images/lbrace6.png"
alt="" width="21" height="104"></td>
<td class="cellRight cellTop"><span class=
"fieldlabel">Transposition</span> <span class=
"dashfill">-----------</span></td>
</tr>
<tr>
<td class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td class="cellLeft cellRight"><span class=
"fieldlabel">Substitution</span> <span class=
"dashfill">-----------</span></td>
</tr>
<tr>
<td class="dashfill cellLeft cellRight cellBottom">-----------</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">Case</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="xd21e6583 cellLeft cellRight">Remarks:</td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight">
<div class="table">
<table class="xd21e6318">
<tr>
<td class="fieldlabel cellLeft cellTop">Solution completed</td>
<td class="dashfill cellTop">---------</td>
<td class="dashfill cellRight cellTop">----------</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="fieldannot cellBottom">(date)</td>
<td class="fieldannot cellRight cellBottom">(hour)</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">Language of text</span> <span class=
"dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="cellLeft cellRight"><span class=
"fieldlabel">Key, (if determined)</span> <span class=
"dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td class="cellLeft"><span class="fieldlabel">Type</span> <span class=
"dashfill">-----------</span></td>
<td colspan="2" class="cellRight"><span class="fieldlabel">File
No.</span> <span class="dashfill">-----------</span></td>
</tr>
<tr>
<td colspan="3" class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td colspan="3" class="dashfill cellLeft cellRight">-----------</td>
</tr>
<tr>
<td colspan="3" class="fieldannot cellLeft cellRight cellBottom">
Examiner.</td>
</tr>
</table>
</div>
</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The probable language of the text is assumed from the
preceding data and, if necessary, from <span class="pagenum">[<a id=
"pb19" href="#pb19" name="pb19">19</a>]</span>internal evidence. Thus a
cipher from a Mexican source and not containing <span class=
"tt">K</span> or <span class="tt">W</span> is probably in Spanish.</p>
<p class="par">The class and case are determined by the rules laid down
later. The space for remarks is to permit notation of any special
features. When the solution is completed, the date and hour are noted,
the language of text and key (if determined) are entered and a type
number, to identify it with other ciphers prepared by the same method
(but not necessarily the same key), is given to it. The file number is
for convenience in filing and in preparation of a card index.</p>
<p class="par">The process of examination in an office with one
examiner, one stenographer and one clerk, might be as follows: On
receipt of a captured cipher with accompanying report, the stenographer
makes four copies of the cipher on the typewriter. The clerk and
stenographer then check the work. The stenographer then proceeds to
fill out the first column and first two lines of the second column of
the record blank from the report of the capturing officer, keeping the
original cipher and two copies with the record. He may also fill out
the first seven lines of the second column, if this data is on the
captured cipher in plain text. In the meantime the clerk is counting
and setting down the whole number of letters of the cipher and the
occurrence of <span class="tt">AEIOU</span>, <span class=
"tt">LNRST</span>, and <span class="tt">JKQXZ</span>, while the
examining officer is looking over the cipher for possible recurring
groups of letters and underlining them when found.</p>
<p class="par">This work being completed, the examining officer is in a
position, ordinarily, to decide on the class of the cipher and he may
have found something in his examination which will lead him to the case
under the class. The clerk in this preliminary count should
<span class="pagenum">[<a id="pb20" href="#pb20" name=
"pb20">20</a>]</span>keep track of the total occurrence of each of the
fifteen check letters and not of the three groups given above. This
takes a little longer but when done, the data for fifteen letters of
the alphabet for a frequency table is completed, leaving only eleven
other letters, and in Spanish, but nine, to be counted, in case it is
necessary to prepare a frequency table.</p>
<p class="par">If the examining officer decides the cipher to be of the
transposition class, no further work with frequency tables is
necessary. The clerk should proceed to count and set down the number of
vowels in each line and column and the examining officer should look
for any occurrence of the letter <span class="tt">Q</span> and try to
connect it with <span class="tt">U</span> and another vowel. The
stenographer may be set to work putting the cipher into rectangles of
different dimensions. The clerk&rsquo;s work gives data for possible
rearrangement, for if the vowels are much out of proportion at any
point, they must be connected with the proper proportion of consonants
as a first step in rearrangement. Work with transposition ciphers must
necessarily include much of the fit and try method. The details of this
work are taken up later.</p>
<p class="par">If a cipher seems to be a substitution cipher, the
examining officer should look over the frequency of occurrence of each
of the fifteen letters counted. If some letters (it is of no importance
at present which ones) occur much more frequently than others and some
occur rarely or not at all, we may safely decide on Case <a href=
"#c4">4</a>, <a href="#c5">5</a> or <a href="#c6">6</a> and let the
clerk proceed to finish the frequency table for the message. On the
other hand, if all the fifteen letters examined occur with somewhere
near the same frequency&mdash;for example, the most common letter
occurring not over three or four times as often as the least common
letter&mdash;we may at once eliminate the first three cases
<span class="pagenum">[<a id="pb21" href="#pb21" name=
"pb21">21</a>]</span>and let the clerk proceed to examine the cipher
for recurring pairs and groups, counting the intervening letters, so
that the examining officer may decide whether <a href="#c7">Case 7</a>,
or some more complicated case, should be chosen.</p>
<p class="par">If something more complicated than <a href="#c7">Case
7</a> has been used and other ciphers are on hand awaiting examination,
the cipher should go into the unsolved file to be worked on when other
work permits, unless the contents of the cipher are believed to be very
important. Every opportunity should be taken to clean up the unsolved
file and, whenever a message is solved, the methods should be tried, if
applicable, to everything remaining in the file.</p>
<p class="par">The first few days or weeks after the establishment of
an examining office will be the most trying time. When solved ciphers
begin to pile up, the methods of the enemy will be more and more
apparent and it will often be possible to determine the method from
knowledge of the name of the sender and receiver.</p>
<p class="par">When a cipher has been solved, the solution should be
prepared in triplicate and given the serial number of the cipher. Any
parts which are not clear, through errors in enciphering or in
transmission, should be underlined or otherwise made conspicuous, so
that the head of the Intelligence Section may note them and, possibly,
from other sources, supply the deficiency.</p>
<p class="par">One of the copies of the cipher and report of
examination, with a copy of the solution, should be turned over at once
to the head of the Intelligence Section or to the Chief of Staff. The
other copies of the solution should be filed with the original cipher,
the report of examination, and all work done on the cipher.
<span class="pagenum">[<a id="pb22" href="#pb22" name=
"pb22">22</a>]</span></p>
<p class="par">Periodically, say once a week or even daily at the
<span class="corr" id="xd21e6715" title=
"Source: begining">beginning</span> of active operations, there should
be an interchange between all examining offices of solved messages
involving new methods used by the enemy. All the examining offices will
thus be kept in touch. It may also be possible to assign certain
hostile radio stations to each examining office to prevent duplication
of work. <span class="pagenum">[<a id="pb23" href="#pb23" name=
"pb23">23</a>]</span></p>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter IV</h2>
<h2 class="main">Classes of Ciphers</h2>
</div>
<div class="divBody">
<p class="par xd21e165"><span class="xd21e165init">T</span>here are, in
general, two classes of ciphers. These are the transposition cipher and
the substitution cipher.</p>
<p class="par">Substitution ciphers may be made up of substituted
letters, numerals, conventional signs or combinations of all three; and
furthermore, for a single letter of the original text there may be
substituted a single letter, numeral or sign or two or more of each, or
a whole word or group of figures, combination of conventional signs, or
combinations of all three of these elements. Thus substitution ciphers
may vary from those of extreme simplicity to those whose complication
defies any ordinary method of analysis and whose solution requires the
possession of long messages and much time and study. Fortunately the
more difficult substitution ciphers are rarely used for military
purposes, on account of the time and care required for enciphering and
deciphering.</p>
<p class="par">Transposition ciphers are limited to the characters of
the original text. These characters are rearranged singly, according to
some predetermined method or key (monoliteral transposition), or whole
words are similarly rearranged (route cipher).</p>
<p class="par">There may also be a combination of transposition and
substitution methods in enciphering a message but in this case it will
fall into the substitution class on first determination and after
solution as a substitution cipher it must be handled as a transposition
cipher. Examples of this case will be given. <span class=
"pagenum">[<a id="pb24" href="#pb24" name="pb24">24</a>]</span></p>
<p class="par">We may also find transposition or substitution methods
applied to words taken from a code book, or to numbers which represent
these words. Thus cipher methods blend into code work, for a code is,
after all, only a specialized substitution cipher.</p>
<p class="par">We can now lay down the rules for determining whether
any given cipher belongs to the substitution class or to the
transposition class.</p>
<p class="par">Count the number of letters in the message, the number
of vowels, <span class="tt">AEIOU</span>, the number of the consonants,
<span class="tt">LNRST</span>, and the number of the consonants,
<span class="tt">JKQXZ</span>.</p>
<p class="par">If the text is English and the cipher is a transposition
cipher, this proportion will hold; vowels <span class="tt">AEIOU</span>
constitute 40% of the whole; consonants <span class="tt">LNRST</span>,
30% and consonants <span class="tt">JKQXZ</span>, 3%.</p>
<p class="par">If the text be Spanish the proportions for a
transposition cipher will be: vowels <span class="tt">AEIOU</span> 45%,
consonants <span class="tt">LNRST</span>, 30%; consonants <span class=
"tt">JKQXZ</span>, 2%.</p>
<p class="par">If these proportions do not hold within 5%, one way or
the other, the cipher is certainly a substitution cipher. Note,
however, that often the end of a message is filled with letters like
<span class="tt">K</span>, <span class="tt">X</span>, <span class=
"tt">Z</span> to complete cipher words and it is best to neglect the
last word or words in making a count. Also, if the cipher be a long
one, this determination can safely be made by taking 100 or 200
consecutive letters of the message, either from the beginning or, if
nulls at the beginning are suspected, from the interior of the
message.</p>
<p class="par">The distinction between the route cipher (transposition)
and the substitution cipher where whole words are substituted for
letters of the original text, must be made on the basis of the words
actually used. It is better to consider such a message as a route
cipher when the words used appear to have some consecutive meaning
bearing on the situation <span class="pagenum">[<a id="pb25" href=
"#pb25" name="pb25">25</a>]</span>at hand. A substitution cipher of
this variety would only be used for transmission of a short message of
great importance and secrecy, and then the chances are that certain
words corresponding to <span class="tt">A</span>, <span class=
"tt">E</span>, <span class="tt">N</span>, <span class="tt">O</span> and
<span class="tt">T</span> would appear with such frequency as to point
at once to the fact that a substitution cipher was used. Watch the
initial or terminal letters in such a cipher; they may spell the
message.</p>
<p class="par">In general, the determination of class by proportion of
vowels, common consonants and rare consonants may be safely followed.
We will now proceed to the examination of the more common varieties of
each class of cipher. <span class="pagenum">[<a id="pb26" href="#pb26"
name="pb26">26</a>]</span></p>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter V</h2>
<h2 class="main">Examination of Transposition Ciphers</h2>
</div>
<div class="divBody">
<p class="par xd21e6810"><span class="xd21e6810init">A</span>fter
having decided that a cipher belongs to the transposition class, it
remains to decide on the variety of cipher used. As, by definition, a
transposition cipher consists wholly of characters of the original
message, rearranged according to some law, we may, in general, say that
such a cipher offers fewer difficulties in solution than a substitution
cipher. A transposition cipher is like a picture puzzle; the parts are
all there and the solution merely involves their correct
arrangement.</p>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case 1.</span>&mdash;Geometrical
ciphers. This case includes all ciphers in which a certain number of
the characters are chosen so that they will form a square or rectangle
of predetermined dimensions; and then these characters are arranged
according to a geometrical design.</p>
<p class="par">Taking the message:</p>
<p class="par xd21e152"><span class="tt">A B C D E F G H I J K L M N O
P Q R S T U V W X</span></p>
<p class="par">of twenty-four letters and assuming a rectangle of six
letters horizontally, and four letters vertically, we may have:</p>
<p id="c1a" class="par">(<i>a</i>) <i>Simple Horizontal</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A B C D E F</td>
<td class="xd21e6834 cellTop">F E D C B A</td>
<td class="xd21e6834 cellTop">S T U V W X</td>
<td class="cellRight cellTop">X W V U T S</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">G H I J K L</td>
<td class="xd21e6834">L K J I H G</td>
<td class="xd21e6834">M N O P Q R</td>
<td class="cellRight">R Q P O N M</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">M N O P Q R</td>
<td class="xd21e6834">R Q P O N M</td>
<td class="xd21e6834">G H I J K L</td>
<td class="cellRight">L K J I H G</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">S T U V W X</td>
<td class="xd21e6834 cellBottom">X W V U T S</td>
<td class="xd21e6834 cellBottom">A B C D E F</td>
<td class="cellRight cellBottom">F E D C B A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p id="c1b" class="par">(<i>b</i>) <i>Simple Vertical</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A E I M Q U</td>
<td class="xd21e6834 cellTop">D H L P T X</td>
<td class="xd21e6834 cellTop">U Q M I E A</td>
<td class="cellRight cellTop">X T P L H D</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">B F J N R V</td>
<td class="xd21e6834">C G K O S W</td>
<td class="xd21e6834">V R N J F B</td>
<td class="cellRight">W S O K G C</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">C G K O S W</td>
<td class="xd21e6834">B F J N R V</td>
<td class="xd21e6834">W S O K G C</td>
<td class="cellRight">V R N J F B</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">D H L P T X</td>
<td class="xd21e6834 cellBottom">A E I M Q U</td>
<td class="xd21e6834 cellBottom">X T P L H D</td>
<td class="cellRight cellBottom">U Q M I E A</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb27" href="#pb27" name=
"pb27">27</a>]</span></p>
<p class="par">(<i>c</i>) <i>Alternate Horizontal</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A B C D E F</td>
<td class="xd21e6834 cellTop">F E D C B A</td>
<td class="xd21e6834 cellTop">X W V U T S</td>
<td class="cellRight cellTop">S T U V W X</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">L K J I H G</td>
<td class="xd21e6834">G H I J K L</td>
<td class="xd21e6834">M N O P Q R</td>
<td class="cellRight">R Q P O N M</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">M N O P Q R</td>
<td class="xd21e6834">R Q P O N M</td>
<td class="xd21e6834">L K J I H G</td>
<td class="cellRight">G H I J K L</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">X W V U T S</td>
<td class="xd21e6834 cellBottom">S T U V W X</td>
<td class="xd21e6834 cellBottom">A B C D E F</td>
<td class="cellRight cellBottom">F E D C B A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">(<i><span class="corr" id="xd21e6976" title=
"Source: b">d</span></i>) <i>Alternate Vertical</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A H I P Q X</td>
<td class="xd21e6834 cellTop">D E L M T U</td>
<td class="xd21e6834 cellTop">X Q P I H A</td>
<td class="cellRight cellTop">U T M L E D</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">B G J O R W</td>
<td class="xd21e6834">C F K N S V</td>
<td class="xd21e6834">W R O J G B</td>
<td class="cellRight">V S N K F C</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">C F K N S V</td>
<td class="xd21e6834">B G J O R W</td>
<td class="xd21e6834">V S N K F C</td>
<td class="cellRight">W R O J G B</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">D E L M T U</td>
<td class="xd21e6834 cellBottom">A H I P Q X</td>
<td class="xd21e6834 cellBottom">U T M L E D</td>
<td class="cellRight cellBottom">X Q P I H A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">(<i>e</i>) <i>Simple Diagonal</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A B D G K O</td>
<td class="xd21e6834 cellTop">G K O S V X</td>
<td class="xd21e6834 cellTop">O K G D B A</td>
<td class="cellRight cellTop">X V S O K G</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">C E H L P S</td>
<td class="xd21e6834">D H L P T W</td>
<td class="xd21e6834">S P L H E C</td>
<td class="cellRight">W T P L H D</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">F I M Q T V</td>
<td class="xd21e6834">B E I M Q U</td>
<td class="xd21e6834">V T Q M I F</td>
<td class="cellRight">U Q M I E B</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">J N R U W X</td>
<td class="xd21e6834 cellBottom">A C F J N R</td>
<td class="xd21e6834 cellBottom">X W U R N J</td>
<td class="cellRight cellBottom">R N J F C A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e7072"></p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A C F J N R</td>
<td class="xd21e6834 cellTop">J N R U W X</td>
<td class="xd21e6834 cellTop">R N J F C A</td>
<td class="cellRight cellTop">X W U R N J</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">B E I M Q U</td>
<td class="xd21e6834">F I M Q T V</td>
<td class="xd21e6834">U Q M I E B</td>
<td class="cellRight">V T Q M I F</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">D H L P T W</td>
<td class="xd21e6834">C E H L P S</td>
<td class="xd21e6834">W T P L H D</td>
<td class="cellRight">S P L H E C</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">G K O S V X</td>
<td class="xd21e6834 cellBottom">A B D G K O</td>
<td class="xd21e6834 cellBottom">X V S O K G</td>
<td class="cellRight cellBottom">O K G D B A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p id="c1f" class="par">(<i>f</i>) <i>Alternate Diagonal</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A B F G N O</td>
<td class="xd21e6834 cellTop">G N O U V X</td>
<td class="xd21e6834 cellTop">O N G F B A</td>
<td class="cellRight cellTop">X V U O N G</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">C E H M P U</td>
<td class="xd21e6834">F H M P T W</td>
<td class="xd21e6834">U P M H E C</td>
<td class="cellRight">W T P M H F</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">D I L Q T V</td>
<td class="xd21e6834">B E I L Q S</td>
<td class="xd21e6834">V T Q L I D</td>
<td class="cellRight">S Q L I E B</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">J K R S W X</td>
<td class="xd21e6834 cellBottom">A C D J K R</td>
<td class="xd21e6834 cellBottom">X W S R K J</td>
<td class="cellRight cellBottom">R K J D C A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e7072"></p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A C D J K R</td>
<td class="xd21e6834 cellTop">J K R S W X</td>
<td class="xd21e6834 cellTop">R K J D C A</td>
<td class="cellRight cellTop">X W S R K J</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">B E I L Q S</td>
<td class="xd21e6834">D I L Q T V</td>
<td class="xd21e6834">S Q L I E B</td>
<td class="cellRight">V T Q L I D</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">F H M P T W</td>
<td class="xd21e6834">C E H M P U</td>
<td class="xd21e6834">W T P M H F</td>
<td class="cellRight">U P M H E C</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">G N O U V X</td>
<td class="xd21e6834 cellBottom">A B F G N O</td>
<td class="xd21e6834 cellBottom">X V U O N G</td>
<td class="cellRight cellBottom">O N G F B A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">(<i>g</i>) <i>Spiral, clockwise</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A B C D E F</td>
<td class="xd21e6834 cellTop">L M N O P A</td>
<td class="xd21e6834 cellTop">I J K L M N</td>
<td class="cellRight cellTop">D E F G H I</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">P Q R S T G</td>
<td class="xd21e6834">K V W X Q B</td>
<td class="xd21e6834">H U V W X O</td>
<td class="cellRight">C R S T U J</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">O X W V U H</td>
<td class="xd21e6834">J U T S R C</td>
<td class="xd21e6834">G T S R Q P</td>
<td class="cellRight">B Q X W V K</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">N M L K J I</td>
<td class="xd21e6834 cellBottom">I H G F E D</td>
<td class="xd21e6834 cellBottom">F E D C B A</td>
<td class="cellRight cellBottom">A P O N M L</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">(<i>h</i>) <i>Spiral, counter clockwise</i>:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">A P O N M L</td>
<td class="xd21e6834 cellTop">N M L K J I</td>
<td class="xd21e6834 cellTop">I H G F E D</td>
<td class="cellRight cellTop">F E D C B A</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">B Q X W V K</td>
<td class="xd21e6834">O X W V U H</td>
<td class="xd21e6834">J U T S R C</td>
<td class="cellRight">G T S R Q P</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">C R S T U J</td>
<td class="xd21e6834">P Q R S T G</td>
<td class="xd21e6834">K V W X Q B</td>
<td class="cellRight">H U V W X O</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">D E F G H I</td>
<td class="xd21e6834 cellBottom">A B C D E F</td>
<td class="xd21e6834 cellBottom">L M N O P A</td>
<td class="cellRight cellBottom">I J K L M N</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It is simply a matter of inspection to read a message in
a cipher of this type, once the dimensions of the rectangles have been
determined. We place the whole or a portion of the message in such
rectangles and read horizontally, vertically and diagonally forward and
backward. Parts of words will at once be apparent and the whole message
is soon deciphered. Two examples will show the process. <span class=
"pagenum">[<a id="pb28" href="#pb28" name="pb28">28</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first xd21e152"><i>Message</i></p>
<p class="par xd21e152"><span class=
"tt">ILVGIOIAEITSRNMANHMNG</span></p>
<p class="par">This message contains eight vowels or 38% out of
twenty-one letters, and the letters <span class="tt">LNRST</span> occur
7 times or 33%, the letters <span class="tt">XQJKZ</span> not
appearing. It is therefore a transposition cipher. Twenty-one letters
immediately suggest seven columns of three letters each or three
columns of seven letters each. Trying the former we have:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellRight cellTop">I L V G I O I</td>
</tr>
<tr>
<td class="cellLeft cellRight">A E I T S R N</td>
</tr>
<tr>
<td class="cellLeft cellRight cellBottom">M A N H M N G</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and reading down each column in succession (<a href=
"#c1b">Case 1-b</a>) reveals the message to be &ldquo;I am leaving this
morning.&rdquo;</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e7347">
<tr>
<td class="xd21e7348 cellLeft cellTop">M S I B R</td>
<td class="xd21e7348 cellTop">O R S E E</td>
<td class="xd21e7348 cellTop">V U E E M</td>
<td class="xd21e7348 cellTop">C O R E R</td>
<td class="xd21e7348 cellTop">E L I D E</td>
<td class="cellRight cellTop">T O E P Q</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">E N R E R</td>
<td class="xd21e7348">N S E R Y</td>
<td class="xd21e7348">E C O L L</td>
<td class="xd21e7348">E R E U S</td>
<td class="xd21e7348">P L U R C</td>
<td class="cellRight">E L O A J</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">A E H U H</td>
<td class="xd21e7348">P F A S O</td>
<td class="xd21e7348">N N O A A</td>
<td class="xd21e7348">E P I U A</td>
<td class="xd21e7348">P P E A C</td>
<td class="cellRight">U Q A R U</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft cellBottom">O P O E I</td>
<td class="xd21e7348 cellBottom">I R R M I</td>
<td class="xd21e7348 cellBottom">A F D A A</td>
<td class="xd21e7348 cellBottom">R Q U B O</td>
<td class="xd21e7348 cellBottom">Z A E G E</td>
<td class="cellRight cellBottom">R S F S X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">There are 120 letters in this message with 57 vowels or
47% vowels, and the letters <span class="tt">LNRST</span> occur 31
times or 26% of the whole.</p>
<p class="par">Non-occurrence of <span class="tt">K</span> and
<span class="tt">W</span> and vowel proportion leads us to the
assumption that it is a transposition cipher of a Spanish text. The
factors of 120 are 5 &times; 3 &times; 2 &times; 2 &times; 2. We may
then have one rectangle of 4 &times; 30 or one of 5 &times; 24 or two
of 5 &times; 12, or three of 5 &times; 8, or four of 5 &times; 6,
<span class="corr" id="xd21e7419" title="Source: of">or</span> five of
3 &times; 8, or ten of 3 &times; 4, or twenty of 3 &times; 2. The
message being in a rectangle of 4 &times; 30, we can inspect it as it
stands and this is clearly not the arrangement if it be a geometrical
transposition cipher at all. It is best however to try the largest
possible rectangles first so we will put it in the form 5 &times; 24,
thus:</p>
<div class="table">
<table class="xd21e7347">
<tr>
<td class="cellLeft cellTop">M</td>
<td class="cellTop">S</td>
<td class="cellTop">I</td>
<td class="cellTop">B</td>
<td class="cellTop">R</td>
<td class="cellTop">O</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">E</td>
<td class="cellTop">E</td>
<td class="cellTop">V</td>
<td class="cellTop">U</td>
<td class="cellTop">E</td>
<td class="cellTop">E</td>
<td class="cellTop">M</td>
<td class="cellTop">C</td>
<td class="cellTop">O</td>
<td class="cellTop">R</td>
<td class="cellTop">E</td>
<td class="cellTop">R</td>
<td class="cellTop">E</td>
<td class="cellTop">L</td>
<td class="cellTop">I</td>
<td class="cellRight cellTop">D</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>T</td>
<td>O</td>
<td>E</td>
<td>P</td>
<td>Q</td>
<td>E</td>
<td>N</td>
<td>R</td>
<td>E</td>
<td>R</td>
<td>N</td>
<td>S</td>
<td>E</td>
<td>R</td>
<td>Y</td>
<td>E</td>
<td>C</td>
<td>O</td>
<td>L</td>
<td>L</td>
<td>E</td>
<td>R</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>S</td>
<td>P</td>
<td>L</td>
<td>U</td>
<td>R</td>
<td>C</td>
<td>E</td>
<td>L</td>
<td>O</td>
<td>A</td>
<td>J</td>
<td>A</td>
<td>E</td>
<td>H</td>
<td>U</td>
<td>H</td>
<td>P</td>
<td>F</td>
<td>A</td>
<td>S</td>
<td>O</td>
<td>N</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>A</td>
<td>A</td>
<td>E</td>
<td>P</td>
<td>I</td>
<td>U</td>
<td>A</td>
<td>P</td>
<td>P</td>
<td>E</td>
<td>A</td>
<td>C</td>
<td>U</td>
<td>Q</td>
<td>A</td>
<td>R</td>
<td>U</td>
<td>O</td>
<td>P</td>
<td>O</td>
<td>E</td>
<td>I</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft cellBottom">R</td>
<td class="cellBottom">R</td>
<td class="cellBottom">M</td>
<td class="cellBottom">I</td>
<td class="cellBottom">A</td>
<td class="cellBottom">F</td>
<td class="cellBottom">D</td>
<td class="cellBottom">A</td>
<td class="cellBottom">A</td>
<td class="cellBottom">R</td>
<td class="cellBottom">Q</td>
<td class="cellBottom">U</td>
<td class="cellBottom">B</td>
<td class="cellBottom">O</td>
<td class="cellBottom">Z</td>
<td class="cellBottom">A</td>
<td class="cellBottom">E</td>
<td class="cellBottom">G</td>
<td class="cellBottom">E</td>
<td class="cellBottom">R</td>
<td class="cellBottom">S</td>
<td class="cellBottom">F</td>
<td class="cellBottom">S</td>
<td class="cellRight cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb29" href="#pb29" name=
"pb29">29</a>]</span></p>
<p class="par">Here an inspection shows this to be Case <a href=
"#c1f">1-f</a>, alternate diagonal, and the text to be
&ldquo;<span class="tt">ME SITUO SOBRE PARRAL PORQUE ME PRESENCIA FUE
REVELADA POR U</span>&rdquo;; here the sense breaks but note that
<span class="tt">U</span> is the twelfth letter of the line and
continue as if the rectangle were 5 &times; 12 and we have
&ldquo;<span class="tt">NA PAREJA QU</span>.&rdquo; Now inspect the
second rectangle of 5 &times; 12 in the same way and the sense
continues &ldquo;<span class="tt">E SE ME ACERCO Y HUBO QUE RECHAZAR
POR EL FUEGO ALLI ESRERO ORDENES FINISX</span>&rdquo;.</p>
<p class="par">The practical way of examining a cipher of this type is
to have several men prepare rectangles of different dimensions, using
the letters of the cipher in the order received. The rectangles can be
inspected very rapidly when once prepared. Note that the dimensions of
any rectangle will rarely be such as to contain more than fifty
letters, on account of the necessity of filling up a rectangle with
nulls if the number of letters of the message is just a little greater
than a multiple of the rectangle. Also large rectangles give, for all
but the diagonal method, whole words in a line or column and these are
easily noted.</p>
<p class="par">The following ciphers come under Case 1:</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 1-i.&mdash;The rail
fence cipher, useful as an operators&rsquo; cipher but permits of no
variation and is therefore read almost as easily as straight text when
the method is known. The message:</p>
<p class="par xd21e152"><span class="tt">HOSTILE CAVALRY HAS
RETIRED</span></p>
<p class="par">is written:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellRight cellTop">&nbsp;O T L C V L Y A R T R
D</td>
</tr>
<tr>
<td class="cellLeft cellRight cellBottom">H S I E A A R H S E I E</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and is sent:</p>
<p class="par xd21e152"><span class="tt">OTLCV LYART RDHSI EAARH
SEIEX</span> <span class="pagenum">[<a id="pb30" href="#pb30" name=
"pb30">30</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 1-j.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e6834 cellLeft cellTop">S S O H S</td>
<td class="xd21e6834 cellTop">T P F O R</td>
<td class="cellRight cellTop">I E E A E</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft">T Q N E T</td>
<td class="xd21e6834">F A I X E</td>
<td class="cellRight">G L F D R</td>
</tr>
<tr>
<td class="xd21e6834 cellLeft cellBottom">A U L R N</td>
<td class="xd21e6834 cellBottom">O S R X L</td>
<td class="cellRight cellBottom">H A T R O</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">To solve this cipher, read down the columns in this
order 8, 1, 15, 2, 14, 3, 13, 4, 12, etc. A variation is to arrange the
cipher so the columns are read upwards. Another is to arrange the
ciphers so the columns are read alternately upward and downward. The
factors of the number of letters in this case give the shape of the
rectangle as usual.</p>
<p class="par">It will be seen that there are a great number of
possible transposition ciphers that come under Case 1 but practically
all of them are useless from a military standpoint because they do not
depend on a key which can be readily and frequently changed. However
such ciphers constantly crop up in cipher examination, being used for
special communication between parties who consider the regular military
ciphers too complicated. Thus some of these expedients have been
used.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Reversed
Writing.</span>&mdash;(Special case of Case <a href=
"#c1a">1-a</a>).</p>
<p class="par"><span class="tt">LEAVING TONIGHT</span> is enciphered
<span class="tt">THGINOT GNIVAEL</span> or it may be reversed by words,
thus <span class="tt">GNIVAEL THGINOT</span> or by groups of five
letters, thus <span class="tt">IVAEL NOTGN XTHGI</span>.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Vertical
Writing.</span>&mdash;(Special case of Case <a href="#c1b">1-b</a>).
Same message is enciphered,</p>
<div class="table">
<table class="xd21e7794">
<tr>
<td class="xd21e7795 cellLeft cellTop">LT</td>
<td class="cellRight cellTop"></td>
</tr>
<tr>
<td class="xd21e7795 cellLeft">EO</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e7795 cellLeft">AN</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e7795 cellLeft">VI</td>
<td class="cellRight">and is sent, <span class="tt">LTEOA NVIIG
NHGTX</span>.</td>
</tr>
<tr>
<td class="xd21e7795 cellLeft">IG</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e7795 cellLeft">NH</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e7795 cellLeft cellBottom">GT</td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb31" href="#pb31" name=
"pb31">31</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 2.&mdash;This case
includes all transposition ciphers in which lines and columns of the
text are rearranged according to some key word or key number. There are
many varieties of this case but their solution usually is arrived at
through the methods suggested for Case 1, that is, arrangement into
appropriate rectangles and examination of lines and columns for words
or syllables. Rearrangement of columns or lines follows until the
solution is completed.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p id="c2a" class="par first"><span class="sc">Case</span> 2-a.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e7348 cellLeft cellTop">HIIGF</td>
<td class="xd21e7348 cellTop">TNGHI</td>
<td class="xd21e7348 cellTop">NTCVN</td>
<td class="xd21e7348 cellTop">IEIOT</td>
<td class="xd21e7348 cellTop">CYIFY</td>
<td class="xd21e7348 cellTop">LHAEA</td>
<td class="xd21e7348 cellTop">ESNBA</td>
<td class="cellRight cellTop">EEEEN</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">RWGBN</td>
<td class="xd21e7348">YDELR</td>
<td class="xd21e7348">OAESG</td>
<td class="xd21e7348">RNEBO</td>
<td class="xd21e7348">VNLDA</td>
<td class="xd21e7348">ICAOA</td>
<td class="xd21e7348">LCNDT</td>
<td class="cellRight">IRGVA</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft cellBottom">CDOIE</td>
<td class="xd21e7348 cellBottom">SEREC</td>
<td class="xd21e7348 cellBottom">DVPEI</td>
<td class="xd21e7348 cellBottom">AFIFL</td>
<td class="xd21e7348 cellBottom">RINEH</td>
<td class="xd21e7348 cellBottom">ETT</td>
<td class="xd21e7348 cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">There are 108 letters in this message and examination
shows it to be a transposition cipher, English text. The number of
letters, 108, immediately suggests a rectangle of 12 &times; 9 or 9
&times; 12 letters. Put into this form we have:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop cellBottom">
<div class="table">
<table class="xd21e7794">
<thead>
<tr class="label">
<td class="xd21e7910 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e7911 cellHeadRight cellHeadTop cellHeadBottom">
<i>Vowels</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e7910 cellLeft">H I I G F T N G H I N T</td>
<td class="xd21e7911 cellRight">3</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">C V N I E I O T C Y I F</td>
<td class="xd21e7911 cellRight">5</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">Y L H A E A E S N B A E</td>
<td class="xd21e7911 cellRight">6</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">E E E N R W G B N Y D E</td>
<td class="xd21e7911 cellRight">4</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">L R O A E S G R N E B O</td>
<td class="xd21e7911 cellRight">5</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">V N L D A I C A O A L C</td>
<td class="xd21e7911 cellRight">5</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">N D T I R G V A C D O I</td>
<td class="xd21e7911 cellRight">4</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">E S E R E C D V P E I A</td>
<td class="xd21e7911 cellRight">6</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft cellBottom">F I F L R I N E H E T T</td>
<td class="xd21e7911 cellRight cellBottom">4</td>
</tr>
</tbody>
</table>
</div>
</td>
<td class="cellRight cellTop cellBottom">
<div class="table">
<table class="xd21e7794">
<thead>
<tr class="label">
<td class="xd21e7910 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e7911 cellHeadRight cellHeadTop cellHeadBottom">
<i>Vowels</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e7910 cellLeft">H I I G F T N G H</td>
<td class="xd21e7911 cellRight">2</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">I N T C V N I E I</td>
<td class="xd21e7911 cellRight">4</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">O T C Y I F Y L H</td>
<td class="xd21e7911 cellRight">2</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">A E A E S N B A E</td>
<td class="xd21e7911 cellRight">6</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">E E E N R W G B N</td>
<td class="xd21e7911 cellRight">3</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">Y D E L R O A E S</td>
<td class="xd21e7911 cellRight">4</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">G R N E B O V N L</td>
<td class="xd21e7911 cellRight">2</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">D A I C A O A L C</td>
<td class="xd21e7911 cellRight">5</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">N D T I R G V A C</td>
<td class="xd21e7911 cellRight">2</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">D O I E S E R E C</td>
<td class="xd21e7911 cellRight">5</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft">D V P E I A F I F</td>
<td class="xd21e7911 cellRight">4</td>
</tr>
<tr>
<td class="xd21e7910 cellLeft cellBottom">L R I N E H E T T</td>
<td class="xd21e7911 cellRight cellBottom">3</td>
</tr>
</tbody>
</table>
</div>
</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The vowel count of the lines shows the first arrangement
to be the more likely. We will now number the columns and try pairing
off certain ones which in no line would give impossible combinations of
letters.</p>
<div class="table" id="t40">
<table class="xd21e8040">
<thead>
<tr class="label">
<td class="xd21e8041 cellHeadLeft cellHeadTop cellHeadBottom">1</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">2</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">3</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">4</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">5</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">6</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">7</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">8</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">9</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">10</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">11</td>
<td class="xd21e8041 cellHeadRight cellHeadTop cellHeadBottom">12</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">H</td>
<td>I</td>
<td>I</td>
<td>G</td>
<td>F</td>
<td>T</td>
<td>N</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>N</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>V</td>
<td>N</td>
<td>I</td>
<td>E</td>
<td>I</td>
<td>O</td>
<td>T</td>
<td>C</td>
<td>Y</td>
<td>I</td>
<td class="cellRight">F</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>L</td>
<td>H</td>
<td>A</td>
<td>E</td>
<td>A</td>
<td>E</td>
<td>S</td>
<td>N</td>
<td>B</td>
<td>A</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>E</td>
<td>E</td>
<td>N</td>
<td>R</td>
<td>W</td>
<td>G</td>
<td>B</td>
<td>N</td>
<td>Y</td>
<td>D</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>R</td>
<td>O</td>
<td>A</td>
<td>E</td>
<td>S</td>
<td>G</td>
<td>R</td>
<td>N</td>
<td>E</td>
<td>B</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>N</td>
<td>L</td>
<td>D</td>
<td>A</td>
<td>I</td>
<td>C</td>
<td>A</td>
<td>O</td>
<td>A</td>
<td>L</td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>D</td>
<td>T</td>
<td>I</td>
<td>R</td>
<td>G</td>
<td>V</td>
<td>A</td>
<td>C</td>
<td>D</td>
<td>O</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>S</td>
<td>E</td>
<td>R</td>
<td>E</td>
<td>C</td>
<td>D</td>
<td>V</td>
<td>P</td>
<td>E</td>
<td>I</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="cellLeft cellBottom">F</td>
<td class="cellBottom">I</td>
<td class="cellBottom">F</td>
<td class="cellBottom">L</td>
<td class="cellBottom">R</td>
<td class="cellBottom">I</td>
<td class="cellBottom">N</td>
<td class="cellBottom">E</td>
<td class="cellBottom">H</td>
<td class="cellBottom">E</td>
<td class="cellBottom">T</td>
<td class="cellRight cellBottom">T</td>
</tr>
</tbody>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb32" href="#pb32" name=
"pb32">32</a>]</span></p>
<p class="par">These combinations appear among others:</p>
<div class="table" id="t41">
<table class="xd21e8040">
<thead>
<tr class="label">
<td class="xd21e8041 cellHeadLeft cellHeadTop cellHeadBottom">1</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">6</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">2</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">4</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">5</td>
<td class="xd21e8041 cellHeadRight cellHeadTop cellHeadBottom">2</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">H</td>
<td>T</td>
<td>I</td>
<td>G</td>
<td>F</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>I</td>
<td>V</td>
<td>I</td>
<td>E</td>
<td class="cellRight">V</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>A</td>
<td>L</td>
<td>A</td>
<td>E</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>W</td>
<td>E</td>
<td>N</td>
<td>R</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>S</td>
<td>R</td>
<td>A</td>
<td>E</td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>I</td>
<td>N</td>
<td>D</td>
<td>A</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>G</td>
<td>D</td>
<td>I</td>
<td>R</td>
<td class="cellRight">D</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>C</td>
<td>S</td>
<td>R</td>
<td>E</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">F</td>
<td class="cellBottom">I</td>
<td class="cellBottom">I</td>
<td class="cellBottom">L</td>
<td class="cellBottom">R</td>
<td class="cellRight cellBottom">I</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">The word <span class="tt">FIGHT</span> stares at us from
the first line; let us arrange the columns thus:</p>
<div class="table" id="t42">
<table class="xd21e8040">
<thead>
<tr class="label">
<td class="xd21e8041 cellHeadLeft cellHeadTop cellHeadBottom">5</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">2</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">4</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">1</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">6</td>
<td class="xd21e8041 cellHeadRight cellHeadTop cellHeadBottom">3</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">F</td>
<td>I</td>
<td>G</td>
<td>H</td>
<td>T</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>V</td>
<td>I</td>
<td>C</td>
<td>I</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>L</td>
<td>A</td>
<td>Y</td>
<td>A</td>
<td class="cellRight">H</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>E</td>
<td>N</td>
<td>E</td>
<td>W</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>R</td>
<td>A</td>
<td>L</td>
<td>S</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>N</td>
<td>D</td>
<td>V</td>
<td>I</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>D</td>
<td>I</td>
<td>N</td>
<td>G</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>S</td>
<td>R</td>
<td>E</td>
<td>C</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft cellBottom">R</td>
<td class="cellBottom">I</td>
<td class="cellBottom">L</td>
<td class="cellBottom">F</td>
<td class="cellBottom">I</td>
<td class="cellRight cellBottom">F</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">We have the words <span class="tt">FIGHTI(NG)</span>,
<span class="tt">VICIN(ITY)</span>, <span class="tt">RENEWE(D)</span>,
<span class="tt">ANDVIL(LA)</span>, <span class="tt">RDINGT(O)</span>,
<span class="tt">RECE(IVED)</span>. With this to go on, we must choose
column 11 as the next one and then in order, columns 8, 10, 7, 12, 9.
But note that the order 11, 8, 10, 7, 12, 9, is the same as the order
5, 2, 4, 1, 6, 3. The message was written in twelve columns and the
columns have been transposed in that order. We may, although it is
entirely unnecessary, speculate on the key word used. It was
probably</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellRight cellTop">M E X I C O</td>
</tr>
<tr>
<td class="cellLeft cellRight cellBottom">4 2 6 3 1 5</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">meaning that the 4th column of the plain text was
transferred in enciphering so it became our 1st, the 2d column remained
the 2d; the 6th column became our 3d, etc.</p>
<p class="par">Actually, this cipher was solved because the word
<span class="tt">VILLA</span> was suspected and all the necessary
letters were found in line six of the arrangement in <span class=
"pagenum">[<a id="pb33" href="#pb33" name="pb33">33</a>]</span>twelve
columns. The order 1, 6, 3, 11, 8 was tried and gave this result.</p>
<div class="table" id="t44">
<table class="xd21e6833">
<thead>
<tr class="label">
<td class="xd21e8041 cellHeadLeft cellHeadTop cellHeadBottom">1</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">6</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">3</td>
<td class="xd21e8041 cellHeadTop cellHeadBottom">11</td>
<td class="xd21e8041 cellHeadRight cellHeadTop cellHeadBottom">8</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">H</td>
<td>T</td>
<td>I</td>
<td>N</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>I</td>
<td>N</td>
<td>I</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>A</td>
<td>H</td>
<td>A</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>W</td>
<td>E</td>
<td>D</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>S</td>
<td>O</td>
<td>B</td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>I</td>
<td>L</td>
<td>L</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>G</td>
<td>T</td>
<td>O</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>C</td>
<td>E</td>
<td>I</td>
<td class="cellRight">V</td>
</tr>
<tr>
<td class="cellLeft cellBottom">F</td>
<td class="cellBottom">I</td>
<td class="cellBottom">F</td>
<td class="cellBottom">T</td>
<td class="cellRight cellBottom">E</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">The remainder of the solution followed the lines already
laid down and, naturally, offered no difficulties, in view of the large
number of connected syllables available.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 2-b.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e8735">
<tr>
<td class="xd21e7348 cellLeft cellTop">SLCOF</td>
<td class="xd21e7348 cellTop">WEETN</td>
<td class="xd21e7348 cellTop">EBRDO</td>
<td class="xd21e7348 cellTop">ORVYM</td>
<td class="xd21e7348 cellRight cellTop">FFEDI</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">NMTEC</td>
<td class="xd21e7348">ROIAR</td>
<td class="xd21e7348">PERHO</td>
<td class="xd21e7348">ESETS</td>
<td class="xd21e7348 cellRight">RFBHL</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">TENAH</td>
<td class="xd21e7348">OPTAU</td>
<td class="xd21e7348">SOMTL</td>
<td class="xd21e7348">RTETT</td>
<td class="xd21e7348 cellRight">ASCBH</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">NIODC</td>
<td class="xd21e7348">RENEN</td>
<td class="xd21e7348">AAPRD</td>
<td class="xd21e7348">LACYE</td>
<td class="xd21e7348 cellRight">ECIIE</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft cellBottom">SGUFN</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is a transposition cipher, English text, and
contains 105 letters. The factors of 105 are 5 &times; 3 &times; 7 so
that we must investigate the following rectangles; 5 &times; 21, 15
&times; 7, three of 5 &times; 7, five of 3 &times; 7 and seven of 5
&times; 3.</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">
<div class="table">
<table class="xd21e8735">
<tr>
<td class="xd21e8796 cellLeft cellTop"></td>
<td colspan="21" class="xd21e8824 cellTop">21 &times; 5</td>
<td class="xd21e8826 xd21e8820 cellRight cellTop">Vowels</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>S</td>
<td>L</td>
<td>C</td>
<td>O</td>
<td>F</td>
<td>W</td>
<td>E</td>
<td>E</td>
<td>T</td>
<td>N</td>
<td>E</td>
<td>B</td>
<td>R</td>
<td>D</td>
<td>O</td>
<td>O</td>
<td>R</td>
<td>V</td>
<td>Y</td>
<td>M</td>
<td>F</td>
<td class="xd21e8820 cellRight">6</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>F</td>
<td>E</td>
<td>D</td>
<td>I</td>
<td>N</td>
<td>M</td>
<td>T</td>
<td>E</td>
<td>C</td>
<td>R</td>
<td>O</td>
<td>I</td>
<td>A</td>
<td>R</td>
<td>P</td>
<td>E</td>
<td>R</td>
<td>H</td>
<td>O</td>
<td>E</td>
<td>S</td>
<td class="xd21e8820 cellRight">9</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>E</td>
<td>T</td>
<td>S</td>
<td>R</td>
<td>F</td>
<td>B</td>
<td>H</td>
<td>L</td>
<td>T</td>
<td>E</td>
<td>N</td>
<td>A</td>
<td>H</td>
<td>O</td>
<td>P</td>
<td>T</td>
<td>A</td>
<td>U</td>
<td>S</td>
<td>O</td>
<td>M</td>
<td class="xd21e8820 cellRight">7</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>T</td>
<td>L</td>
<td>R</td>
<td>T</td>
<td>E</td>
<td>T</td>
<td>T</td>
<td>A</td>
<td>S</td>
<td>C</td>
<td>B</td>
<td>H</td>
<td>N</td>
<td>I</td>
<td>O</td>
<td>D</td>
<td>C</td>
<td>R</td>
<td>E</td>
<td>N</td>
<td>E</td>
<td class="xd21e8820 cellRight">6</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>N</td>
<td>A</td>
<td>A</td>
<td>P</td>
<td>R</td>
<td>D</td>
<td>L</td>
<td>A</td>
<td>C</td>
<td>Y</td>
<td>E</td>
<td>E</td>
<td>C</td>
<td>I</td>
<td>I</td>
<td>E</td>
<td>S</td>
<td>G</td>
<td>U</td>
<td>F</td>
<td>N</td>
<td class="xd21e8820 cellRight">9</td>
</tr>
<tr>
<td class="xd21e8041 xd21e8796 cellLeft cellBottom">Vowels</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">2</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">2</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">0</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">4</td>
<td class="xd21e8041 cellBottom">0</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">1</td>
<td class="xd21e8041 cellBottom">3</td>
<td class="xd21e8041 cellBottom">2</td>
<td class="xd21e8041 cellRight cellBottom">1</td>
</tr>
</table>
</div>
The vowel count of the columns of the rectangle 5 &times; 21 is very
satisfactory. Let us consider it as three blocks of 5 &times; 7 each,
since we must do this ultimately, and make a vowel count of columns for
these blocks.</td>
<td class="cellRight cellTop cellBottom">
<div class="table">
<table class="xd21e8735">
<tr>
<td class="xd21e8796 cellLeft cellTop"></td>
<td colspan="5" class="xd21e8824 cellTop">5 &times; 21</td>
<td class="xd21e8826 xd21e8820 cellRight cellTop">Vowels</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>S</td>
<td>L</td>
<td>C</td>
<td>O</td>
<td>F</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>W</td>
<td>E</td>
<td>E</td>
<td>T</td>
<td>N</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>E</td>
<td>B</td>
<td>R</td>
<td>D</td>
<td>O</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>O</td>
<td>R</td>
<td>V</td>
<td>Y</td>
<td>M</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>F</td>
<td>F</td>
<td>E</td>
<td>D</td>
<td>I</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>N</td>
<td>M</td>
<td>T</td>
<td>E</td>
<td>C</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>R</td>
<td>O</td>
<td>I</td>
<td>A</td>
<td>R</td>
<td class="xd21e8820 cellRight">3</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>P</td>
<td>E</td>
<td>R</td>
<td>H</td>
<td>O</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>E</td>
<td>S</td>
<td>E</td>
<td>T</td>
<td>S</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>R</td>
<td>F</td>
<td>B</td>
<td>H</td>
<td>L</td>
<td class="xd21e8820 cellRight">0</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>T</td>
<td>E</td>
<td>N</td>
<td>A</td>
<td>H</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>O</td>
<td>P</td>
<td>T</td>
<td>A</td>
<td>U</td>
<td class="xd21e8820 cellRight">3</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>S</td>
<td>O</td>
<td>M</td>
<td>T</td>
<td>L</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>R</td>
<td>T</td>
<td>E</td>
<td>T</td>
<td>T</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>A</td>
<td>S</td>
<td>C</td>
<td>B</td>
<td>H</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>N</td>
<td>I</td>
<td>O</td>
<td>D</td>
<td>C</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>R</td>
<td>E</td>
<td>N</td>
<td>E</td>
<td>N</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>A</td>
<td>A</td>
<td>P</td>
<td>R</td>
<td>D</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>L</td>
<td>A</td>
<td>C</td>
<td>Y</td>
<td>E</td>
<td class="xd21e8820 cellRight">2</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>E</td>
<td>C</td>
<td>I</td>
<td>I</td>
<td>E</td>
<td class="xd21e8820 cellRight">4</td>
</tr>
<tr>
<td class="xd21e8796 cellLeft"></td>
<td>S</td>
<td>G</td>
<td>U</td>
<td>F</td>
<td>N</td>
<td class="xd21e8820 cellRight">1</td>
</tr>
<tr>
<td class="xd21e8041 xd21e8796 cellLeft cellBottom">Vowels</td>
<td class="xd21e8041 cellBottom">7</td>
<td class="xd21e8041 cellBottom">9</td>
<td class="xd21e8041 cellBottom">8</td>
<td class="xd21e8041 cellBottom">7</td>
<td class="xd21e8041 cellRight cellBottom">6</td>
</tr>
</table>
</div>
</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb34" href="#pb34" name=
"pb34">34</a>]</span></p>
<div class="table">
<table class="xd21e7794">
<tr>
<td class="xd21e9471 cellLeft cellTop"></td>
<td colspan="5" class="xd21e9471 cellRight cellTop"><i>Column</i></td>
</tr>
<tr>
<td class="xd21e9471 cellLeft"></td>
<td class="xd21e9471">1</td>
<td class="xd21e9471">2</td>
<td class="xd21e9471">3</td>
<td class="xd21e9471">4</td>
<td class="cellRight">5</td>
</tr>
<tr>
<td class="xd21e9471 cellLeft">Vowels, 1st block</td>
<td class="xd21e9471">2</td>
<td class="xd21e9471">2</td>
<td class="xd21e9471">3</td>
<td class="xd21e9471">2</td>
<td class="cellRight">2</td>
</tr>
<tr>
<td class="xd21e9471 cellLeft">Vowels, 2d block</td>
<td class="xd21e9471">2</td>
<td class="xd21e9471">3</td>
<td class="xd21e9471">2</td>
<td class="xd21e9471">2</td>
<td class="cellRight">2</td>
</tr>
<tr>
<td class="xd21e9471 cellLeft cellBottom">Vowels, 3d block</td>
<td class="xd21e9471 cellBottom">3</td>
<td class="xd21e9471 cellBottom">4</td>
<td class="xd21e9471 cellBottom">3</td>
<td class="xd21e9471 cellBottom">2</td>
<td class="cellRight cellBottom">2</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is also excellent, so we will try three blocks 5
&times; 7 and see if rearrangement of <i>horizontal lines</i> will give
results reading the columns vertically.</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e9541 cellLeft cellTop">1</td>
<td class="xd21e9471 cellTop">S L C O F</td>
<td class="xd21e9471 cellTop">P E R H O</td>
<td class="cellRight cellTop">A S C B H</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">2</td>
<td class="xd21e9471">W E E T N</td>
<td class="xd21e9471">E S E T S</td>
<td class="cellRight">N I O D C</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">3</td>
<td class="xd21e9471">E B R D O</td>
<td class="xd21e9471">R F B H L</td>
<td class="cellRight">R E N E N</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">4</td>
<td class="xd21e9471">O R V Y M</td>
<td class="xd21e9471">T E N A H</td>
<td class="cellRight">A A P R D</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">5</td>
<td class="xd21e9471">F F E D I</td>
<td class="xd21e9471">O P T A U</td>
<td class="cellRight">L A C Y E</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">6</td>
<td class="xd21e9471">N M T E C</td>
<td class="xd21e9471">S O M T L</td>
<td class="cellRight">E C I I E</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft cellBottom">7</td>
<td class="xd21e9471 cellBottom">R O I A R</td>
<td class="xd21e9471 cellBottom">R T E T T</td>
<td class="cellRight cellBottom">S G U F N</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Among other combinations are:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e9541 cellLeft cellTop">3</td>
<td class="xd21e9471 cellTop">E B R D O</td>
<td class="xd21e9471 cellTop">R F B H L</td>
<td class="cellRight cellTop">R E N E N</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">2</td>
<td class="xd21e9471">W E E T N</td>
<td class="xd21e9471">E S E T S</td>
<td class="cellRight">N I O D C</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">1</td>
<td class="xd21e9471">S L C O F</td>
<td class="xd21e9471">P E R H O</td>
<td class="cellRight">A S C B H</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">&nbsp;</td>
<td class="xd21e9471"></td>
<td class="xd21e9471"></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e9541 cellLeft">5</td>
<td class="xd21e9471">F F E D I</td>
<td class="xd21e9471">O P T A U</td>
<td class="cellRight">L A C Y E</td>
</tr>
<tr>
<td class="xd21e9541 cellLeft cellBottom">7</td>
<td class="xd21e9471 cellBottom">R O I A R</td>
<td class="xd21e9471 cellBottom">R T E T T</td>
<td class="cellRight cellBottom">S G U F N</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The addition of line 6 above line 3 and line 4 below
line 7 will complete this cipher. The successive columns should be read
downward.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 2-c. In this case,
both lines and columns are rearranged by means of a key word or key
words. The method of solution is the same as Case 2-a and 2-b except
that the lines must be rearranged after the columns have been correctly
arranged, or in some cases, vice versa. This cipher is not infrequently
met with because it seems to offer safety by use of two key words and
by the great but only apparent complexity of the method.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e8735">
<tr>
<td class="xd21e7348 cellLeft cellTop">WVGAE</td>
<td class="xd21e7348 cellTop">EGENL</td>
<td class="xd21e7348 cellTop">TFTOH</td>
<td class="xd21e7348 cellTop">TEIEF</td>
<td class="cellRight cellTop">RBTSE</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft">INENG</td>
<td class="xd21e7348">ONWRM</td>
<td class="xd21e7348">GXIXN</td>
<td class="xd21e7348">GOITN</td>
<td class="cellRight">ROMRO</td>
</tr>
<tr>
<td class="xd21e7348 cellLeft cellBottom">ESPAL</td>
<td class="xd21e7348 cellBottom">HNEAC</td>
<td class="xd21e7348 cellBottom">UDNNH</td>
<td class="xd21e7348 cellBottom">DERME</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is a transposition cipher, English text and
<span class="pagenum">[<a id="pb35" href="#pb35" name=
"pb35">35</a>]</span>the number of letters, 70, leads us to try
rectangles of 10 &times; 7 and 7 &times; 10.</p>
<div class="table">
<table class="xd21e283">
<thead>
<tr class="label">
<td class="xd21e9721 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td class="xd21e9722 cellHeadTop cellHeadBottom"><i>Vowels</i></td>
<td class="xd21e9721 cellHeadTop cellHeadBottom"></td>
<td class="xd21e9724 cellHeadRight cellHeadTop cellHeadBottom">
<i>Vowels</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e9721 cellLeft">W V G A E E G E N L</td>
<td class="xd21e9722">4</td>
<td class="xd21e9721">W V G A E E G</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">T F T O H T E I E F</td>
<td class="xd21e9722">3</td>
<td class="xd21e9721">E N L T F T O</td>
<td class="xd21e9724 cellRight">2</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">R B T S E I N E N G</td>
<td class="xd21e9722">3</td>
<td class="xd21e9721">H T E I E F R</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">O N W R M G X I X N</td>
<td class="xd21e9722">2</td>
<td class="xd21e9721">B T S E I N E</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">G O I T N R O M R O</td>
<td class="xd21e9722">4</td>
<td class="xd21e9721">N G O N W R M</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">E S P A L H N E A C</td>
<td class="xd21e9722">4</td>
<td class="xd21e9721">G X I X N G O</td>
<td class="xd21e9724 cellRight">2</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft">U D N N H D E R M E</td>
<td class="xd21e9722">3</td>
<td class="xd21e9721">I T N R O M R</td>
<td class="xd21e9724 cellRight">2</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft"></td>
<td class="xd21e9722"></td>
<td class="xd21e9721">O E S P A L H</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft"></td>
<td class="xd21e9722"></td>
<td class="xd21e9721">N E A C U D N</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="xd21e9721 cellLeft cellBottom"></td>
<td class="xd21e9722 cellBottom"></td>
<td class="xd21e9721 cellBottom">N H D E R M E</td>
<td class="xd21e9724 cellRight cellBottom">2</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">The first form looks the more likely from the vowel
count. We proceed to number the columns and lines and try rearrangement
of columns so as to obtain possible letter combinations from every
line.</p>
<div class="table" id="t55">
<table class="xd21e8735">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">1</td>
<td class="cellTop">2</td>
<td class="cellTop">3</td>
<td class="cellTop">4</td>
<td class="cellTop">5</td>
<td class="cellTop">6</td>
<td class="cellTop">7</td>
<td class="cellTop">8</td>
<td class="cellTop">9</td>
<td class="cellRight cellTop">10</td>
</tr>
<tr>
<td class="cellLeft">1</td>
<td>W</td>
<td>V</td>
<td>G</td>
<td>A</td>
<td>E</td>
<td>E</td>
<td>G</td>
<td>E</td>
<td>N</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">2</td>
<td>T</td>
<td>F</td>
<td>T</td>
<td>O</td>
<td>H</td>
<td>T</td>
<td>E</td>
<td>I</td>
<td>E</td>
<td class="cellRight">F</td>
</tr>
<tr>
<td class="cellLeft">3</td>
<td>R</td>
<td>B</td>
<td>T</td>
<td>S</td>
<td>E</td>
<td>I</td>
<td>N</td>
<td>E</td>
<td>N</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="cellLeft">4</td>
<td>O</td>
<td>N</td>
<td>W</td>
<td>R</td>
<td>M</td>
<td>G</td>
<td>X</td>
<td>I</td>
<td>X</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">5</td>
<td>G</td>
<td>O</td>
<td>I</td>
<td>T</td>
<td>N</td>
<td>R</td>
<td>O</td>
<td>M</td>
<td>R</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="cellLeft">6</td>
<td>E</td>
<td>S</td>
<td>P</td>
<td>A</td>
<td>L</td>
<td>H</td>
<td>N</td>
<td>E</td>
<td>A</td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="cellLeft cellBottom">7</td>
<td class="cellBottom">U</td>
<td class="cellBottom">D</td>
<td class="cellBottom">N</td>
<td class="cellBottom">N</td>
<td class="cellBottom">H</td>
<td class="cellBottom">D</td>
<td class="cellBottom">E</td>
<td class="cellBottom">R</td>
<td class="cellBottom">M</td>
<td class="cellRight cellBottom">E</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Among other combinations we have these:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e8041 xd21e10021 cellLeft cellTop"></td>
<td class="xd21e8041 cellTop">3</td>
<td class="xd21e8041 xd21e10023 cellTop">5</td>
<td class="xd21e8041 cellTop">1</td>
<td class="xd21e8041 xd21e10023 cellTop">4</td>
<td class="xd21e8041 cellTop">2</td>
<td class="xd21e8041 xd21e10023 cellTop">8</td>
<td class="xd21e8041 cellTop">10</td>
<td class="xd21e8041 xd21e10023 cellTop">6</td>
<td class="xd21e8041 cellTop">9</td>
<td class="xd21e8041 cellRight cellTop">7</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">1</td>
<td>G</td>
<td class="xd21e10023">E</td>
<td>W</td>
<td class="xd21e10023">A</td>
<td>V</td>
<td class="xd21e10023">E</td>
<td>L</td>
<td class="xd21e10023">E</td>
<td>N</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">2</td>
<td>T</td>
<td class="xd21e10023">H</td>
<td>T</td>
<td class="xd21e10023">O</td>
<td>F</td>
<td class="xd21e10023">I</td>
<td>F</td>
<td class="xd21e10023">T</td>
<td>E</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">3</td>
<td>T</td>
<td class="xd21e10023">E</td>
<td>R</td>
<td class="xd21e10023">S</td>
<td>B</td>
<td class="xd21e10023">E</td>
<td>G</td>
<td class="xd21e10023">I</td>
<td>N</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">4</td>
<td>W</td>
<td class="xd21e10023">M</td>
<td>O</td>
<td class="xd21e10023">R</td>
<td>N</td>
<td class="xd21e10023">I</td>
<td>N</td>
<td class="xd21e10023">G</td>
<td>X</td>
<td class="cellRight">X</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">5</td>
<td>I</td>
<td class="xd21e10023">N</td>
<td>G</td>
<td class="xd21e10023">T</td>
<td>O</td>
<td class="xd21e10023">M</td>
<td>O</td>
<td class="xd21e10023">R</td>
<td>R</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">6</td>
<td>P</td>
<td class="xd21e10023">L</td>
<td>E</td>
<td class="xd21e10023">A</td>
<td>S</td>
<td class="xd21e10023">E</td>
<td>C</td>
<td class="xd21e10023">H</td>
<td>A</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft cellBottom">7</td>
<td class="cellBottom">N</td>
<td class="xd21e10023 cellBottom">H</td>
<td class="cellBottom">U</td>
<td class="xd21e10023 cellBottom">N</td>
<td class="cellBottom">D</td>
<td class="xd21e10023 cellBottom">R</td>
<td class="cellBottom">E</td>
<td class="xd21e10023 cellBottom">D</td>
<td class="cellBottom">M</td>
<td class="cellRight cellBottom">E</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">A very casual inspection of the lines shows that they
should be rearranged in order 6, 1, 2, 7, 3, 5, 4, as follows:</p>
<div class="table" id="t57">
<table class="xd21e6833">
<tr>
<td class="xd21e8041 xd21e10021 cellLeft cellTop"></td>
<td class="xd21e8041 cellTop">3</td>
<td class="xd21e8041 cellTop">5</td>
<td class="xd21e8041 cellTop">1</td>
<td class="xd21e8041 cellTop">4</td>
<td class="xd21e8041 cellTop">2</td>
<td class="xd21e8041 cellTop">8</td>
<td class="xd21e8041 cellTop">10</td>
<td class="xd21e8041 cellTop">6</td>
<td class="xd21e8041 cellTop">9</td>
<td class="xd21e8041 cellRight cellTop">7</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">6</td>
<td>P</td>
<td>L</td>
<td>E</td>
<td>A</td>
<td>S</td>
<td>E</td>
<td>C</td>
<td>H</td>
<td>A</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">1</td>
<td>G</td>
<td>E</td>
<td>W</td>
<td>A</td>
<td>V</td>
<td>E</td>
<td>L</td>
<td>E</td>
<td>N</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">2</td>
<td>T</td>
<td>H</td>
<td>T</td>
<td>O</td>
<td>F</td>
<td>I</td>
<td>F</td>
<td>T</td>
<td>E</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">7</td>
<td>N</td>
<td>H</td>
<td>U</td>
<td>N</td>
<td>D</td>
<td>R</td>
<td>E</td>
<td>D</td>
<td>M</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">3</td>
<td>T</td>
<td>E</td>
<td>R</td>
<td>S</td>
<td>B</td>
<td>E</td>
<td>G</td>
<td>I</td>
<td>N</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft">5</td>
<td>I</td>
<td>N</td>
<td>G</td>
<td>T</td>
<td>O</td>
<td>M</td>
<td>O</td>
<td>R</td>
<td>R</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="xd21e10021 cellLeft cellBottom">4</td>
<td class="cellBottom">W</td>
<td class="cellBottom">M</td>
<td class="cellBottom">O</td>
<td class="cellBottom">R</td>
<td class="cellBottom">N</td>
<td class="cellBottom">I</td>
<td class="cellBottom">N</td>
<td class="cellBottom">G</td>
<td class="cellBottom">X</td>
<td class="cellRight cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Although of no particular importance, it may be stated
that the column key in this case was <span class="tt">GRAND</span>
<span class="pagenum">[<a id="pb36" href="#pb36" name=
"pb36">36</a>]</span>and the line key was <span class=
"tt">CENTRAL</span>, both used as in enciphering <a href="#c2a">Case
2-a</a>.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case 3</span>. Route ciphers. In
this case, whole words of the message are transposed according to some
of the methods of Case 1 or 2 or their equivalents. The route cipher is
little used at present. Its development and use during the Civil War
was caused by the inability of the telegraphers of that day to handle
regular cipher matter correctly and rapidly. It was, even in those
days, frankly only a delaying cipher and, to be of any value, had to be
filled with meaningless words to conceal the message proper. An example
from the Signal Book will suffice to show the general character of
route ciphers. To one familiar with monoliteral transposition ciphers,
even the best of route ciphers offers but little difficulty.</p>
<p class="par">&ldquo;To encipher the message &lsquo;<span class=
"tt">MOVE DAYLIGHT. ENEMY APPROACHING FROM NORTH. PRISONERS SAY
STRENGTH ONE HUNDRED THOUSAND. MEET HIM AS PLANNED.</span>&rsquo;
arrange as follows:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">MOVE</td>
<td class="cellTop">STRENGTH</td>
<td class="cellTop">PLANNED</td>
<td class="cellRight cellTop">SAY</td>
</tr>
<tr>
<td class="cellLeft">DAYLIGHT</td>
<td>ONE</td>
<td>AS</td>
<td class="cellRight">PRISONERS</td>
</tr>
<tr>
<td class="cellLeft">ENEMY</td>
<td>HUNDRED</td>
<td>HIM</td>
<td class="cellRight">NORTH</td>
</tr>
<tr>
<td class="cellLeft cellBottom">APPROACHING</td>
<td class="cellBottom">THOUSAND</td>
<td class="cellBottom">MEET</td>
<td class="cellRight cellBottom">FROM</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Here the route is down the first column, up the fourth,
down the second and up the third.&rdquo;</p>
<p class="par">This cipher was often complicated by the introduction of
nulls for every fifth word. Thus the above message might be sent:</p>
<div class="blockquote">
<p class="par first"><span class="tt">MOVE STRENGTH PLANNED SAY
<i>NEVER</i> DAYLIGHT ONE AS PRISONERS <i>LEAVING</i> ENEMY HUNDRED HIM
NORTH <i>UNCHANGED</i> APPROACHING THOUSAND MEET FROM
<i>COME</i>.</span></p>
</div>
<p class="par"></p>
<p class="par">The words in italics are nulls and not a part of
<span class="pagenum">[<a id="pb37" href="#pb37" name=
"pb37">37</a>]</span>the message and the receiver eliminates them
before arranging his message in columns to get the sense of it.</p>
<p class="par">As an additional complication, it was customary for each
correspondent to have a dictionary or code in which the names of all
prominent generals and places and many of the prominent verbs,&mdash;as
to march, to sail, to encamp, to attack, to retreat,&mdash;were
represented by other words.</p>
<p class="par">A route cipher using the code words of the War
Department code might have some advantages over the method of
enciphering code messages as prescribed in that Code.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">General Remarks on Transposition Ciphers</h3>
</div>
<div class="divBody">
<p class="par first">It is the consensus of opinion of experts that the
transposition cipher is not the best one for military purposes. It does
not fulfill the first, second, and third of <span class="corr" id=
"xd21e10500" title="Source: Kirckhoff&rsquo;s">Kerckhoffs&rsquo;</span>
requirements as to indecipherability, safety when apparatus and method
fall into the hands of the enemy, and dependability on a readily
changeable key word.</p>
<p class="par">However, transposition ciphers are often encountered.
They are favorites with those who find the substitution ciphers too
difficult and too tedious to handle and who believe that their
transposition methods are either absolutely indecipherable or
sufficiently so for the purpose of concealing the text of a message for
the time being. They seem to be particularly popular with secret agents
and spies, presumably because special apparatus is rarely necessary in
enciphering and deciphering.</p>
<p class="par">Although the number of transposition methods is legion,
they can practically all be considered under one of the three cases
already discussed. It is surprising how often transposition ciphers
prepared <span class="pagenum">[<a id="pb38" href="#pb38" name=
"pb38">38</a>]</span>by complicated rules, will, on analysis, be seen
to be very simple.</p>
<p class="par">To be successful in solving transposition ciphers, one
should constantly practice reading backward and up and down columns, so
that the common combinations of letters are as quickly identified when
seen thus as when encountered in straight text. Combinations like
<span class="tt">EHT</span>, <span class="tt">LLIW</span>, <span class=
"tt">ROF</span>, <span class="tt">DNA</span>, etc., should be
appreciated immediately as common words written backward.</p>
<p class="par">A study of the table of frequency of digraphs or pairs
is also excellent practice and such a table should be at hand when a
transposition cipher is under consideration. It assists greatly if Case
2 be encountered and is of considerable use in solving Case 1.</p>
<p class="par">The solution of route ciphers is necessarily one of try
and fit, with the knowledge that such ciphers usually are read up and
down columns. It is not believed that route ciphers will often be met
with at the present day. <span class="pagenum">[<a id="pb39" href=
"#pb39" name="pb39">39</a>]</span></p>
</div>
</div>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter VI</h2>
<h2 class="main">Examination of Substitution Ciphers</h2>
</div>
<div class="divBody">
<p class="par xd21e247"><span class="xd21e247init">W</span>hen an
unknown cipher has been put into the substitution class by the methods
already described we may proceed to decide on the variety of
substitution cipher which has been used.</p>
<p class="par">There are a few purely mechanical ways of solving some
of the simple cases of substitution ciphers but as a general rule some
or all of the following determinations must be made:</p>
<p class="par">1. By preparation of a frequency table for the message
we determine whether one or more substitution alphabets have been used
and, if one only has been used, this table leads to the solution.</p>
<p class="par">2. By certain rules we determine how many alphabets have
been used, if there are more than one, and then isolate and analyze
each alphabet by means of a frequency table.</p>
<p class="par">3. If the two preceding steps give no results we have to
deal with a cipher with a running key, a cipher of the Playfair type,
or a cipher where two or more characters are substituted for each
letter of the text. Some special cases under this third head will be
given but, in general, military ciphers of the substitution class will
usually be found to come under the first two heads, on account of the
time and care required in the preparation and deciphering of messages
by the last named methods and the necessity, in many cases, of using
complicated machines for these processes. <span class="pagenum">[<a id=
"pb40" href="#pb40" name="pb40">40</a>]</span></p>
<div id="c4" class="div2 section">
<div class="divBody">
<p id="c4a" class="par first"><span class="sc">Case</span> 4-a.</p>
<p class="par xd21e152"><i>Message</i></p>
<p class="par xd21e152"><span class="tt">OBQFO BPBRP QBAML OBHIF PILFQ
FJBOX OFLNR BIXOZ EL</span></p>
<p class="par">From the recurrence of <span class="tt">B</span>,
<span class="tt">F</span> and <span class="tt">O</span>, we may
conclude that a single substitution alphabet was used for this message.
If so and if the alphabet runs in the same order and direction as the
regular alphabet, the simplest way to discover the meaning of the
message is to take the first two words and write alphabets under each
letter as follows, until some line makes sense:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellRight cellTop">O B Q F O B P B R P</td>
</tr>
<tr>
<td class="cellLeft cellRight">P C R G P C Q C S Q</td>
</tr>
<tr>
<td class="cellLeft cellRight">Q D S H Q D R D T R</td>
</tr>
<tr>
<td class="cellLeft cellRight cellBottom">R E T I R E S E U S</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The word <span class="tt">RETIRESE</span> occurs in the
fourth line, and, if the whole message be handled in this way we find
the rest of the fourth line to read <span class="tt">USTED POR EL MISMO
ITINERARIO QUE MARCHO</span>. The message was enciphered using an
alphabet where <span class="tt">A</span> = <span class="tt">X</span>,
<span class="tt">B</span> = <span class="tt">Y</span>, <span class=
"tt">C</span> = <span class="tt">Z</span>, <span class="tt">D</span> =
<span class="tt">A</span>, etc. noting that as this message is in
Spanish the letters <span class="tt">K</span> and <span class=
"tt">W</span> do not appear in the alphabet. <span class=
"pagenum">[<a id="pb41" href="#pb41" name="pb41">41</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p id="c4b" class="par first">Case 4-b.</p>
<p class="par xd21e152"><i>Message</i></p>
<p class="par xd21e152"><span class="tt">HUJZH UIUPN OZYTS VQXMI SMOMX
MQHUD UMREI SESJU AG</span></p>
<p class="par">This is a message in Spanish. We will handle it as in
<a href="#c4a">case 4-a</a>, setting down the whole message.</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">HUJZHUIU</td>
<td class="cellTop">PNOZY</td>
<td class="cellTop">TSV</td>
<td class="cellTop">QX</td>
<td class="cellTop"><span class="underline">MISMO</span></td>
<td class="cellTop">MXMQHUDUMR</td>
<td class="cellTop">EIS</td>
<td class="cellRight cellTop">ESJUAG</td>
</tr>
<tr>
<td class="cellLeft">IVLAIVJV</td>
<td>QOPAZ</td>
<td>UTX</td>
<td>RY</td>
<td>A=A</td>
<td>NYNRIVEVNS</td>
<td>FJT</td>
<td class="cellRight">FTLVBH</td>
</tr>
<tr>
<td class="cellLeft">JXMBJXLX</td>
<td>RPQBA</td>
<td>VUY</td>
<td>SZ</td>
<td></td>
<td>OZOSJXFXOT</td>
<td>GLU</td>
<td class="cellRight">GUMXCI</td>
</tr>
<tr>
<td class="cellLeft">LYNCLYMY</td>
<td>SQRCB</td>
<td>XVZ</td>
<td>TA</td>
<td></td>
<td>PAPTLYGYPU</td>
<td>HMV</td>
<td class="cellRight">HVNYDJ</td>
</tr>
<tr>
<td class="cellLeft">MZODMZNZ</td>
<td>TRSDC</td>
<td>YXA</td>
<td>UB</td>
<td></td>
<td>QBQUMZHZQV</td>
<td>INX</td>
<td class="cellRight">IXOZEL</td>
</tr>
<tr>
<td class="cellLeft">NAPENAOA</td>
<td><span class="underline">USTED</span></td>
<td>ZYB</td>
<td>VC</td>
<td></td>
<td>RCRVNAIARX</td>
<td>JOY</td>
<td class="cellRight">JYPAFM</td>
</tr>
<tr>
<td class="cellLeft">OBQFOBPB</td>
<td>A=U</td>
<td>AZC</td>
<td>XD</td>
<td></td>
<td>SDSXOBJBSY</td>
<td>LPZ</td>
<td class="cellRight">LZQBGN</td>
</tr>
<tr>
<td class="cellLeft">PCRGPCQC</td>
<td></td>
<td>BAD</td>
<td>YE</td>
<td></td>
<td>TETYPCLCTZ</td>
<td>MQA</td>
<td class="cellRight"><span class="underline">MARCHO</span></td>
</tr>
<tr>
<td class="cellLeft">QDSHQDRD</td>
<td></td>
<td>CBE</td>
<td>ZF</td>
<td></td>
<td>UFUZQDMDUA</td>
<td>NRB</td>
<td class="cellRight">A=S</td>
</tr>
<tr>
<td class="cellLeft"><span class="underline">RETIRESE</span></td>
<td></td>
<td>DCF</td>
<td>AG</td>
<td></td>
<td>VGVARENEVB</td>
<td>OSC</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">A=Q</td>
<td></td>
<td>EDG</td>
<td>BH</td>
<td></td>
<td>XHXBSFOFXC</td>
<td>PTD</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>FEH</td>
<td>CI</td>
<td></td>
<td>YIYCTGPGYD</td>
<td><span class="underline">QUE</span></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>GFI</td>
<td>DJ</td>
<td></td>
<td>ZJZDUHQHZE</td>
<td>A=O</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>HGJ</td>
<td><span class="underline">EL</span></td>
<td></td>
<td>ALAEVIRIAF</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>IHL</td>
<td>A=M</td>
<td></td>
<td>BMBFXJSJBG</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>JIM</td>
<td></td>
<td></td>
<td>CNCGYLTLCH</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>LJN</td>
<td></td>
<td></td>
<td>DODHZMUMDI</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>MLO</td>
<td></td>
<td></td>
<td>EPEIANVNEJ</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>NMP</td>
<td></td>
<td></td>
<td>FQFJBOXOFL</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>ONQ</td>
<td></td>
<td></td>
<td>GRGLCPYPGM</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td><span class="underline">POR</span></td>
<td></td>
<td></td>
<td>HSHMDQZQHN</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td>A=E</td>
<td></td>
<td></td>
<td><span class="underline">ITINERARIO</span></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">A=D</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Here each word of the message comes out on a different
line, and noting in each case the letter corresponding to <span class=
"tt">A</span>, we have the word <span class="tt">QUEMADOS</span> which
is the key. The cipher alphabet changed with each word of the
message.</p>
<p class="par">A variation of this case is where the cipher alphabet
changes according to a key word but the change comes every five letters
or every ten letters of the message instead of every word. The text of
the message can be picked up in this case with a little study.</p>
<p class="par">Note in using case 4 that if we are deciphering a
Spanish message we use the alphabet without <span class="tt">K</span>
or <span class="tt">W</span> as a rule, altho if the letters
<span class="tt">K</span> or <span class="tt">W</span> appear in
<span class="pagenum">[<a id="pb42" href="#pb42" name=
"pb42">42</a>]</span>the cipher it is evidence that the regular English
alphabet is used.</p>
</div>
</div>
<div id="c5" class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 5-a.</p>
<p class="par xd21e152"><i>Message</i></p>
<p class="par"><span class="tt">DNWLW MXYQJ ANRSA RLPTE CABCQ RLNEC
LMIWL XZQTT QIWRY ZWNSM BKNWR YMAPL ASDAN</span></p>
<p class="par">This message contains <span class="tt">K</span> and
<span class="tt">W</span> and therefore we expect the English alphabet
to be used. The frequency of occurrence of <span class="tt">A</span>,
<span class="tt">L</span>, <span class="tt">N</span>, <span class=
"tt">R</span> and <span class="tt">W</span> has lead us to examine it
under case <a href="#c4">4</a> but without result. Let us set down the
first two words and decipher them with a cipher disk set <span class=
"tt">A</span> to <span class="tt">A</span> and then proceed as in case
<a href="#c4">4</a>.</p>
<div class="table">
<table>
<tr>
<td colspan="2" class="cellLeft cellTop">Cipher message</td>
<td class="cellRight cellTop">DNWLWMXYQJ</td>
</tr>
<tr>
<td class="cellLeft">Deciphered <span class="tt">A</span> to</td>
<td>A</td>
<td class="cellRight">XNEPEODCKR</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>B</td>
<td class="cellRight">YOFQFPEDLS</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>C</td>
<td class="cellRight">ZPGRGQFEMT</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>D</td>
<td class="cellRight">AQHSHRGFNU</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">E</td>
<td class="cellRight cellBottom">BRITISHGOV</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The message is thus found to be enciphered with a cipher
disk set <span class="tt">A</span> to <span class="tt">E</span> and the
text is: <span class="tt">BRITISH GOVERNMENT PLACED CONTRACTS WITH
FOLLOWING FIRMS DURING SEPTEMBER</span>.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 5-b.</p>
<p class="par">Same as <a href="#c4b">case 4-b</a> except that the
cipher message must be deciphered by means of a cipher disk set
<span class="tt">A</span> to <span class="tt">A</span> before
proceeding to make up the columns of alphabets. The words of the
deciphered message will be found on separate lines, the lines being
indicated as a rule by a key word which can be determined as in
<a href="#c4b">case 4-b</a>.</p>
<p class="par">The question of alphabetic frequency has already been
discussed in considering the mechanism of language. It is a convenient
thing to put the frequency tables in a graphic form and to use a
similar graphic form in comparing unknown alphabets with the standard
frequency tables. For instance the standard Spanish frequency table put
in graphic <span class="pagenum">[<a id="pb43" href="#pb43" name=
"pb43">43</a>]</span>form is here presented in order to compare with it
the frequency table for the message discussed in <a href="#c4a">case
4-a</a>.</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td colspan="3" class="cellLeft cellTop">Standard Spanish frequency
table</td>
<td colspan="3" class="cellRight cellTop">Table for Message Case
4-a</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>111111111111111111111111111</td>
<td class="xd21e9724">27</td>
<td>A</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>B</td>
<td>1111111</td>
<td class="xd21e9724 cellRight">7</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>111111111</td>
<td class="xd21e9724">9</td>
<td>C</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>1111111111</td>
<td class="xd21e9724">10</td>
<td>D</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>1111111111111111111111111111</td>
<td class="xd21e9724">28</td>
<td>E</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>F</td>
<td>11111</td>
<td class="xd21e9724 cellRight">5</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>111</td>
<td class="xd21e9724">3</td>
<td>G</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>H</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>111111111111</td>
<td class="xd21e9724">12</td>
<td>I</td>
<td>111</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>1</td>
<td class="xd21e9724">1</td>
<td>J</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>1111111111</td>
<td class="xd21e9724">10</td>
<td>L</td>
<td>111</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>111111</td>
<td class="xd21e9724">6</td>
<td>M</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>111111111111</td>
<td class="xd21e9724">12</td>
<td>N</td>
<td>1</td>
<td class="xd21e9724 cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>1111111111111111</td>
<td class="xd21e9724">16</td>
<td>O</td>
<td>111111</td>
<td class="xd21e9724 cellRight">6</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>11111</td>
<td class="xd21e9724">5</td>
<td>P</td>
<td>111</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>Q</td>
<td>111</td>
<td class="xd21e9724 cellRight">3</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>111111111111111</td>
<td class="xd21e9724">15</td>
<td>R</td>
<td>11</td>
<td class="xd21e9724 cellRight">2</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>11111111111111</td>
<td class="xd21e9724">14</td>
<td>S</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>11111111</td>
<td class="xd21e9724">8</td>
<td>T</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>1111111</td>
<td class="xd21e9724">7</td>
<td>U</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>V</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td class="xd21e9724"></td>
<td>X</td>
<td>11</td>
<td class="xd21e9724 cellRight">2</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>11</td>
<td class="xd21e9724">2</td>
<td>Y</td>
<td></td>
<td class="xd21e9724 cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">1</td>
<td class="xd21e9724 cellBottom">1</td>
<td class="cellBottom">Z</td>
<td class="cellBottom">1</td>
<td class="xd21e9724 cellRight cellBottom">1</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Our first assumption might be that <span class=
"tt">B</span> = <span class="tt">A</span> and <span class="tt">F</span>
= <span class="tt">E</span> but it is evident at once that in that
case, <span class="tt">S</span>, <span class="tt">T</span>,
<span class="tt">U</span> and <span class="tt">V</span> (equal to
<span class="tt">R</span>, <span class="tt">S</span>, <span class=
"tt">T</span> and <span class="tt">U</span>) do not occur and a message
even this short without <span class="tt">R</span>, <span class=
"tt">S</span>, <span class="tt">T</span> or <span class="tt">U</span>
is practically impossible. By trying <span class="tt">B</span> =
<span class="tt">E</span> we find that the two tables agree in a
general way very well and this is all that can be expected with such a
short message. The longer the message the nearer would its frequency
table agree with the standard table. Note that if a cipher disk has
been used, the alphabet runs the other way and we must count upward in
working with a graphic table. Note also that if, in a fairly long
message, it is impossible to co&ouml;rdinate the graphic table, reading
either up or down, with the standard table and yet some letters occur
much more frequently than others and some do not occur at all, we have
a mixed alphabet to deal with. The example chosen for <a href=
"#c6a">case 6-a</a> is of this character. An examination of the
frequency table given under that case shows that it bears no graphic
resemblance to <span class="pagenum">[<a id="pb44" href="#pb44" name=
"pb44">44</a>]</span>the standard table. However, as will be seen in
<a href="#c7b">case 7-b</a>, the preparation of graphic tables enables
us to state definitely that the same order of letters is followed in
each of a number of mixed alphabets.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">General Remarks</h3>
</div>
<div class="divBody">
<p class="par first">Any substitution cipher, enciphered by a single
alphabet composed of letters, figures or conventional signs, can be
handled by the methods of case 6. For example, the messages under case
4-a and 5-a are easily solved by these methods. But note that the
messages under case 4-b and 5-b cannot so be solved because several
alphabets are used. We will see later that there are methods of
segregating the different alphabets in some cases where several are
used and then each of the alphabets is to be handled as below.</p>
</div>
</div>
<div id="c6" class="div2 section">
<div class="divBody">
<p id="c6a" class="par first"><span class="sc">Case</span> 6-a.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="blockquote">
<p class="par first xd21e152"><span class="tt">QDBYP BXHYS OXPCP YSHCS
EDRBS ZPTPB BSCSB PSHSZ AJHCD OSEXV HPODA PBPSZ BSVXY XSHCD</span></p>
</div>
<p class="par"></p>
<p class="par">This message was received from a source which makes us
sure it is in Spanish. The occurrence of <span class="tt">B</span>,
<span class="tt">H</span>, <span class="tt">P</span> and <span class=
"tt">S</span> has tempted us to try the first two words as in case 4
and 5 but without result. We now prepare a frequency table, noting at
the same time the <span class="corr" id="xd21e11606" title=
"Source: preceeding">preceding</span> and following letter. This latter
proceeding takes little longer than the preparation of an ordinary
frequency table and gives most valuable information. <span class=
"pagenum">[<a id="pb45" href="#pb45" name="pb45">45</a>]</span></p>
<p class="par"><b>Frequency Table</b></p>
<div class="table">
<table class="xd21e283">
<thead>
<tr class="label">
<td colspan="2" class=
"xd21e11616 cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td colspan="2" class="xd21e10023 cellHeadTop cellHeadBottom">
Prefix</td>
<td colspan="2" class="cellHeadRight cellHeadTop cellHeadBottom">
Suffix</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e11616 cellLeft">A</td>
<td class="xd21e10023">11</td>
<td class="xd21e10023">2</td>
<td class="xd21e287">ZD</td>
<td>JP</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">B</td>
<td class="xd21e10023">11111111</td>
<td class="xd21e10023">8</td>
<td class="xd21e287">DPRPBSPZ</td>
<td>YXSBSPPS</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">C</td>
<td class="xd21e10023">11111</td>
<td class="xd21e10023">5</td>
<td class="xd21e287">PHSHH</td>
<td>PSSDD</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">D</td>
<td class="xd21e10023">11111</td>
<td class="xd21e10023">5</td>
<td class="xd21e287">QECOC</td>
<td>BROA</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">E</td>
<td class="xd21e10023">11</td>
<td class="xd21e10023">2</td>
<td class="xd21e287">SS</td>
<td>DX</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">F</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">G</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">H</td>
<td class="xd21e10023">111111</td>
<td class="xd21e10023">6</td>
<td class="xd21e287">XSSJVS</td>
<td>YCSCPC</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">I</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">J</td>
<td class="xd21e10023">1</td>
<td class="xd21e10023">1</td>
<td class="xd21e287">A</td>
<td>H</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">L</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">M</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">N</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">O</td>
<td class="xd21e10023">111</td>
<td class="xd21e10023">3</td>
<td class="xd21e287">SDP</td>
<td>XSD</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">P</td>
<td class="xd21e10023">111111111</td>
<td class="xd21e10023">9</td>
<td class="xd21e287">YXCZTBHAB</td>
<td>BCYTBSOBS</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">Q</td>
<td class="xd21e10023">1</td>
<td class="xd21e10023">1</td>
<td class="xd21e287"></td>
<td>D</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">R</td>
<td class="xd21e10023">1</td>
<td class="xd21e10023">1</td>
<td class="xd21e287">D</td>
<td>B</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">S</td>
<td class="xd21e10023">111111111111</td>
<td class="xd21e10023">12</td>
<td class="xd21e287">YYCBBCPHOPBX</td>
<td>OHEZCBHZEZVH</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">T</td>
<td class="xd21e10023">1</td>
<td class="xd21e10023">1</td>
<td class="xd21e287">P</td>
<td>P</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">U</td>
<td class="xd21e10023"></td>
<td class="xd21e10023"></td>
<td class="xd21e287"></td>
<td></td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">V</td>
<td class="xd21e10023">11</td>
<td class="xd21e10023">2</td>
<td class="xd21e287">XS</td>
<td>HX</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">X</td>
<td class="xd21e10023">11111</td>
<td class="xd21e10023">5</td>
<td class="xd21e287">BOEVY</td>
<td>HPVYS</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft">Y</td>
<td class="xd21e10023">1111</td>
<td class="xd21e10023">4</td>
<td class="xd21e287">BHPX</td>
<td>PSSX</td>
</tr>
<tr>
<td class="xd21e11616 cellLeft cellBottom">Z</td>
<td class="xd21e10023 cellBottom">111</td>
<td class="xd21e10023 cellBottom">3</td>
<td class="xd21e287 cellBottom">SSS</td>
<td class="cellBottom">PAB</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">It is clear from an examination of this table that we
have to deal with a single alphabet but one in which the letters do not
occur in their regular order.</p>
<p class="par">We may assume that <span class="tt">P</span> and
<span class="tt">S</span> are probably <span class="tt">A</span> and
<span class="tt">E</span>, both on account of the frequency with which
they occur and the variety of their prefixes and suffixes. If this is
so, then <span class="tt">B</span> and <span class="tt">H</span>, are
probably consonants and may represent <span class="tt">R</span> and
<span class="tt">N</span> respectively. <span class="tt">D</span> and
<span class="tt">X</span> are then vowels by the same method of
analysis. Noting that <span class="tt">HC</span> occurs three times and
taking <span class="tt">H</span> as <span class="tt">N</span> we
conclude that <span class="tt">C</span> is probably <span class=
"tt">T</span>. Substitute these values in the last three words of
<span class="pagenum">[<a id="pb46" href="#pb46" name=
"pb46">46</a>]</span>the message because the letters assumed occur
rather frequently there.</p>
<div class="table">
<table class="xd21e11940">
<tr>
<td class="cellLeft cellTop">PBPSZBSV</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellTop">X</td>
<td class="cellTop">SHC</td>
<td class="cellRight cellTop">D</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>I</td>
<td></td>
<td>I</td>
<td></td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">ARAE_RE_</td>
<td></td>
<td>_</td>
<td></td>
<td>ENT</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">O</td>
<td class="cellBottom"></td>
<td class="cellBottom">O</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom">O</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Now <span class="tt">Z</span> is always prefixed by
<span class="tt">S</span> and may be <span class="tt">L</span>. Taking
<span class="tt">X=I</span> and <span class="tt">D=O</span>, (they are
certainly vowels), <span class="tt">V=G</span> and <span class=
"tt">Y=M</span>, we have</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellRight cellTop cellBottom">ARA EL
REGIMIENTO</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Substituting these values in the rest of the message we
have</p>
<div class="table">
<table class="xd21e11940">
<tr>
<td class="cellLeft cellTop">Q</td>
<td class="cellTop">DBYPBXH</td>
<td class="cellTop">YSOXPCP</td>
<td class="cellTop">YSHCSED</td>
<td class="cellRight cellTop">RBSZPTPB</td>
</tr>
<tr>
<td class="cellLeft">_</td>
<td>ORMARIN</td>
<td>ME_IATA</td>
<td>MENTE_O</td>
<td class="cellRight">_RELA_AR</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>BSCSB</td>
<td>PSHSZ</td>
<td>AJHCD</td>
<td class="cellRight">OSEXVHPODA</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">RETER</td>
<td class="cellBottom">AENEL</td>
<td class="cellBottom">__NTO</td>
<td class="cellRight cellBottom">_E_IGNA_O_</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">We may now take <span class="tt">Q=F</span>,
<span class="tt">O=D</span>, <span class="tt">E=S</span>, <span class=
"tt">R=B</span>, <span class="tt">T=C</span>, <span class=
"tt">A=P</span> and <span class="tt">J=U</span> and the message is
complete. We are assisted in our last assumption by noting that
<span class="tt">S=E</span> and <span class="tt">E=S</span>, etc., and
we may on that basis reconstruct the entire alphabet. The letters in
parenthesis do not occur in the message but may be safely assumed to be
correct.</p>
<div class="table">
<table class="xd21e12110">
<tr>
<td class="cellLeft cellTop">Ordinary</td>
<td class="cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">J</td>
<td class="cellTop">L</td>
<td class="cellTop">M</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">T</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Cipher</td>
<td class="cellBottom">P</td>
<td class="cellBottom">R</td>
<td class="cellBottom">T</td>
<td class="cellBottom">O</td>
<td class="cellBottom">S</td>
<td class="cellBottom">(Q)</td>
<td class="cellBottom">(V)</td>
<td class="cellBottom">N</td>
<td class="cellBottom">(X)</td>
<td class="cellBottom">(U)</td>
<td class="cellBottom">(Z)</td>
<td class="cellBottom">(Y)</td>
<td class="cellBottom">(H)</td>
<td class="cellBottom">D</td>
<td class="cellBottom">A</td>
<td class="cellBottom">F</td>
<td class="cellBottom">B</td>
<td class="cellBottom">E</td>
<td class="cellBottom">C</td>
<td class="cellBottom">J</td>
<td class="cellBottom">G</td>
<td class="cellBottom">I</td>
<td class="cellBottom">M</td>
<td class="cellRight cellBottom">L</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It is always well to attempt the reconstruction of the
entire alphabet for use in case any more cipher messages written in it
are received.&mdash;&mdash; <span class="pagenum">[<a id="pb47" href=
"#pb47" name="pb47">47</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 6-b.</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="blockquote">
<p class="par first">Lt. J. B. Smith, Royal Flying Corps, Calais,
France.</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">DACFT</td>
<td class="cellTop">RRBHA</td>
<td class="cellTop">MOOUE</td>
<td class="cellTop">AENOI</td>
<td class="cellRight cellTop">ZTIET</td>
</tr>
<tr>
<td class="cellLeft">ASMOS</td>
<td>EOHIE</td>
<td>YOCKF</td>
<td>NOHOE</td>
<td class="cellRight">NOUTH</td>
</tr>
<tr>
<td class="cellLeft">OMEAH</td>
<td>NILGO</td>
<td>OSAHU</td>
<td>OHOUE</td>
<td class="cellRight">APCHS</td>
</tr>
<tr>
<td class="cellLeft">TLNDA</td>
<td>CFTEN</td>
<td>INTWN</td>
<td>BAFOH</td>
<td class="cellRight">GROHT</td>
</tr>
<tr>
<td class="cellLeft">AEIOH</td>
<td>ABRIS</td>
<td>ODACF</td>
<td>TRREN</td>
<td class="cellRight">OSTSM</td>
</tr>
<tr>
<td class="cellLeft">AYBIS</td>
<td>DFTEN</td>
<td>EFAPH</td>
<td>OSMNI</td>
<td class="cellRight">ZTIEA</td>
</tr>
<tr>
<td class="cellLeft">HLILL</td>
<td>TWSOU</td>
<td>GDENO</td>
<td>UTHOM</td>
<td class="cellRight">EAHBH</td>
</tr>
<tr>
<td class="cellLeft">AMOOU</td>
<td>EAYOE</td>
<td>QISUU</td>
<td>OLEHA</td>
<td class="cellRight">DENOE</td>
</tr>
<tr>
<td class="cellLeft">NHOOQ</td>
<td>OBBOR</td>
<td>TSLHO</td>
<td>BAHEO</td>
<td class="cellRight">UBHOB</td>
</tr>
<tr>
<td class="cellLeft cellBottom">IHTSW</td>
<td class="cellBottom">ENOHO</td>
<td class="cellBottom">PAHIH</td>
<td class="cellBottom">ITUAS</td>
<td class="cellRight cellBottom">BIHTL</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par xd21e12345">Graham-White.</p>
</div>
<p class="par"></p>
<p class="par">The address and signature indicate that this message is
in English.</p>
<p class="par">There are 250 letters in the cipher; the vowels
<span class="tt">AEIOU</span> occur 109 times or 43.6%, the letters
<span class="tt">LNRST</span> occur 62 times or 24.8%, and the letters
<span class="tt">KQVXZ</span> occur 5 times or 2%. The proportion in
the case of the vowels is somewhat too large and, in the case of the
letters <span class="tt">LRNST</span>, it is too small. It is then
questionable whether this is a transposition cipher altho, at first
glance it might appear to be one.</p>
<p class="par">On examination for parts of possible words we are at
once struck by the occurrence at irregular intervals of recurring
groups, viz:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e10023 cellLeft cellTop">DACFTRR</td>
<td class="xd21e10023 cellTop">ENO</td>
<td class="cellRight cellTop">BHAMOOUEA</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft">DACFTEN</td>
<td class="xd21e10023">ENOUTHOMEAH</td>
<td class="cellRight">BHAMOOUEA</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft"></td>
<td class="xd21e10023">ENO</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e10023 cellLeft">DACFTRR</td>
<td class="xd21e10023">DENOUTHOMEAH</td>
<td class="cellRight">IZTIE</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft">FTEN</td>
<td class="xd21e10023">DENO</td>
<td class="cellRight">IZTIE</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft cellBottom"></td>
<td class="xd21e10023 cellBottom">ENO</td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is a strong indication that the cipher is a
substitution cipher, so, to make an examination a frequency table will
be constructed.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Frequency Table</h3>
</div>
<div class="divBody">
<p class="par first"></p>
<div class="table">
<table class="xd21e12110">
<tr>
<td class="cellLeft cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">J</td>
<td class="cellTop">K</td>
<td class="cellTop">L</td>
<td class="cellTop">M</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">T</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">W</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft cellBottom">23</td>
<td class="cellBottom">11</td>
<td class="cellBottom">7</td>
<td class="cellBottom">6</td>
<td class="cellBottom">24</td>
<td class="cellBottom">7</td>
<td class="cellBottom">3</td>
<td class="cellBottom">26</td>
<td class="cellBottom">16</td>
<td class="cellBottom">0</td>
<td class="cellBottom">1</td>
<td class="cellBottom">8</td>
<td class="cellBottom">8</td>
<td class="cellBottom">15</td>
<td class="cellBottom">36</td>
<td class="cellBottom">3</td>
<td class="cellBottom">2</td>
<td class="cellBottom">8</td>
<td class="cellBottom">14</td>
<td class="cellBottom">17</td>
<td class="cellBottom">11</td>
<td class="cellBottom">1</td>
<td class="cellBottom">3</td>
<td class="cellBottom">0</td>
<td class="cellBottom">3</td>
<td class="cellRight cellBottom">2</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb48" href="#pb48" name=
"pb48">48</a>]</span></p>
<p class="par">Superficially, this looks like a normal frequency table,
but <span class="tt">O</span> is the dominant letter, followed by
<span class="tt">H</span>, <span class="tt">E</span>, <span class=
"tt">A</span>, <span class="tt">T</span>, <span class="tt">I</span>,
<span class="tt">N</span>, <span class="tt">S</span>, in the order
named. It is certainly Case 6 if it is a substitution cipher at
all.</p>
<p class="par">Let us see what can be done by assuming <span class=
"tt">O=E</span>; the triplet <span class="tt">ENO</span>, occurring six
times might well be <span class="tt">THE</span> and <span class=
"tt">E=T</span> and <span class="tt">N=H</span>. A glance at the
frequency table shows this to be reasonable. Now substitute these
letters in some likely groups. <span class="tt">FNOHOENO</span> becomes
<span class="tt">_HE_ETHE</span>; <span class="tt">FTEN</span> becomes
<span class="tt">_TH</span>; <span class="tt">ENOENHO</span> becomes
<span class="tt">THETH_E</span>; <span class="tt">ENOHO</span> becomes
<span class="tt">THE_E</span>. A bit of study will show that
<span class="tt">F=W</span>, <span class="tt">T=I</span> and
<span class="tt">H=R</span> and the frequency table bears this out
except that <span class="tt">H(=R)</span> seems to occur too
frequently. The recurring groups containing <span class="tt">DAC</span>
(see above) occur in such a way that we may be sure <span class=
"tt">DAC</span> is one word, <span class="tt">FTRR</span> is another
and <span class="tt">FTEN(=WITH)</span> is a third. Now <span class=
"tt">FTRR</span> becomes <span class="tt">WI__</span>, which can only
be completed by a double letter. <span class="tt">LL</span> fills the
bill and we may say <span class="tt">R=L</span>. As <span class=
"tt">DAC</span> starts the message and is followed by <span class=
"tt">FTRR (=WILL)</span> it is reasonable to try <span class=
"tt">DAC=YOU</span>. Looking up <span class="tt">DAC</span> in the
frequency table it is evident that we strain nothing by this
assumption. We now have:</p>
<div class="table">
<table class="xd21e7794">
<tr>
<td class="cellLeft cellTop">Letters of cipher</td>
<td class="xd21e7910 cellRight cellTop">ONTAHECFD</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Letters of message</td>
<td class="xd21e7910 cellRight cellBottom">EHIORTUWY</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Now take the group <span class="tt">ENOUTHOMEAH</span>
which occurs twice. This becomes <span class="tt">THE_IRE_TOR</span>
and if we substitute <span class="tt">U=D</span> and <span class=
"tt">M=C</span> we have <span class="tt">THE DIRECTOR</span>. Next the
group <span class="tt">(FTRR)BHAMOOUEA</span> becomes <span class=
"tt">(WILL) _ROCEEDTO</span> and the context gives word with missing
letter as <span class="tt">PROCEED</span>, from which <span class=
"tt">B=P</span>. Next the group <span class="tt">(ENO)
IZTIETASMOSEOHIEYOCK(FNOHO)</span> becomes <span class=
"tt">(THE)__I_TIO_CE_TER_T_EU_(WHERE)</span> and the group <span class=
"tt">(FTEN)EFAPHOSMNIZTIEAHL</span> becomes <span class=
"tt">(WITH)TWO_RE_CH__I_TOR_</span>. <span class="pagenum">[<a id=
"pb49" href="#pb49" name="pb49">49</a>]</span>The substitution of
<span class="tt">A</span> for <span class="tt">I</span>, <span class=
"tt">V</span> for <span class="tt">Z</span>, <span class="tt">N</span>
for <span class="tt">S</span> and <span class="tt">F</span> for
<span class="tt">P</span> makes the latter group read <span class=
"tt">(WITH TWO FRENCH AVIATORS</span> and the former read <span class=
"tt">(THE)AVIATION CENTER AT _EU_(WHERE)</span>.</p>
<p class="par">Now the word <span class="tt">YOCK = (_EU_)</span> is
the name of a place, evidently. <span class="corr" id="xd21e12747"
title="Source: WE">We</span> find another group containing <span class=
"tt">Y</span>, viz: <span class="tt">ENOSTSMAYBISD</span> which becomes
<span class="tt">THENINCO_PANY</span> so that evidently we should
substitute <span class="tt">M</span> for <span class="tt">Y</span>. The
other occurrence of <span class="tt">Y (=M)</span> is in the group
<span class="tt">EAYOEQISU</span> which becomes <span class=
"tt">TOMET_AND</span>. A reasonable knowledge of geography gives us the
words <span class="tt">MEUX</span> and <span class="tt">METZ</span> so
that <span class="tt">X</span> should be substituted for <span class=
"tt">K</span> and <span class="tt">Z</span> for <span class=
"tt">Q</span>.</p>
<p class="par">We now have sufficient letters for a complete
deciphering of the message.</p>
<div class="table">
<table class="xd21e7794">
<tr>
<td class="cellLeft cellTop">Letters of cipher</td>
<td class="xd21e7910 cellRight cellTop">ABCDEFGHIKLMNOPQRSTUVWYZ</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Letters of message</td>
<td class="xd21e7910 cellRight cellBottom">
OPUYTW_RAXSCHEFZLNID__MV</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The message deciphers:</p>
<div class="blockquote">
<p class="par first"><span class="tt">YOU WILL PROCEED TO THE AVIATION
CENTER AT MEUX WHERE THE DIRECTOR HAS _EEN ORDERED TO FURNISH YOU WITH
A HI_H POWER _LERIOT AEROPLANE. YOU WILL THEN IN COMPANY WITH TWO
FRENCH AVIATORS ASSI_NED _Y THE DIRECTOR PROCEED TO METZ AND DESTROY
THE THREE ZEPPELINS REPORTED PREPARIN_ THERE FOR A RAID ON
PARIS.</span></p>
</div>
<p class="par"></p>
<p class="par">The substitution of <span class="tt">B</span> for
<span class="tt">G</span>, <span class="tt">G</span> for <span class=
"tt">W</span> and <span class="tt">K</span> for <span class=
"tt">V</span> completes the cipher. This cipher is difficult only
because the cipher alphabet is made up, not haphazard, but
scientifically with proper consideration for the natural frequency of
occurrence of the letters. In cipher work it is dangerous to neglect
proper analysis and jump at conclusions.</p>
<p class="par">In the study of Mexican substitution ciphers, several
alphabets have been found which are made up in a general way, like the
one discussed in this case.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<p><span class="pagenum">[<a id="pb50" href="#pb50" name=
"pb50">50</a>]</span></p>
</div>
<div class="divBody">
<p class="par"><span class="sc">Case</span> 6-c.&mdash;It is a
convenience in dealing with ciphers made up of numbers or conventional
signs to substitute arbitrary letters for the numbers and signs.
Suppose we have the message:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="xd21e10023 cellLeft cellTop">&rdquo;??2&amp;</td>
<td class="xd21e10023 cellTop">45x15</td>
<td class="xd21e10023 cellTop">)&ldquo;8&amp;#</td>
<td class="xd21e10023 cellTop">&amp;&amp;1x4</td>
<td class="cellRight cellTop">%&amp;4&amp;%</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft cellBottom">6x?&amp;&rdquo;</td>
<td class="xd21e10023 cellBottom">8&amp;*x4</td>
<td class="xd21e10023 cellBottom">6&deg;*&deg;&amp;</td>
<td class="xd21e10023 cellBottom">%&ldquo;4&amp;&rdquo;</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">By arbitrary substitution of letters this is made</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">ABBCD</td>
<td class="cellTop">EFGHF</td>
<td class="cellTop">IJKDL</td>
<td class="cellTop">DDHGE</td>
<td class="cellRight cellTop">MDEDM</td>
</tr>
<tr>
<td class="cellLeft cellBottom">NGBDA</td>
<td class="cellBottom">KDOGE</td>
<td class="cellBottom">NPOPD</td>
<td class="cellBottom">MAEDA</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This message is now in convenient shape to handle as
Case 6-a and on solution is found to read:</p>
<div class="blockquote">
<p class="par first"><span class="tt">ALL PERSONS HAVE BEEN ORDERED TO
LEAVE FORTIFIED AREA.</span></p>
</div>
<p class="par"></p>
<p class="par">In the same way the message</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">1723</td>
<td class="cellTop">3223</td>
<td class="cellTop">2825</td>
<td class="cellTop">1828</td>
<td class="cellTop">3630</td>
<td class="cellTop">2336</td>
<td class="cellTop">1423</td>
<td class="cellTop">2827</td>
<td class="cellTop">2324</td>
<td class="cellTop">3120</td>
<td class="cellTop">2317</td>
<td class="cellRight cellTop">3123</td>
</tr>
<tr>
<td class="cellLeft">3036</td>
<td>2120</td>
<td>2415</td>
<td>3029</td>
<td>1512</td>
<td>2831</td>
<td>1721</td>
<td>2715</td>
<td>2811</td>
<td>2715</td>
<td>1923</td>
<td class="cellRight">3030</td>
</tr>
<tr>
<td class="cellLeft cellBottom">1215</td>
<td class="cellBottom">1130</td>
<td class="cellBottom">2128</td>
<td class="cellBottom">3623</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">is found to be made up entirely of numbers between 11
and 36 with the numbers 23, 28 and 30 occurring most frequently. This
immediately suggests an alphabet made up of the numbers from 11 to 36
inclusive and each cipher group of figures represents two letters. By
arbitrary substitution of letters for groups of two numbers we
obtain:</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">AB</td>
<td class="cellTop">CB</td>
<td class="cellTop">DE</td>
<td class="cellTop">FD</td>
<td class="cellTop">GH</td>
<td class="cellTop">BG</td>
<td class="cellTop">IB</td>
<td class="cellTop">DJ</td>
<td class="cellTop">BK</td>
<td class="cellTop">LM</td>
<td class="cellTop">BA</td>
<td class="cellRight cellTop">LB</td>
</tr>
<tr>
<td class="cellLeft">HG</td>
<td>NM</td>
<td>OP</td>
<td>HQ</td>
<td>PR</td>
<td>DL</td>
<td>AN</td>
<td>JP</td>
<td>DS</td>
<td>JP</td>
<td>TB</td>
<td class="cellRight">HH</td>
</tr>
<tr>
<td class="cellLeft cellBottom">RP</td>
<td class="cellBottom">SH</td>
<td class="cellBottom">ND</td>
<td class="cellBottom">GB</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and this message is also in shape to handle as Case 6-a.
It reads, on solution,</p>
<div class="blockquote">
<p class="par first"><span class="tt">SEVEN HUNDRED MEN LEFT YESTERDAY
FOR POINTS ON LOWER RIO GRANDE.</span></p>
</div>
<p class="par"><span class="pagenum">[<a id="pb51" href="#pb51" name=
"pb51">51</a>]</span></p>
</div>
</div>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="main">Chapter VII</h2>
</div>
<div class="divBody">
<p class="par xd21e247"><span class="xd21e247init">W</span>e will now
consider the class of substitution ciphers where a number of alphabets
are used, the number and choice of alphabets depending on a key word or
equivalent and being used periodically throughout the message.</p>
<p class="par">In this class belong the methods of Vigenere, Porta,
Beaufort, St. Cyr, and many others. These methods date back several
hundred years, but variations of them are constantly appearing as new
ciphers. The Larrabee cipher, used for communication between government
departments, is the Vigenere cipher of the 17th Century. The cipher
disk method is practically the Vigenere cipher with reversed
alphabets.</p>
<p class="par">In using these ciphers, there is provided a number of
different cipher alphabets, usually twenty-six, and each cipher
alphabet is identified by a different letter or number. A key word or
phrase (or key number) is agreed upon by the correspondents. The
message to be enciphered is written in lines containing a number of
letters which is a multiple of the number of letters of the key. The
key is written as the first line. Then each column under a letter of
the key is enciphered by the cipher alphabet pertaining to that letter
of the key. For example, let us take the message, &ldquo;All radio
messages must hereafter be put in cipher,&rdquo; with the key
<span class="sc">Grant</span>, using the Vigenere cipher alphabets
given below. Each of these alphabets is <span class="corr" id=
"xd21e13053" title="Source: identfied">identified</span> by the first
or left hand letter which represents <span class="tt">A</span> of the
text. We thus will <span class="pagenum">[<a id="pb52" href="#pb52"
name="pb52">52</a>]</span>use in turn the alphabets beginning with
<span class="tt">G</span>, with <span class="tt">R</span>, with
<span class="tt">A</span>, with <span class="tt">N</span>, and with
<span class="tt">T</span>.</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">G</td>
<td class="cellTop">R</td>
<td class="cellTop">A</td>
<td class="cellTop">N</td>
<td class="cellTop">T</td>
<td class="cellTop">G</td>
<td class="cellTop">R</td>
<td class="cellTop">A</td>
<td class="cellTop">N</td>
<td class="cellRight cellTop">T</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>L</td>
<td>L</td>
<td>R</td>
<td>A</td>
<td>D</td>
<td>I</td>
<td>O</td>
<td>M</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>S</td>
<td>A</td>
<td>G</td>
<td>E</td>
<td>S</td>
<td>M</td>
<td>U</td>
<td>S</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>E</td>
<td>R</td>
<td>E</td>
<td>A</td>
<td>F</td>
<td>T</td>
<td>E</td>
<td>R</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>P</td>
<td>U</td>
<td>T</td>
<td>I</td>
<td>N</td>
<td>C</td>
<td>I</td>
<td>P</td>
<td class="cellRight">H</td>
</tr>
<tr>
<td class="cellLeft cellBottom">E</td>
<td class="cellBottom">R</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Using the alphabet indicated by <span class=
"tt">G</span>, we get</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">G</td>
<td class="cellRight cellTop">J</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td class="cellRight">Y</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft cellBottom">K</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Continuing for the other alphabets, we get</p>
<div class="table">
<table class="xd21e6833">
<tr>
<td class="cellLeft cellTop">G</td>
<td class="cellTop">C</td>
<td class="cellTop">L</td>
<td class="cellTop">E</td>
<td class="cellTop">T</td>
<td class="cellTop">J</td>
<td class="cellTop">Z</td>
<td class="cellTop">O</td>
<td class="cellTop">Z</td>
<td class="cellRight cellTop">X</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>J</td>
<td>A</td>
<td>T</td>
<td>X</td>
<td>Y</td>
<td>D</td>
<td>U</td>
<td>F</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>V</td>
<td>R</td>
<td>R</td>
<td>T</td>
<td>L</td>
<td>K</td>
<td>E</td>
<td>E</td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td>G</td>
<td>U</td>
<td>G</td>
<td>B</td>
<td>T</td>
<td>T</td>
<td>I</td>
<td>C</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="cellLeft cellBottom">K</td>
<td class="cellBottom">I</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This method of arranging the message into lines and
columns and then enciphering whole columns with each cipher alphabet is
much shorter than the method of handling each letter of the message
separately. The chance of error is also greatly reduced.</p>
<p class="par">All these cipher methods can be operated by means of
squares containing the various alphabets, cipher disks or arrangements
of fixed and sliding alphabets. For example, this was the original
cipher of Vigenere: <span class="pagenum">[<a id="pb53" href="#pb53"
name="pb53">53</a>]</span></p>
<div class="table">
<table class="xd21e7347">
<tr>
<td class="cellLeft cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">J</td>
<td class="cellTop">K</td>
<td class="cellTop">L</td>
<td class="cellTop">M</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">T</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">W</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td class="cellRight">A</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td class="cellRight">D</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td class="cellRight">F</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td class="cellRight">G</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td class="cellRight">H</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td class="cellRight">J</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td class="cellRight">K</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td class="cellRight">P</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td class="cellRight">Q</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td>X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td class="cellRight">V</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td class="cellRight">W</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>Z</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td>J</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td>U</td>
<td>V</td>
<td>W</td>
<td class="cellRight">X</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">A</td>
<td class="cellBottom">B</td>
<td class="cellBottom">C</td>
<td class="cellBottom">D</td>
<td class="cellBottom">E</td>
<td class="cellBottom">F</td>
<td class="cellBottom">G</td>
<td class="cellBottom">H</td>
<td class="cellBottom">I</td>
<td class="cellBottom">J</td>
<td class="cellBottom">K</td>
<td class="cellBottom">L</td>
<td class="cellBottom">M</td>
<td class="cellBottom">N</td>
<td class="cellBottom">O</td>
<td class="cellBottom">P</td>
<td class="cellBottom">Q</td>
<td class="cellBottom">R</td>
<td class="cellBottom">S</td>
<td class="cellBottom">T</td>
<td class="cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">X</td>
<td class="cellRight cellBottom">Y</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The first horizontal alphabet is the alphabet of the
plain text. Each substitution alphabet is designated by the letter at
the left of a horizontal line. For example, if the key word is
<span class="tt">BAD</span>, the second, first and fourth alphabets are
used in turn and the word <span class="tt">WILL</span> is enciphered
<span class="tt">XIOM</span>.</p>
<p class="par">The Larrabee cipher is merely a slightly different
arrangement of the Vigenere cipher and is printed on a card in this
form: <span class="pagenum">[<a id="pb54" href="#pb54" name=
"pb54">54</a>]</span></p>
<div class="table">
<table class="xd21e14817">
<tr>
<td rowspan="2" class="xd21e6545 xd21e14818 cellLeft cellTop">
<span class="xd21e14820">A</span></td>
<td class="xd21e14818 cellRight cellTop"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="cellRight"><span class=
"tt">abcdefghijklmnopqrstuvwxyz</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e6545 xd21e14818 cellLeft"><span class=
"xd21e14820">B</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="cellRight"><span class=
"tt">bcdefghijklmnopqrstuvwxyza</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">C</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">cdefghijklmnopqrstuvwxyzab</span></td>
</tr>
<tr>
<td colspan="2" class="xd21e14858 cellLeft cellRight">etc.</td>
</tr>
<tr>
<td rowspan="2" class="xd21e6545 xd21e14818 cellLeft"><span class=
"xd21e14820">Y</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="cellRight">yzabcdefghijklmnopqrstuvwx</td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft cellBottom">
<span class="xd21e14820">Z</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight cellBottom"><span class=
"tt">zabcdefghijklmnopqrstuvwxy</span></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The large letters at the left are the letters of the key
word. It will be noted that these letters correspond to the first
letters of the cipher alphabets (in small letters) as in the Vigenere
cipher.</p>
<p class="par">A much simpler arrangement of the Vigenere cipher is the
use of a fixed and sliding alphabet. Either the fixed or sliding
alphabet must be double in order to get coincidence for every letter
when <span class="tt">A</span> is set to the letter of the key
word.</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td colspan="3" class="xd21e14894 cellLeft cellRight cellTop"><b>Fixed
Alphabet of Text</b></td>
</tr>
<tr>
<td colspan="3" class="xd21e14898 cellLeft cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14902 cellLeft"></td>
<td class="xd21e14904"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
<td class="xd21e14902 cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="xd21e14912 cellBottom"><b>Movable Alphabet of
Cipher</b></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">As shown here, <span class="tt">A</span> of the fixed or
text alphabet coincides with <span class="tt">T</span> of the movable
cipher alphabet. This is the setting where <span class="tt">T</span> is
the letter of the key word in use. The lower movable alphabet is moved
for each letter of the message and the <span class="tt">A</span> of the
fixed alphabet is made to coincide in turn with each letter of the key
before the corresponding letter of the text is enciphered. It is
obviously only a step from this arrangement to that of a cipher disk,
where the <span class="pagenum">[<a id="pb55" href="#pb55" name=
"pb55">55</a>]</span>fixed alphabet, (a single one will now serve) is
printed in a circle and the movable alphabet, also in a circle, is on a
separate rotatable disk. Coincidence of any letter on the disk with
<span class="tt">A</span> of the fixed alphabet is obtained by rotating
the disk.</p>
<p class="par">The well known U. S. Army Cipher Disk has just such an
arrangement of the fixed alphabet but the alphabet of the disk is
reversed. This has several advantages in simplicity of operation but
none in increasing the indecipherability of the cipher prepared with
it. The arrangement of fixed and sliding alphabets which is equivalent
to the U. S. Army cipher disk is this:</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td colspan="3" class="xd21e14894 cellLeft cellRight cellTop"><b>Fixed
Alphabet</b></td>
</tr>
<tr>
<td colspan="3" class="xd21e14898 cellLeft cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14902 cellLeft"></td>
<td class="xd21e14904"><span class=
"tt">ZYXWVUTSRQPONMLKJIHGFEDCBA</span></td>
<td class="xd21e14902 cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="xd21e14912 cellBottom"><b>Movable Alphabet</b></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It will be noticed that with this arrangement of running
the alphabets in opposite directions, it becomes immaterial which
alphabet is used for the text and which for the cipher for if
<span class="tt">A</span> = <span class="tt">G</span> then <span class=
"tt">G</span> = <span class="tt">A</span>. This is not true of the
Vigenere cipher.</p>
<p class="par">It is perfectly feasible to substitute a card for the U.
S. Army cipher disk. It would have this form:</p>
<div class="table">
<table class="xd21e7794">
<tr>
<td class="cellLeft cellTop"></td>
<td class="xd21e7910 cellRight cellTop">ABCDEFGHIJKLMNOPQRSTUVWXYZ</td>
</tr>
<tr>
<td class="cellLeft">1</td>
<td class="xd21e7910 cellRight">AZYXWVUTSRQPONMLKJIHGFEDCB</td>
</tr>
<tr>
<td class="cellLeft">2</td>
<td class="xd21e7910 cellRight">BAZYXWVUTSRQPONMLKJIHGFEDC</td>
</tr>
<tr>
<td class="cellLeft">3</td>
<td class="xd21e7910 cellRight">CBAZYXWVUTSRQPONMLKJIHGFED</td>
</tr>
<tr>
<td colspan="2" class="xd21e14858 cellLeft cellRight">etc.</td>
</tr>
<tr>
<td class="cellLeft">25</td>
<td class="xd21e7910 cellRight">YXWVUTSRQPONMLKJIHGFEDCBAZ</td>
</tr>
<tr>
<td class="cellLeft cellBottom">26</td>
<td class="xd21e7910 cellRight cellBottom">
ZYXWVUTSRQPONMLKJIHGFEDCBA</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The first horizontal line is the alphabet of the text.
The other twenty-six lines are the cipher alphabets each corresponding
to the letter of the key word which is at the left of the line.
<span class="pagenum">[<a id="pb56" href="#pb56" name=
"pb56">56</a>]</span></p>
<p class="par">One of the ciphers of Porta was prepared with a card of
this kind:</p>
<div class="table">
<table class="xd21e14817">
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft cellTop">
<span class="xd21e14820">AB</span></td>
<td class="xd21e14818 cellRight cellTop"><span class=
"tt">ABCDEFGHIJKLM</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">NOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">CD</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLM</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">ZNOPQRSTUVWXY</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">EF</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLM</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">YZABCDEFGHIJK</span></td>
</tr>
<tr>
<td colspan="2" class="xd21e14858 cellLeft cellRight">etc.</td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">WX</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLM</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">PQRSTUVWXYZNO</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft cellBottom">
<span class="xd21e14820">YZ</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLM</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight cellBottom"><span class=
"tt">OPQRSTUVWXYZN</span></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">In this cipher the large letters at the left correspond
to the letters of the key and, in each alphabet, the lower letter is
substituted for the upper and vice versa. For example, with key
<span class="tt">BAD</span> to encipher <span class="tt">WILL</span> we
would get <span class="tt">JVXY</span>. Note that with either
<span class="tt">B</span> or <span class="tt">A</span> as the key
letter, the first alphabet would be used.</p>
<p class="par">A combination of the Vigenere and Porta ciphers is
this:</p>
<div class="table">
<table class="xd21e14817">
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft cellTop">
<span class="xd21e14820">A</span></td>
<td class="xd21e14818 cellRight cellTop"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">BC</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">BCDEFGHIJKLMNOPQRSTUVWXYZA</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">DE</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">CDEFGHIJKLMNOPQRSTUVWXYZAB</span></td>
</tr>
<tr>
<td colspan="2" class="xd21e14858 cellLeft cellRight">etc.</td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">VW</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">LMNOPQRSTUVWXYZABCDEFGHIJK</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft"><span class=
"xd21e14820">XY</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight"><span class=
"tt">MNOPQRSTUVWXYZABCDEFGHIJKL</span></td>
</tr>
<tr>
<td rowspan="2" class="xd21e14845 xd21e14818 cellLeft cellBottom">
<span class="xd21e14820">Z</span></td>
<td class="xd21e14818 cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14852 cellRight cellBottom"><span class=
"tt">NOPQRSTUVWXYZABCDEFGHIJKLM</span></td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb57" href="#pb57" name=
"pb57">57</a>]</span></p>
<p class="par">Here again the large letters at the left correspond to
the letters of the key and, in each pair of alphabets, the upper one is
that of the plain text and the lower is that of the cipher.</p>
<p class="par">This cipher can also be operated by a fixed and sliding
alphabet.</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td colspan="3" class="xd21e14894 cellLeft cellRight cellTop"><b>Fixed
Alphabet</b></td>
</tr>
<tr>
<td colspan="3" class="xd21e14898 cellLeft cellRight"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
</tr>
<tr>
<td class="xd21e14902 cellLeft"></td>
<td class="xd21e14904"><span class=
"tt">ABCDEFGHIJKLMNOPQRSTUVWXYZ</span></td>
<td class="xd21e14902 cellRight"></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td class="xd21e15216"><b>Sliding Alphabet of Cipher</b></td>
</tr>
<tr>
<td class="cellLeft"></td>
<td class="xd21e14912">
\/&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>Index</b></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="xd21e15229 cellBottom">
<div class="table">
<table class="xd21e14892">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop"><span class="tt">BDFHJLNPRTVX</span></td>
<td class="cellRight cellTop"></td>
</tr>
<tr>
<td class="cellLeft"><span class="tt">A</span></td>
<td></td>
<td><span class="tt">Z</span></td>
<td class="xd21e15250 cellRight"><b>Letters of Key.</b></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom"><span class="tt">CEGIKMOQSUWY</span></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The other ciphers mentioned are merely variations of
these that have been discussed. It is immaterial, in the following
analysis, which variety has been used. The analysis is really based on
what can be done with a cipher made up with a mixed cipher alphabet
which may be moved with reference to the fixed alphabet of the text,
(See Case 7-b). Clearly this is a much more difficult proposition than
dealing with a cipher in which the cipher alphabets run in their
regular sequence, either backward or forward. In fact, in the analysis
of Case 7, we may consider any cipher prepared by the method of
Vigenere or any of its variations as a special and simple case.</p>
<p class="par">It was long ago discovered that, in any cipher of this
class, (1) two like groups of letters in the cipher are most probably
the result of two like groups of letters of the text enciphered by the
same alphabets and (2) the number of letters in one group plus the
number of letters to the beginning of the second group is a multiple of
the number of alphabets used. It is evident, of course, that we may
have similar groups in the cipher which are not the result of
enciphering <span class="pagenum">[<a id="pb58" href="#pb58" name=
"pb58">58</a>]</span>similar groups of the text by the same alphabets
but if we take all recurring groups in a message and investigate the
number of intervening letters, we will find that the majority of such
cases will conform to these two principles.</p>
<p class="par">Changing the key word and message to illustrate more
clearly the above points, the following is quoted from the Signal Book,
1914, with reference to the use of the cipher disk in preparing a
message with a key word.<a class="noteref" id="xd21e15272src" href=
"#xd21e15272" name="xd21e15272src">1</a></p>
<p class="par">&ldquo;&mdash;This simple disk can be used with a cipher
word or, preferably, cipher words, known only to the correspondents....
Using the key word &lsquo;disk&rsquo; to encipher the message
&lsquo;Artillery commander will order all guns withdrawn,&rsquo; we
will proceed as follows: Write out the message to be enciphered and
above it write the key word ... letter over letter, thus:</p>
<div class="table">
<table class="xd21e15277">
<tr>
<td class="xd21e15278 cellLeft cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="xd21e15278 cellTop"></td>
<td class="cellRight cellTop"></td>
</tr>
<tr>
<td class="xd21e15278 cellLeft">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="xd21e15278">DISK</td>
<td class="cellRight">DIS</td>
</tr>
<tr>
<td class="xd21e15278 cellLeft">ARTI</td>
<td class="xd21e15278">LLER</td>
<td class="xd21e15278">YCOM</td>
<td class="xd21e15278">MAND</td>
<td class="xd21e15278">ERWI</td>
<td class="xd21e15278">LLOR</td>
<td class="xd21e15278">DERA</td>
<td class="xd21e15278">LLGU</td>
<td class="xd21e15278">NSWI</td>
<td class="xd21e15278">THDR</td>
<td class="cellRight">AWN</td>
</tr>
<tr>
<td class="xd21e15278 cellLeft"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="xd21e15278"></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e15278 cellLeft">DRZC</td>
<td class="xd21e15278">SXOT</td>
<td class="xd21e15278">FGEY</td>
<td class="xd21e15278">RIFH</td>
<td class="xd21e15278">ZRWC</td>
<td class="xd21e15278">SXET</td>
<td class="xd21e15278">AEBK</td>
<td class="xd21e15278">SXMQ</td>
<td class="xd21e15278">QQWC</td>
<td class="xd21e15278">XBPT</td>
<td class="cellRight">DMP</td>
</tr>
<tr>
<td class="xd21e15278 cellLeft cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="xd21e15278 cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">&ldquo;Now bring the &lsquo;a&rsquo; of the upper disk
under the first letter of the key word on the lower disk, in this case
&lsquo;D&rsquo;. The first letter of the message to be enciphered is
&lsquo;A&rsquo;: &lsquo;d&rsquo; is found to be the letter connected
with &lsquo;A&rsquo;, and it is put down as the first cipher letter.
The letter &lsquo;a&rsquo; is then brought under &lsquo;I&rsquo; which
is the second letter of the key word. &lsquo;R&rsquo; is to be
enciphered and &lsquo;r&rsquo; is found to be the second cipher
letter.... Proceed in this manner until the last letter of the key word
is used and beginning again with the letter &lsquo;D&rsquo;, so
continue until all letters of <span class="pagenum">[<a id="pb59" href=
"#pb59" name="pb59">59</a>]</span>the message have been enciphered.
Divided into groups of five letters, it will be as follows:</p>
<p class="par xd21e152">&ldquo;<span class="tt">DRZCS XOTFG EYRIF HZRWC
SXETA EBKSX MQQQW CKBPT DMF</span>.&rdquo;</p>
<p class="par">So much for the Signal Book; now let us examine the
above message for pairs or similar groups and count the intervening
letters to demonstrate principles (1) and (2);</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td class="xd21e15437 cellLeft cellTop">CSX</td>
<td class="cellTop">&mdash;</td>
<td class="xd21e10023 cellTop">CSX</td>
<td class="xd21e15437 cellTop">16</td>
<td class="cellTop">=</td>
<td class="cellRight cellTop">4 &times; 4</td>
</tr>
<tr>
<td class="xd21e15437 cellLeft">SX</td>
<td>&mdash;</td>
<td class="xd21e10023">SX</td>
<td class="xd21e15437">16</td>
<td>=</td>
<td class="cellRight">4 &times; 4</td>
</tr>
<tr>
<td class="xd21e15437 cellLeft">SX</td>
<td>&mdash;</td>
<td class="xd21e10023">SX</td>
<td class="xd21e15437">8</td>
<td>=</td>
<td class="cellRight">2 &times; 4</td>
</tr>
<tr>
<td class="xd21e15437 cellLeft cellBottom">WC</td>
<td class="cellBottom">&mdash;</td>
<td class="xd21e10023 cellBottom">WC</td>
<td class="xd21e15437 cellBottom">16</td>
<td class="cellBottom">=</td>
<td class="cellRight cellBottom">4 &times; 4</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The key word might contain 2, 4 or 8 letters from the
evidence but we may eliminate 2 as unlikely and preparation of
frequency tables of each of the four alphabets would soon show that 4
is the correct number.</p>
<p class="par">A later and more extensive example (Case <a href=
"#c7a">7-a</a>) will show pairs not separated by multiples of the
number of alphabets used, but the evidence in nearly every case will be
practically conclusive. Especially is this so if chance assists us by
giving groups of three or more letters like the group <span class=
"tt">CSX</span> in the above example. The number of alphabets having
been determined each alphabet is handled by the methods of Case
<a href="#c6">6</a> already discussed.</p>
<div id="c7" class="div2 section">
<div class="divBody">
<p id="c7a" class="par first"><span class="sc">Case</span>
7-a.&mdash;The following message appeared in the &ldquo;personal&rdquo;
column of a London paper:</p>
<div class="blockquote">
<p class="par first">&ldquo;M. B. Will deposit &pound;27 14s 5d
tomorrow,&rdquo;</p>
</div>
<p class="par"></p>
<p class="par">and the next day we find this one: <span class=
"pagenum">[<a id="pb60" href="#pb60" name="pb60">60</a>]</span></p>
<div class="blockquote">
<p class="par first"><span class="tt">M.B. CT OSB UHGI TP IPEWF H CEWIL
NSTTLE FJNVX XTYLS FWKKHI BJLSI SQ VOI BKSM XMKUL SK NVPONPN GSW OL.
IEAG NPSI HYJISFZ CYY NPUXQG TPRJA VXMXI AP EHVPPR TH WPPNEL. UVZUA
MMYVSF KNTS ZSZ UAJPQ DLMMJXL JR RA PORTELOGJ CSULTWNI XMKUHW XGLN
ELCPOWY OL. ULJTL BVJ TLBWTPZ XLD K ZISZNK OSY DL RYJUAJSSGK. TLFNS UVD
VV FQGCYL FJHVSI YJL NEXV PO WTOL PYYYHSH GQBOH AGZTIQ EYFAX YPMP SQA
CI XEYVXNPPAII UV TLFTWMC FU WBWXGUHIWU. AIIWG HSI YJVTI BJV XMQN SFX
DQB LRTY TZ QTXLNISVZ. GIFT AII UQSJGJ OHZ XFOWFV BKAI CTWY
DSWTLTTTPKFRHG IVX QCAFV TP DIIS JBF ESF JSC MCCF HNGK ESBP DJPQ NLU
CTW ROSB CSM.</span></p>
</div>
<p class="par"></p>
<p class="par">The messages in question appeared in an English
newspaper. It is fair to presume then that the cipher is in English.
This is checked negatively by the fact that it contains the letter
<span class="tt">W</span> which is not used in any of the Latin
languages and that the last fifteen words of the message consist of
from two to four letters each, an impossible thing in German. It
contains 108 groups which are probably words, as there are 473 letters
or an average of 4.4 letters per group, while we normally expect an
average of about 5 letters per group. The vowels <span class=
"tt">AEIOU</span> number 90 and the letters <span class=
"tt">JKQXZ</span> number 78. It is thus a substitution cipher (20% of
473=94.6).</p>
<p class="par">Recurring words and similar groups are <span class=
"tt">AIIWG</span>, <span class="tt">AII</span>; <span class=
"tt">BKSM</span>, <span class="tt">BKAI</span>; <span class=
"tt">CT</span>, <span class="tt">CTWY</span>, <span class=
"tt">CTW</span>; <span class="tt">DLMMJXL</span>, <span class=
"tt">DL</span>; <span class="tt">ESF</span>, <span class=
"tt">ESBP</span>; <span class="tt">FJNVX</span>, <span class=
"tt">FJHVSI</span>; <span class="tt">NPSI</span>, <span class=
"tt">NPUXQG</span>; <span class="tt">OSB</span>, <span class=
"tt">OSY</span>, <span class="tt">ROSB</span>; <span class=
"tt">OL</span>, <span class="tt">OL</span>; <span class=
"tt">PORTELOGJ</span>, <span class="tt">PO</span>; <span class=
"tt">SQ</span>, <span class="tt">SQA</span>; <span class=
"tt">TP</span>, <span class="tt">TP</span>; <span class=
"tt">TLBWTPZ</span>, <span class="tt">TLFNS</span>, <span class=
"tt">TLFTWMC</span>; <span class="tt">UVZUA</span>, <span class=
"tt">UVD</span>, <span class="tt">UV</span>; <span class=
"tt">XMKUL</span>, <span class="tt">XMKUHW</span>; <span class=
"tt">YJL</span>, <span class="tt">YJVTI</span>. <span class=
"pagenum">[<a id="pb61" href="#pb61" name="pb61">61</a>]</span></p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Frequency Table for the Message</h3>
</div>
<div class="divBody">
<p class="par first"></p>
<div class="table">
<table class="xd21e12110">
<tr>
<td class="xd21e15658 cellLeft cellTop">A</td>
<td class="xd21e15658 cellTop">B</td>
<td class="xd21e15658 cellTop">C</td>
<td class="xd21e15658 cellTop">D</td>
<td class="xd21e15658 cellTop">E</td>
<td class="xd21e15658 cellTop">F</td>
<td class="xd21e15658 cellTop">G</td>
<td class="xd21e15658 cellTop">H</td>
<td class="xd21e15658 cellTop">I</td>
<td class="xd21e15658 cellTop">J</td>
<td class="xd21e15658 cellTop">K</td>
<td class="xd21e15658 cellTop">L</td>
<td class="xd21e15658 cellTop">M</td>
<td class="xd21e15658 cellTop">N</td>
<td class="xd21e15658 cellTop">O</td>
<td class="xd21e15658 cellTop">P</td>
<td class="xd21e15658 cellTop">Q</td>
<td class="xd21e15658 cellTop">R</td>
<td class="xd21e15658 cellTop">S</td>
<td class="xd21e15658 cellTop">T</td>
<td class="xd21e15658 cellTop">U</td>
<td class="xd21e15658 cellTop">V</td>
<td class="xd21e15658 cellTop">W</td>
<td class="xd21e15658 cellTop">X</td>
<td class="xd21e15658 cellTop">Y</td>
<td class="xd21e15658 cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft cellBottom">15</td>
<td class="cellBottom">13</td>
<td class="cellBottom">15</td>
<td class="cellBottom">8</td>
<td class="cellBottom">13</td>
<td class="cellBottom">20</td>
<td class="cellBottom">16</td>
<td class="cellBottom">16</td>
<td class="cellBottom">30</td>
<td class="cellBottom">21</td>
<td class="cellBottom">13</td>
<td class="cellBottom">27</td>
<td class="cellBottom">14</td>
<td class="cellBottom">19</td>
<td class="cellBottom">15</td>
<td class="cellBottom">26</td>
<td class="cellBottom">13</td>
<td class="cellBottom">9</td>
<td class="cellBottom">33</td>
<td class="cellBottom">30</td>
<td class="cellBottom">17</td>
<td class="cellBottom">12</td>
<td class="cellBottom">19</td>
<td class="cellBottom">20</td>
<td class="cellBottom">19</td>
<td class="cellRight cellBottom">11</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This clearly eliminates Cases 4, 5 and 6.</p>
<p class="par">Referring to the recurring words and groups above noted,
we figure the number of letters between each.</p>
<div class="table">
<table class="xd21e283">
<tr>
<td class="xd21e15774 cellLeft cellTop">AII</td>
<td class="cellTop">...</td>
<td class="xd21e15776 cellTop">AII</td>
<td class="xd21e15777 cellTop">45</td>
<td class="cellTop">=</td>
<td class="cellRight cellTop">3&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">BK</td>
<td>...</td>
<td class="xd21e15776">BK</td>
<td class="xd21e15777">345</td>
<td>=</td>
<td class="cellRight">23&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">CT</td>
<td>...</td>
<td class="xd21e15776">CT</td>
<td class="xd21e15777">403</td>
<td></td>
<td class="cellRight">No factors</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">CTW</td>
<td>...</td>
<td class="xd21e15776">CTW</td>
<td class="xd21e15777">60</td>
<td>=</td>
<td class="cellRight">2&times;2&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">DL</td>
<td>...</td>
<td class="xd21e15776">DL</td>
<td class="xd21e15777">75</td>
<td>=</td>
<td class="cellRight">3&times;5&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">ES</td>
<td>...</td>
<td class="xd21e15776">ES</td>
<td class="xd21e15777">14</td>
<td>=</td>
<td class="cellRight">2&times;7</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">FJ</td>
<td>...</td>
<td class="xd21e15776">FJ</td>
<td class="xd21e15777">187</td>
<td></td>
<td class="cellRight">No factors</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">NP</td>
<td>...</td>
<td class="xd21e15776">NP</td>
<td class="xd21e15777">14</td>
<td>=</td>
<td class="cellRight">2&times;7</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">OL</td>
<td>...</td>
<td class="xd21e15776">OL</td>
<td class="xd21e15777">120</td>
<td>=</td>
<td class="cellRight">2&times;2&times;2&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">OS</td>
<td>...</td>
<td class="xd21e15776">OS</td>
<td class="xd21e15777">220</td>
<td>=</td>
<td class="cellRight">11&times;2&times;2&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">OSB</td>
<td>...</td>
<td class="xd21e15776">OSB</td>
<td class="xd21e15777">465</td>
<td>=</td>
<td class="cellRight">31&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">PO</td>
<td>...</td>
<td class="xd21e15776">PO</td>
<td class="xd21e15777">105</td>
<td>=</td>
<td class="cellRight">7&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">SQ</td>
<td>...</td>
<td class="xd21e15776">SQ</td>
<td class="xd21e15777">250</td>
<td>=</td>
<td class="cellRight">2&times;5&times;5&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">TLF</td>
<td>...</td>
<td class="xd21e15776">TLF</td>
<td class="xd21e15777">80</td>
<td>=</td>
<td class="cellRight">2&times;2&times;2&times;2&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">TP</td>
<td>...</td>
<td class="xd21e15776">TP</td>
<td class="xd21e15777">405</td>
<td>=</td>
<td class="cellRight">3&times;3&times;3&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">UV</td>
<td>...</td>
<td class="xd21e15776">UV</td>
<td class="xd21e15777">115</td>
<td>=</td>
<td class="cellRight">23&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">XMKU</td>
<td>...</td>
<td class="xd21e15776">XMKU</td>
<td class="xd21e15777">120</td>
<td>=</td>
<td class="cellRight">2&times;2&times;2&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft">UV</td>
<td>...</td>
<td class="xd21e15776">UV</td>
<td class="xd21e15777">73</td>
<td></td>
<td class="cellRight">No factors</td>
</tr>
<tr>
<td class="xd21e15774 cellLeft cellBottom">YJ</td>
<td class="cellBottom">...</td>
<td class="xd21e15776 cellBottom">YJ</td>
<td class="xd21e15777 cellBottom">85</td>
<td class="cellBottom">=</td>
<td class="cellRight cellBottom">17&times;5</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The dominant factor is clearly 5, so we may consider
that five alphabets were used, indicating a keyword of five letters.
Writing the message in lines of five letters each and making a
frequency table for each of the five columns so formed, we find the
following:</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Frequency Tables</h3>
</div>
<div class="divBody">
<p class="par first"></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td colspan="2" class="cellLeft cellTop"><i>Colum 1</i></td>
<td colspan="2" class="cellTop"><i>Column 2</i></td>
<td colspan="2" class="cellTop"><i>Column 3</i></td>
<td colspan="2" class="cellTop"><i>Column 4</i></td>
<td colspan="2" class="cellRight cellTop"><i>Column 5</i></td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>11</td>
<td>A</td>
<td>111111111</td>
<td>A</td>
<td>1</td>
<td>A</td>
<td>1</td>
<td>A</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td></td>
<td>B</td>
<td>111</td>
<td>B</td>
<td>111</td>
<td>B</td>
<td></td>
<td>B</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>1111111</td>
<td>C</td>
<td>1</td>
<td>C</td>
<td>111</td>
<td>C</td>
<td>1111</td>
<td>C</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>11</td>
<td>D</td>
<td>11</td>
<td>D</td>
<td>1</td>
<td>D</td>
<td></td>
<td>D</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>1111</td>
<td>E</td>
<td></td>
<td>E</td>
<td>11</td>
<td>E</td>
<td>1111111</td>
<td>E</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>111</td>
<td>F</td>
<td></td>
<td>F</td>
<td>111111111</td>
<td>F</td>
<td>111</td>
<td>F</td>
<td class="cellRight">11111</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>111111111</td>
<td>G</td>
<td></td>
<td>G</td>
<td>111</td>
<td>G</td>
<td>11</td>
<td>G</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>111</td>
<td>H</td>
<td>11111</td>
<td>H</td>
<td>111</td>
<td>H</td>
<td>111</td>
<td>H</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>11</td>
<td>I</td>
<td>11</td>
<td>I</td>
<td>1111111</td>
<td>I</td>
<td>11111111111111111</td>
<td>I</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>11111</td>
<td>J</td>
<td>1</td>
<td>J</td>
<td>111111</td>
<td>J</td>
<td></td>
<td>J</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td>111111</td>
<td>K</td>
<td>11111</td>
<td>K</td>
<td></td>
<td>K</td>
<td>1</td>
<td>K</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td></td>
<td>L</td>
<td>1111111111111111111</td>
<td>L</td>
<td>11</td>
<td>L</td>
<td>11111</td>
<td>L</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td></td>
<td>M</td>
<td></td>
<td>M</td>
<td>1111111</td>
<td>M</td>
<td>1111</td>
<td>M</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>1111111</td>
<td>N</td>
<td>111</td>
<td>N</td>
<td>1111</td>
<td>N</td>
<td></td>
<td>N</td>
<td class="cellRight">11111</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>11111</td>
<td>O</td>
<td></td>
<td>O</td>
<td>111111111</td>
<td>O</td>
<td>1</td>
<td>O</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>1111111</td>
<td>P</td>
<td>1111111</td>
<td>P</td>
<td>11111111</td>
<td>P</td>
<td>1111</td>
<td>P</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>11111</td>
<td>Q</td>
<td></td>
<td>Q</td>
<td></td>
<td>Q</td>
<td>11</td>
<td>Q</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td></td>
<td>R</td>
<td>1</td>
<td>R</td>
<td>1</td>
<td>R</td>
<td>111111</td>
<td>R</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td></td>
<td>S</td>
<td>11111111</td>
<td>S</td>
<td>111111</td>
<td>S</td>
<td>111111111111</td>
<td>S</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>1111111</td>
<td>T</td>
<td>111</td>
<td>T</td>
<td>11111</td>
<td>T</td>
<td>1</td>
<td>T</td>
<td class="cellRight">11111111111111</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>1111111</td>
<td>U</td>
<td>111</td>
<td>U</td>
<td>111111</td>
<td>U</td>
<td></td>
<td>U</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>11111</td>
<td>V</td>
<td></td>
<td>V</td>
<td>11</td>
<td>V</td>
<td>11111</td>
<td>V</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td>111</td>
<td>W</td>
<td>1111</td>
<td>W</td>
<td></td>
<td>W</td>
<td>11111</td>
<td>W</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>11</td>
<td>X</td>
<td></td>
<td>X</td>
<td>1111</td>
<td>X</td>
<td>11111111</td>
<td>X</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>1111</td>
<td>Y</td>
<td>11111</td>
<td>Y</td>
<td></td>
<td>Y</td>
<td>111</td>
<td>Y</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom">Z</td>
<td class="cellBottom">11111</td>
<td class="cellBottom">Z</td>
<td class="cellBottom">111</td>
<td class="cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom">Z</td>
<td class="cellRight cellBottom">111</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">In the table for Column 1, the letter <span class=
"tt">G</span> occurs 9 <span class="pagenum">[<a id="pb62" href="#pb62"
name="pb62">62</a>]</span>times. Let us consider it tentatively as
<span class="tt">E</span>. Then if the cipher alphabet runs regularly
and in the direction of the regular alphabet, <span class="tt">C</span>
(7 times) = <span class="tt">A</span> and the cipher alphabet bears a
close resemblance to the regular frequency table. Note <span class=
"tt">TUV</span> (= <span class="tt">RST</span>) occurring respectively
7, 7, and 5 times and the non-occurrence of <span class="tt">B</span>,
<span class="tt">L</span>, <span class="tt">M</span>, <span class=
"tt">R</span>, <span class="tt">S</span>, <span class="tt">Z</span>, (=
<span class="tt">Z</span>, <span class="tt">J</span>, <span class=
"tt">K</span>, <span class="tt">P</span>, <span class="tt">Q</span>,
and <span class="tt">X</span> respectively.)</p>
<p class="par">In the next table, <span class="tt">L</span> occurs 19
times and taking it for <span class="tt">E</span> with the alphabet
running in the same way, <span class="tt">A=H</span>. The first word of
our message, <span class="tt">CT</span>, thus becomes <span class=
"tt">AM</span> when deciphered with these two alphabets and the first
two letters of the key are <span class="tt">C H</span>.</p>
<p class="par">Similarly in the third table we may take either
<span class="tt">F</span> or <span class="tt">O</span> for <span class=
"tt">E</span>, but a casual examination shows that the former is
correct and <span class="tt">A=B</span> (even if we were looking for a
vowel for the next letter of the keyword).</p>
<p class="par">In the fourth table, <span class="tt">I</span> is
clearly <span class="tt">E</span> and <span class="tt">A=E</span>. The
fifth table shows T=14 and J=9. If we take <span class="tt">T=E</span>
we find that we would have many letters which should not occur. On the
other hand, if we take <span class="tt">J=E</span> then <span class=
"tt">T=O</span> and in view of the many E&rsquo;s already accounted for
in the other columns, this may be all right. It checks as correct if we
apply the last three alphabets to the second word of our message,
<span class="tt">OSB</span>, which deciphers <span class=
"tt">NOW</span>. Using these alphabets to decipher the whole message,
we find it to read:</p>
<div class="blockquote">
<p class="par first">&ldquo;M. B. Am now safe on board a barge moored
below Tower Bridge where no one will think of looking for me. Have good
friends but little money owing to action of police. Trust, little girl,
you still believe in my innocence although things seem against me.
There are reasons why I should not be questioned. Shall try to embark
before the mast in some outward bound vessel. Crews will not be
scrutinized so sharply as passengers. There are those who will let you
know my movements. Fear the police may <span class="pagenum">[<a id=
"pb63" href="#pb63" name="pb63">63</a>]</span>tamper with your
correspondence but later on when hue and cry have died down will let
you know all.&rdquo;</p>
</div>
<p class="par"></p>
<p class="par">The key to this message is <span class="tt">CHBEF</span>
which is not intelligible as a word but if put into figures indicating
that the 2d, 7th, 1st, 4th, and 5th letter beyond the corresponding
letter of the message has been used the key becomes 27145 and we may
connect it with the &ldquo;personal&rdquo; which appeared in the same
paper the day before reading:</p>
<div class="blockquote">
<p class="par first">&ldquo;M. B. Will deposit &pound;27 14s 5d
tomorrow.&rdquo;</p>
</div>
<p class="par"></p>
</div>
</div>
<div id="c7b" class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 7-b<span class="corr"
id="xd21e16744" title="Not in source">.</span></p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e16751">
<tr>
<td class="cellLeft cellTop">DDLRM</td>
<td class="cellTop">ERGLM</td>
<td class="cellTop">UJTLL</td>
<td class="cellTop">CHERS</td>
<td class="cellTop">LSOEE</td>
<td class="cellRight cellTop">SMEJU</td>
</tr>
<tr>
<td class="cellLeft">ZJIMU</td>
<td>DAEES</td>
<td>DUTDB</td>
<td>GUGPN</td>
<td>RCHOB</td>
<td class="cellRight">EQEIE</td>
</tr>
<tr>
<td class="cellLeft">OOACD</td>
<td>EIOOG</td>
<td>COLJL</td>
<td>PDUVM</td>
<td>IGIYX</td>
<td class="cellRight">QQTOT</td>
</tr>
<tr>
<td class="cellLeft">DJCPJ</td>
<td>OISLY</td>
<td>DUASI</td>
<td>UPFNE</td>
<td>AECOB</td>
<td class="cellRight">OESHO</td>
</tr>
<tr>
<td class="cellLeft">BETND</td>
<td>QXUCY</td>
<td>LUQOY</td>
<td>EHYDU</td>
<td>LXPEQ</td>
<td class="cellRight">FIXZE</td>
</tr>
<tr>
<td class="cellLeft">PDCNZ</td>
<td>ENELQ</td>
<td>MJTSQ</td>
<td>ECFIE</td>
<td>ARNDN</td>
<td class="cellRight">ETSCF</td>
</tr>
<tr>
<td class="cellLeft">IFQSE</td>
<td>TDDNP</td>
<td>UUZHQ</td>
<td>CDTXQ</td>
<td>IRMER</td>
<td class="cellRight">GLXBE</td>
</tr>
<tr>
<td class="cellLeft">IQRXJ</td>
<td>FBSQD</td>
<td>LDSVI</td>
<td>XUMTB</td>
<td>AEQEB</td>
<td class="cellRight">YLECO</td>
</tr>
<tr>
<td class="cellLeft">IYCUD</td>
<td>QTPYS</td>
<td>VOQBL</td>
<td>ULYRO</td>
<td>YHEFM</td>
<td class="cellRight">OYMUY</td>
</tr>
<tr>
<td class="cellLeft">ROYMU</td>
<td>EQBLV</td>
<td>UBREY</td>
<td>GHYTQ</td>
<td>CMUBR</td>
<td class="cellRight">EQTOF</td>
</tr>
<tr>
<td class="cellLeft">VSDDU</td>
<td>DAFFS</td>
<td>CEBSV</td>
<td>TIOYE</td>
<td>TCLQX</td>
<td class="cellRight">DVNLQ</td>
</tr>
<tr>
<td class="cellLeft">XYTSI</td>
<td>MZULX</td>
<td>BAXQR</td>
<td>ECVTD</td>
<td>ETGOB</td>
<td class="cellRight">CCUYF</td>
</tr>
<tr>
<td class="cellLeft cellBottom">TTNXL</td>
<td class="cellBottom">UNEFS</td>
<td class="cellBottom">IVIJR</td>
<td class="cellBottom">ZHSBY</td>
<td class="cellBottom">LLTSI</td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">On the preliminary determination, we have the following
count of letters out of a total of 385:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">A</td>
<td class="cellTop">8</td>
<td class="cellTop">L</td>
<td class="cellTop">23</td>
<td class="cellTop">J</td>
<td class="cellRight cellTop">9</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>38</td>
<td>N</td>
<td>11</td>
<td>Q</td>
<td class="cellRight">22</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>19</td>
<td>R</td>
<td>14</td>
<td>V</td>
<td class="cellRight">9</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>21</td>
<td>S</td>
<td>20</td>
<td>X</td>
<td class="cellRight">13</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>24</td>
<td>T</td>
<td>21</td>
<td>Z</td>
<td class="cellRight">6</td>
</tr>
<tr>
<td class="cellLeft">Total</td>
<td><span class="sum">110</span></td>
<td>Total</td>
<td><span class="sum">89</span></td>
<td>Total</td>
<td class="cellRight"><span class="sum">59</span></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">28%</td>
<td class="cellBottom"></td>
<td class="cellBottom">23%</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom">15%</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Every letter except <span class="tt">K</span> and
<span class="tt">W</span> occurs at least six times. We may say then
that it is a substitution cipher, Spanish text, and certainly not Case
4, 5 or 6. We will now analyze it for recurring pairs or groups
<span class="pagenum">[<a id="pb64" href="#pb64" name=
"pb64">64</a>]</span>to determine, if it be Case 7, how many alphabets
were used. The following is a complete list of such recurring groups
and pairs with the number of letters intervening and the factors
thereof. In work of this kind, the groups of three or more letters are
always much more valuable than single pairs. For example, the groups,
<span class="tt">HOBE</span>, <span class="tt">OYMU</span>,
<span class="tt">RMERGL</span> and <span class="tt">UBRE</span> show,
without question, that six alphabets were used. It is not necessary, as
a rule, to make a complete list like the following:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="xd21e17041 cellLeft cellTop">AE</td>
<td class="cellTop">74=2&times;37</td>
<td class="xd21e17041 cellTop">IE</td>
<td class="cellTop">110=2&times;5&times;11</td>
<td class="xd21e17041 cellTop">RE</td>
<td class="cellRight cellTop">50=2&times;5&times;5</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">AE</td>
<td>120=2&times;2&times;2&times;3&times;5</td>
<td class="xd21e17041">IM</td>
<td>302=2&times;151</td>
<td class="xd21e17041">RMERGL</td>
<td class="cellRight">198=2&times;3&times;3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">BE</td>
<td>88=2&times;2&times;2&times;11</td>
<td class="xd21e17041">IO</td>
<td>250=2&times;5&times;5&times;5</td>
<td class="xd21e17041">SC</td>
<td class="cellRight">132=2&times;2&times;3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CD</td>
<td>132=2&times;2&times;3&times;11</td>
<td class="xd21e17041">IX</td>
<td>78=2&times;3&times;13</td>
<td class="xd21e17041">SD</td>
<td class="cellRight">262=2&times;131</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CFI</td>
<td>12=2&times;2&times;3</td>
<td class="xd21e17041">LY</td>
<td>158=2&times;79</td>
<td class="xd21e17041">SI</td>
<td class="cellRight">230=2&times;5&times;23</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CH</td>
<td>36=2&times;2&times;3&times;3</td>
<td class="xd21e17041">JT</td>
<td>150=2&times;3&times;5&times;5</td>
<td class="xd21e17041">SI</td>
<td class="cellRight">34=2&times;17</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CO</td>
<td>42=2&times;3&times;7</td>
<td class="xd21e17041">LL</td>
<td>367 No factors</td>
<td class="xd21e17041">SI</td>
<td class="cellRight">264=2&times;2&times;2&times;3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CO</td>
<td>126=2&times;3&times;3&times;7</td>
<td class="xd21e17041">LQ</td>
<td>164=2&times;2&times;41</td>
<td class="xd21e17041">SI</td>
<td class="cellRight">12=2&times;2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">CU</td>
<td>114=2&times;3&times;19</td>
<td class="xd21e17041">LQX</td>
<td>6=2&times;3</td>
<td class="xd21e17041">SL</td>
<td class="cellRight">78=2&times;3&times;13</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DD</td>
<td>186=2&times;3&times;31</td>
<td class="xd21e17041">LU</td>
<td>124=2&times;2&times;31</td>
<td class="xd21e17041">SQ</td>
<td class="cellRight">54=2&times;3&times;3&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DD</td>
<td>116=2&times;2&times;29</td>
<td class="xd21e17041">LU</td>
<td>110=2&times;5&times;11</td>
<td class="xd21e17041">SV</td>
<td class="cellRight">27=3&times;3&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DE</td>
<td>285=5&times;57</td>
<td class="xd21e17041">LU</td>
<td>234=2&times;3&times;3&times;13</td>
<td class="xd21e17041">SV</td>
<td class="cellRight">63=3&times;3&times;7</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DL</td>
<td>218=2&times;109</td>
<td class="xd21e17041">LX</td>
<td>66=2&times;3&times;11</td>
<td class="xd21e17041">SV</td>
<td class="cellRight">90=2&times;3&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DN</td>
<td>14=2&times;7</td>
<td class="xd21e17041">LXB</td>
<td>132=2&times;2&times;3&times;11</td>
<td class="xd21e17041">TD</td>
<td class="cellRight">47 No factors</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DQ</td>
<td>120=2&times;2&times;2&times;3&times;5</td>
<td class="xd21e17041">LY</td>
<td>158=2&times;79</td>
<td class="xd21e17041">TD</td>
<td class="cellRight">165=3&times;5&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DU</td>
<td>36=2&times;2&times;3&times;3</td>
<td class="xd21e17041">ME</td>
<td>22=2&times;11</td>
<td class="xd21e17041">TD</td>
<td class="cellRight">96=2&times;2&times;2&times;2&times;2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DU</td>
<td>24=2&times;2&times;2&times;3</td>
<td class="xd21e17041">MU</td>
<td>24=2&times;2&times;2&times;3</td>
<td class="xd21e17041">TN</td>
<td class="cellRight">239 No factors</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DU</td>
<td>38=2&times;19</td>
<td class="xd21e17041">MU</td>
<td>240=2&times;2&times;2&times;2&times;3&times;5</td>
<td class="xd21e17041">TS</td>
<td class="cellRight">14=2&times;7</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">DU</td>
<td>165=3&times;5&times;11</td>
<td class="xd21e17041">MU</td>
<td>18=2&times;3&times;3</td>
<td class="xd21e17041">TS</td>
<td class="cellRight">156=2&times;2&times;3&times;13</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EA</td>
<td>30=2&times;3&times;5</td>
<td class="xd21e17041">ND</td>
<td>47 No factors</td>
<td class="xd21e17041">TSI</td>
<td class="cellRight">50=2&times;5&times;5</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EB</td>
<td>78=2&times;3&times;13</td>
<td class="xd21e17041">NE</td>
<td>48=2&times;2&times;2&times;2&times;3</td>
<td class="xd21e17041">UBRE</td>
<td class="cellRight">12=2&times;2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EC</td>
<td>180=2&times;2&times;3&times;3&times;5</td>
<td class="xd21e17041">NE</td>
<td>18=2&times;3&times;3</td>
<td class="xd21e17041">UD</td>
<td class="cellRight">60=2&times;2&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ECO</td>
<td>126=2&times;3&times;3&times;7</td>
<td class="xd21e17041">NE</td>
<td>192=2&times;2&times;2&times;2&times;2&times;2&times;3</td>
<td class="xd21e17041">UDA</td>
<td class="cellRight">270=2&times;3&times;3&times;3&times;5</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EES</td>
<td>14=2&times;7</td>
<td class="xd21e17041">OB</td>
<td>6=2&times;3</td>
<td class="xd21e17041">UL</td>
<td class="cellRight">114=2&times;3&times;19</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EF</td>
<td>105=3&times;5&times;7</td>
<td class="xd21e17041">OB</td>
<td>234=2&times;3&times;3&times;13</td>
<td class="xd21e17041">ULX</td>
<td class="cellRight">198=2&times;3&times;3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EI</td>
<td>8=2&times;2&times;2</td>
<td class="xd21e17041">OE</td>
<td>93=3&times;31</td>
<td class="xd21e17041">UY</td>
<td class="cellRight">89 No factors</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EI</td>
<td>152=2&times;2&times;2&times;19</td>
<td class="xd21e17041">OI</td>
<td>144=2&times;2&times;2&times;2&times;3&times;3</td>
<td class="xd21e17041">UZ</td>
<td class="cellRight">162=2&times;3&times;3&times;3&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EQ</td>
<td>88=2&times;2&times;2&times;11</td>
<td class="xd21e17041">OO</td>
<td>7 No factors</td>
<td class="xd21e17041">VI</td>
<td class="cellRight">148=2&times;2&times;37</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EQ</td>
<td>264=2&times;2&times;2&times;3&times;11</td>
<td class="xd21e17041">OY</td>
<td>6=2&times;3</td>
<td class="xd21e17041">VT</td>
<td class="cellRight">33=3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EQ</td>
<td>44=2&times;2&times;11</td>
<td class="xd21e17041">OY</td>
<td>46=2&times;23</td>
<td class="xd21e17041">XQ</td>
<td class="cellRight">114=2&times;3&times;19</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">EQE</td>
<td>176=2&times;2&times;2&times;2&times;11</td>
<td class="xd21e17041">OYMU</td>
<td>6=2&times;3</td>
<td class="xd21e17041">XQ</td>
<td class="cellRight">
144=2&times;2&times;2&times;2&times;3&times;3<span class=
"pagenum">[<a id="pb65" href="#pb65" name="pb65">65</a>]</span></td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ER</td>
<td>12=2&times;2&times;3</td>
<td class="xd21e17041">PD</td>
<td>75=3&times;5&times;5</td>
<td class="xd21e17041">XU</td>
<td class="cellRight">99=3&times;3&times;11</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ES</td>
<td>78=2&times;3&times;13</td>
<td class="xd21e17041">QBL</td>
<td>24=2&times;2&times;2&times;3</td>
<td class="xd21e17041">YE</td>
<td class="cellRight">184=2&times;2&times;2&times;23</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ET</td>
<td>135=3&times;3&times;5</td>
<td class="xd21e17041">QC</td>
<td>95=5&times;19</td>
<td class="xd21e17041">YL</td>
<td class="cellRight">106=2&times;53</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ET</td>
<td>9=3&times;3</td>
<td class="xd21e17041">QE</td>
<td>108=2&times;2&times;3&times;3&times;3</td>
<td class="xd21e17041">YL</td>
<td class="cellRight">
144=2&times;2&times;2&times;2&times;3&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ET</td>
<td>54=2&times;3&times;3&times;3</td>
<td class="xd21e17041">QE</td>
<td>68=2&times;2&times;17</td>
<td class="xd21e17041">YM</td>
<td class="cellRight">6=2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">ET</td>
<td>31 No factors</td>
<td class="xd21e17041">QR</td>
<td>132=2&times;2&times;3&times;11</td>
<td class="xd21e17041">YRO</td>
<td class="cellRight">12=2&times;2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft">HE</td>
<td>245=5&times;7&times;7</td>
<td class="xd21e17041">QTO</td>
<td>210=2&times;3&times;5&times;7</td>
<td class="xd21e17041">ZE</td>
<td class="cellRight">6=2&times;3</td>
</tr>
<tr>
<td class="xd21e17041 cellLeft cellBottom">HOBE</td>
<td class="cellBottom">66=2&times;3&times;11</td>
<td class="xd21e17041 cellBottom">QX</td>
<td class="cellBottom">198=2&times;3&times;3&times;11</td>
<td class="xd21e17041 cellBottom">ZH</td>
<td class="cellRight cellBottom">183=3&times;61</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Out of one hundred and one recurring pairs we have fifty
with the factors 2&times;3=6; out of twelve recurring triplets, nine
have these factors; and the four recurring groups of four or more
letters all have these factors. The percentages are respectively 49.5%,
75% and 100% and we may be certain from this that six alphabets were
used. But, before the six frequency tables are made up, there is one
more point to be considered; why are there so many recurring groups
which do not have six as a factor? The answer is that one or more of
the alphabets is repeated in each cycle; that is, a key word of the
form <span class="tt">HAVANA</span> has been used. If this were the key
word, the second, fourth and sixth alphabets would be the same. We will
see later that in this example the second and sixth alphabets are the
same and this introduces the great number of recurring groups without
the factor 6.</p>
<p class="par">We will now proceed to make a frequency table for each
alphabet. As the message is written in thirty columns, we take the
first, seventh, thirteenth, etc., as constituting the first alphabet;
the second, eighth, fourteenth, etc., as constituting the second
alphabet and so on. The prefix and suffix letter is noted for each
occurrence of each letter. The importance of this will be appreciated
when the form of the frequency tables is examined. None bears any
resemblance to the normal frequency table except that each is evidently
a mixed up alphabet. The <span class="pagenum">[<a id="pb66" href=
"#pb66" name="pb66">66</a>]</span>numbers after &ldquo;Prefix&rdquo;
and &ldquo;Suffix&rdquo; refer to the alphabet to which these belong,
for convenience in future reference.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Frequency Tables</h3>
</div>
<div class="divBody">
<p class="par first"></p>
<div class="table">
<table class="xd21e17574">
<thead>
<tr class="label">
<td colspan="5" class="cellHeadLeft cellHeadTop"><span class="sc">First
Alphabet</span></td>
<td colspan="5" class="cellHeadRight cellHeadTop"><span class=
"sc">Second Alphabet</span></td>
</tr>
<tr class="label">
<td class="cellHeadLeft"></td>
<td>Letter</td>
<td></td>
<td>Prefix (6)</td>
<td>Suffix (2)</td>
<td></td>
<td>Letter</td>
<td></td>
<td>Prefix (1)</td>
<td class="cellHeadRight">Suffix (3)</td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">A</td>
<td>111</td>
<td>3</td>
<td>DUD</td>
<td>ESF</td>
<td>A</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>11111111</td>
<td>8</td>
<td>OOOFEEOS</td>
<td>EOESYSCY</td>
<td>B</td>
<td>111</td>
<td>3</td>
<td>TQQ</td>
<td class="cellRight">ALL</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>C</td>
<td>1</td>
<td>1</td>
<td>B</td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>1111</td>
<td>4</td>
<td>TYT</td>
<td>DJUD</td>
<td>D</td>
<td>111111</td>
<td>6</td>
<td>DTPDXT</td>
<td class="cellRight">LBCNVE</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>1</td>
<td>1</td>
<td>E</td>
<td>S</td>
<td>E</td>
<td>11111111111 1</td>
<td>1</td>
<td>ABNBNINRRYN</td>
<td class="cellRight">EOATLATYQTF</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>F</td>
<td>111</td>
<td>3</td>
<td>QIA</td>
<td class="cellRight">IQF</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>G</td>
<td>11</td>
<td>2</td>
<td>RR</td>
<td class="cellRight">LL</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>H</td>
<td>1</td>
<td>1</td>
<td>Z</td>
<td class="cellRight">O</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>11111111</td>
<td>8</td>
<td>EOFFEOVS</td>
<td>OSEFQYJ</td>
<td>I</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>J</td>
<td>1111</td>
<td>4</td>
<td>ZLDI</td>
<td class="cellRight">ILCR</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>1</td>
<td>1</td>
<td>O</td>
<td>J</td>
<td>L</td>
<td>1</td>
<td>1</td>
<td>T</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>1</td>
<td>1</td>
<td>F</td>
<td>O</td>
<td>M</td>
<td>1</td>
<td>1</td>
<td>V</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>1111</td>
<td>4</td>
<td>FEDU</td>
<td>EEEE</td>
<td>N</td>
<td>1</td>
<td>1</td>
<td>P</td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>1</td>
<td>1</td>
<td>E</td>
<td>O</td>
<td>O</td>
<td>1111111</td>
<td>7</td>
<td>OIBQRMR</td>
<td class="cellRight">AOEYYYY</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>11</td>
<td>2</td>
<td>GE</td>
<td>ND</td>
<td>P</td>
<td>1</td>
<td>1</td>
<td>T</td>
<td class="cellRight">Y</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>1111</td>
<td>4</td>
<td>UEOE</td>
<td>OFBB</td>
<td>Q</td>
<td>11111</td>
<td>5</td>
<td>XXITX</td>
<td class="cellRight">OIRCR</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>1111111</td>
<td>7</td>
<td>EEEYYBB</td>
<td>GSGOOEE</td>
<td>R</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td>1</td>
<td>1</td>
<td>D</td>
<td>V</td>
<td>S</td>
<td>11111111</td>
<td>8</td>
<td>REIATBVB</td>
<td class="cellRight">LMLIQQDV</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>11111111</td>
<td>8</td>
<td>JUJMQYVF</td>
<td>LDSBPQDT</td>
<td>T</td>
<td>1</td>
<td>1</td>
<td>T</td>
<td class="cellRight">N</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>U</td>
<td>111</td>
<td>3</td>
<td>XDZ</td>
<td class="cellRight">CLL</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>11</td>
<td>2</td>
<td>UF</td>
<td>MS</td>
<td>V</td>
<td>1</td>
<td>1</td>
<td>S</td>
<td class="cellRight">I</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>111111</td>
<td>6</td>
<td>YQTQQA</td>
<td>QUQDYQ</td>
<td>X</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>1</td>
<td>1</td>
<td>O</td>
<td>E</td>
<td>Y</td>
<td>1111</td>
<td>4</td>
<td>BIXB</td>
<td class="cellRight">LCTL</td>
</tr>
<tr>
<td class="cellLeft">Z</td>
<td>111</td>
<td>3</td>
<td>UUM</td>
<td>JHU</td>
<td>Z</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr class="label">
<td colspan="5" class="cellHeadLeft"><span class="sc">Third
Alphabet</span></td>
<td colspan="5" class="cellHeadRight"><span class="sc">Fourth
Alphabet</span></td>
</tr>
<tr class="label">
<td class="cellHeadLeft"></td>
<td>Letter</td>
<td></td>
<td>Prefix (2)</td>
<td>Suffix (4)</td>
<td></td>
<td>Letter</td>
<td></td>
<td>Prefix (3<span class="corr" id="xd21e18132" title=
"Not in source">)</span></td>
<td class="cellHeadRight">Suffix (5)</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>1111</td>
<td>4</td>
<td>OEEB</td>
<td>CERE</td>
<td>A</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>1</td>
<td>1</td>
<td>D</td>
<td>G</td>
<td>B</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>111111</td>
<td>6</td>
<td>JUDYQC</td>
<td>PYNUMU</td>
<td>C</td>
<td>11111</td>
<td>5</td>
<td>LRAQT</td>
<td class="cellRight">HHDDL</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>1</td>
<td>1</td>
<td>S</td>
<td>D</td>
<td>D</td>
<td>11</td>
<td>2</td>
<td>QD</td>
<td class="cellRight">LU</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>111</td>
<td>3</td>
<td>EOD</td>
<td>SST</td>
<td>E</td>
<td>11111111</td>
<td>8</td>
<td>MQAYQALR</td>
<td class="cellRight">JICHCQCC</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>11</td>
<td>2</td>
<td>FE</td>
<td>SS</td>
<td>F</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>G</td>
<td>1111</td>
<td>4</td>
<td>BOIY</td>
<td class="cellRight">UCIH</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>H</td>
<td>1</td>
<td>1</td>
<td>Y</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>111111</td>
<td>6</td>
<td>JMSFQV</td>
<td>MGUXRX</td>
<td>I</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>J</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>11111111111111</td>
<td>14</td>
<td>DGLSJSUEGYBBUY</td>
<td>RMCSPYXQXEUVXL</td>
<td>L</td>
<td>1</td>
<td>1</td>
<td>L</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>1</td>
<td>1</td>
<td>S</td>
<td>E</td>
<td>M</td>
<td>11111</td>
<td>5</td>
<td>LIYYC</td>
<td class="cellRight">UUUUU</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>11</td>
<td>2</td>
<td>DT</td>
<td>PX</td>
<td>N</td>
<td>111</td>
<td>3</td>
<td>TCV</td>
<td class="cellRight">DZL</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>1</td>
<td>1</td>
<td>O</td>
<td>G</td>
<td>O</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>P</td>
<td>111</td>
<td>3</td>
<td>LCN</td>
<td class="cellRight">DJU</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>1111111</td>
<td>7</td>
<td>EQSFHSE</td>
<td>ETESCDT</td>
<td>Q</td>
<td>1</td>
<td>1</td>
<td>L</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>1111</td>
<td>4</td>
<td>NQQJ</td>
<td>CXEZ</td>
<td>R</td>
<td>111</td>
<td>3</td>
<td>LAI</td>
<td class="cellRight">MNM</td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>S</td>
<td>111111111</td>
<td>9</td>
<td>LEETQYFTF</td>
<td class="cellRight">ODHCEVCII</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>1111</td>
<td>4</td>
<td>EEEY</td>
<td>NSCS</td>
<td>T</td>
<td>1111</td>
<td>4</td>
<td>QQVE</td>
<td class="cellRight">OOIG</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>U</td>
<td>1111</td>
<td>4</td>
<td>ICLC</td>
<td class="cellRight">PDLY</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>11</td>
<td>2</td>
<td>SD</td>
<td>TN</td>
<td>V</td>
<td>1</td>
<td>1</td>
<td>L</td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>X</td>
<td>1111111</td>
<td>7</td>
<td>LILRILN</td>
<td class="cellRight">PZBUBL</td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>111111</td>
<td>6</td>
<td>OPOOOE</td>
<td>ESHMMG</td>
<td>Y</td>
<td>11</td>
<td>2</td>
<td>LC</td>
<td class="cellRight">DLJ</td>
</tr>
<tr>
<td class="cellLeft">Z</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>Z</td>
<td>1</td>
<td>1</td>
<td>R</td>
<td class="cellRight">H <span class="pagenum">[<a id="pb67" href=
"#pb67" name="pb67">67</a>]</span></td>
</tr>
<tr class="label">
<td colspan="5" class="cellHeadLeft"><span class="sc">Fifth
Alphabet</span></td>
<td colspan="5" class="cellHeadRight"><span class="sc">Sixth
Alphabet</span></td>
</tr>
<tr class="label">
<td class="cellHeadLeft cellHeadBottom"></td>
<td class="cellHeadBottom">Letter</td>
<td class="cellHeadBottom"></td>
<td class="cellHeadBottom">Prefix (4)</td>
<td class="cellHeadBottom">Suffix (6)</td>
<td class="cellHeadBottom"></td>
<td class="cellHeadBottom">Letter</td>
<td class="cellHeadBottom"></td>
<td class="cellHeadBottom">Prefix (5)</td>
<td class="cellHeadRight cellHeadBottom">Suffix (1)</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>A</td>
<td>1</td>
<td>1</td>
<td>B</td>
<td class="cellRight">X</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>11</td>
<td>2</td>
<td>XX</td>
<td>EA</td>
<td>B</td>
<td>11</td>
<td>2</td>
<td>UU</td>
<td class="cellRight">RR</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>1111111</td>
<td>7</td>
<td>GDDSDSD</td>
<td>OOFFOEV</td>
<td>C</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>111111</td>
<td>6</td>
<td>SCPYNCU</td>
<td>UEUUQTQ</td>
<td>D</td>
<td>1111</td>
<td>4</td>
<td>UNLU</td>
<td class="cellRight">ANSA</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>11</td>
<td>2</td>
<td>SH</td>
<td>TP</td>
<td>E</td>
<td>1111111111111</td>
<td>13</td>
<td>MHOIDPZZMBQUC</td>
<td class="cellRight">RREOIQPNRIBQB</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>F</td>
<td>1111111</td>
<td>7</td>
<td>PCCJEOC</td>
<td class="cellRight">NIIBMVT</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>1</td>
<td>1</td>
<td>U</td>
<td>T</td>
<td>G</td>
<td>1</td>
<td>1</td>
<td>U</td>
<td class="cellRight">P</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>111111</td>
<td>6</td>
<td>CCSDGZ</td>
<td>EOOYYS</td>
<td>H</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>11111</td>
<td>5</td>
<td>EGTSS</td>
<td>EYOMV</td>
<td>I</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>111</td>
<td>3</td>
<td>EPX</td>
<td>UOP</td>
<td>J</td>
<td>11</td>
<td>2</td>
<td>UM</td>
<td class="cellRight">TT</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>111111</td>
<td>6</td>
<td>YDUCNX</td>
<td>UDYQQU</td>
<td>L</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>111</td>
<td>3</td>
<td>RQR</td>
<td>EJE</td>
<td>M</td>
<td>11</td>
<td>2</td>
<td>UI</td>
<td class="cellRight">TZ</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>1</td>
<td>1</td>
<td>R</td>
<td>D</td>
<td>N</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>111</td>
<td>3</td>
<td>STT</td>
<td>ETF</td>
<td>O</td>
<td>111111111</td>
<td>9</td>
<td>HCJCHCVIG</td>
<td class="cellRight">BLIBBIQYB</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>11</td>
<td><span class="corr" id="xd21e18964" title="Source: 0">2</span></td>
<td>UX</td>
<td>FE</td>
<td>P</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>1</td>
<td>1</td>
<td>E</td>
<td>E</td>
<td>Q</td>
<td>1111</td>
<td>4</td>
<td>DDLL</td>
<td class="cellRight">XTXX</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>R</td>
<td></td>
<td>0</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>S</td>
<td>11</td>
<td>2</td>
<td>HT</td>
<td class="cellRight">BI</td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td>1</td>
<td>1</td>
<td>L</td>
<td>S</td>
<td>T</td>
<td>111</td>
<td>3</td>
<td>OED</td>
<td class="cellRight">DDX</td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td>1111111111</td>
<td>10</td>
<td>MMGPXMMVMD</td>
<td>JDGUMYEBBD</td>
<td>U</td>
<td>1111111</td>
<td>7</td>
<td>JDDDLUL</td>
<td class="cellRight">ZTVAQZN</td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td>1</td>
<td>1</td>
<td>S</td>
<td>O</td>
<td>V</td>
<td>11</td>
<td>2</td>
<td>CI</td>
<td class="cellRight">TI</td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td></td>
<td>0</td>
<td></td>
<td></td>
<td>X</td>
<td><span class="corr" id="xd21e19119" title=
"Not in source">1</span></td>
<td>0</td>
<td>I</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td>1</td>
<td>1</td>
<td>U</td>
<td>F</td>
<td>Y</td>
<td>11111</td>
<td>5</td>
<td>IHLUH</td>
<td class="cellRight">XDRRT</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom">11</td>
<td class="cellBottom">2</td>
<td class="cellBottom">XN</td>
<td class="cellBottom">EE</td>
<td class="cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom">0</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">We will now set down some of the determinations which
can be made at once from these frequency tables. Clearly several mixed
alphabets have been used. As was to be expected from the analysis of
the recurring groups, we note that the frequency tables for alphabets 2
and 6 are of so nearly the same general form that certainly these two
alphabets are one and the same. If a Spanish word has been used as a
key word, this means that <span class="tt">A</span> is probably
represented by a vowel in these two alphabets and probably equals
<span class="tt">A</span> or <span class="tt">O</span>, because these
two letters are such common finals in Spanish.</p>
<p class="par">1st Alphabet. Probable vowels <span class="tt">T</span>,
<span class="tt">X</span>; probable common consonants, <span class=
"tt">B</span>, <span class="tt">I</span>, <span class="tt">N</span>,
<span class="tt">R</span>. We conclude this because of the frequency of
occurrence of <span class="tt">T</span> and <span class="tt">X</span>
and the variety of their prefixes and suffixes. On the other hand,
<span class="tt">B</span>, <span class="tt">I</span>, <span class=
"tt">N</span>, and <span class="tt">R</span> have for prefixes and
suffixes, in a majority of cases, <span class="tt">E</span>,
<span class="tt">F</span>, <span class="tt">O</span> and <span class=
"tt">S</span> which are the probable vowels in the 2d and 6th
alphabets.</p>
<p class="par">2d and 6th Alphabets.&mdash;Probable vowels <span class=
"tt">E</span>, <span class="tt">F</span>, <span class="tt">O</span>,
<span class="tt">S</span>; probable common consonants, <span class=
"tt">D</span>, <span class="tt">J</span>, <span class="tt">Q</span>,
<span class="tt">U</span>, <span class="tt">Y</span>. <span class=
"pagenum">[<a id="pb68" href="#pb68" name="pb68">68</a>]</span></p>
<p class="par">3d Alphabet.&mdash;Probable vowels <span class=
"tt">C</span>, <span class="tt">I</span>, <span class="tt">L</span>;
probable common consonants <span class="tt">A</span>, <span class=
"tt">Q</span>, <span class="tt">T</span>, <span class=
"tt">Y</span>.</p>
<p class="par">4th Alphabet.&mdash;Probable vowels, <span class=
"tt">E</span>, <span class="tt">G</span>, <span class="tt">S</span>,
<span class="tt">T</span>; probable common consonants, <span class=
"tt">C</span>, <span class="tt">M</span>, <span class="tt">N</span>,
<span class="tt">P</span>, <span class="tt">U</span>, <span class=
"tt">X</span>.</p>
<p class="par">5th Alphabet.&mdash;Probable vowels, <span class=
"tt">D</span>, <span class="tt">L</span>, <span class="tt">U</span>;
probable common consonants, <span class="tt">C</span>, <span class=
"tt">H</span>, <span class="tt">I</span>.</p>
<p class="par">Now this cipher may have been made up from five distinct
alphabets with letters chosen at random but it is much more likely to
have been prepared with a cipher disk or equivalent, having the regular
alphabet on the fixed disk and the mixed alphabet on the movable disk.
An equivalent form of apparatus (not using the mixed alphabet in
question) is one like this:</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td colspan="3" class="xd21e14894 cellLeft cellRight cellTop"><b>Fixed
Alphabet of Text</b></td>
</tr>
<tr>
<td colspan="3" class="xd21e14898 cellLeft cellRight"><span class=
"tt">ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ</span></td>
</tr>
<tr>
<td class="xd21e14902 cellLeft"></td>
<td class="xd21e14894"><span class=
"tt">PCJVRQZBAODFSUTMXIYHLGEN</span></td>
<td class="xd21e14902 cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="xd21e14912 cellBottom"><b>Movable Alphabet of
Cipher</b></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Here <span class="tt">A</span> of the plain text is
enciphered by <span class="tt">S</span> and the other letters come as
they will. If we move the cipher alphabet one space to the left,
<span class="tt">A</span> will be enciphered by <span class=
"tt">U</span> and the whole sequence of the alphabet will be
changed.</p>
<p class="par">We will therefore use some such form as the above and
see if we can insert our letters, as they are determined, in such a way
as to have each of the cipher slips identical. We may start thus:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="xd21e7910 cellRight cellTop">
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ</td>
</tr>
<tr>
<td class="cellLeft">1st <i>Alphabet</i></td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;x</td>
</tr>
<tr>
<td class="cellLeft">2d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ol&nbsp;qei&nbsp;ms&nbsp;&nbsp;d&nbsp;c&nbsp;u</td>
</tr>
<tr>
<td class="cellLeft">3d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ol&nbsp;qei&nbsp;ms&nbsp;&nbsp;d&nbsp;c&nbsp;u</td>
</tr>
<tr>
<td class="cellLeft">4th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ol&nbsp;qei&nbsp;ms&nbsp;&nbsp;d&nbsp;c&nbsp;u</td>
</tr>
<tr>
<td class="cellLeft">5th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;d&nbsp;c&nbsp;u&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ol&nbsp;qei&nbsp;&nbsp;ms</td>
</tr>
<tr>
<td class="cellLeft cellBottom">6th</td>
<td class="xd21e7910 cellRight cellBottom">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;ol&nbsp;qei&nbsp;ms&nbsp;&nbsp;d&nbsp;c&nbsp;&nbsp;u</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">In the 1st alphabet, <span class="tt">T</span> and
<span class="tt">X</span> are placed as <span class="tt">A</span> and
<span class="tt">E</span> respectively on the basis of frequency. In
the 2d and 6th alphabets, <span class="tt">O</span> and <span class=
"tt">E</span> are placed as <span class="tt">A</span> and <span class=
"tt">E</span> respectively on the basis of frequency. In the 4th
<span class="pagenum">[<a id="pb69" href="#pb69" name=
"pb69">69</a>]</span>alphabet, <span class="tt">E</span> and
<span class="tt">S</span> are placed as <span class="tt">A</span> and
<span class="tt">E</span>, and in the 5th, <span class="tt">D</span>,
<span class="tt">U</span> and <span class="tt">L</span> are placed as
<span class="tt">A</span>, <span class="tt">E</span> and <span class=
"tt">O</span> for the same reason. We now have an excess of E&rsquo;s
and a deficiency of A&rsquo;s, which will be corrected if, in the 3d
alphabet, we place <span class="tt">L</span>, <span class="tt">I</span>
and <span class="tt">C</span> as <span class="tt">A</span>,
<span class="tt">E</span> and <span class="tt">O</span> respectively.
As a check, this gives us <span class="tt">TOLEDO</span> as the key
word.</p>
<p class="par">In the second alphabet, <span class="tt">O</span> is
four letters to the left of <span class="tt">E</span>; we may place
<span class="tt">O</span> four letters to the left of <span class=
"tt">E</span> in the fourth and it comes under <span class=
"tt">V</span>. Note that in the fourth frequency table <span class=
"tt">O</span> (= <span class="tt">V</span>) does not occur. In the same
way in the fourth alphabet, <span class="tt">S</span> is four letters
to the right of <span class="tt">E</span>; placing it in the same
position with respect to <span class="tt">E</span> in the second and
sixth, we have <span class="tt">S</span> under <span class=
"tt">I</span>. We have already noted that <span class="tt">S</span>
probably represents a vowel in these two alphabets. In this way, we may
add <span class="tt">D</span> and <span class="tt">U</span> to the
third alphabet from their position in the fifth with respect to
<span class="tt">L</span> and we may add <span class="tt">I</span> and
<span class="tt">O</span> to the fifth from their position in the third
with respect to <span class="tt">L</span>. In every case we check
results from the frequency tables and find nothing unlikely in the
results.</p>
<p class="par">Now in the second and sixth, let us try <span class=
"tt">Q</span>, <span class="tt">D</span> and <span class="tt">U</span>
as <span class="tt">D</span>, <span class="tt">N</span> and
<span class="tt">R</span> respectively. We may add these letters to the
third, fourth and fifth alphabets by the method of observing the number
of letters to the right or left of some letter already fixed. We now
add <span class="tt">L</span> to the second, third, fourth and sixth
from its position with reference to <span class="tt">D</span> and
<span class="tt">U</span> in the fifth. <span class="tt">M</span> is
probably <span class="tt">D</span> in the fourth and we may add it to
each of the alphabets, except the first, in the same way. The table is
now complete as shown.</p>
<p class="par">Let us try these letters on the first line of the
message and see if some other letters will be self-evident.</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop">Alphabet</td>
<td class="cellTop">1&nbsp;</td>
<td class="cellTop">2&nbsp;</td>
<td class="cellTop">3&nbsp;</td>
<td class="cellTop">4&nbsp;</td>
<td class="cellTop">5&nbsp;</td>
<td class="cellTop">6&nbsp;</td>
<td class="cellTop">1&nbsp;</td>
<td class="cellTop">2&nbsp;</td>
<td class="cellTop">3&nbsp;</td>
<td class="cellTop">4&nbsp;</td>
<td class="cellTop">5&nbsp;</td>
<td class="cellTop">6&nbsp;</td>
<td class="cellTop">1&nbsp;</td>
<td class="cellTop">2&nbsp;</td>
<td class="cellTop">3&nbsp;</td>
<td class="cellTop">4&nbsp;</td>
<td class="cellTop">5&nbsp;</td>
<td class="cellTop">6&nbsp;</td>
<td class="cellTop">1&nbsp;</td>
<td class="cellTop">2&nbsp;</td>
<td class="cellTop">3&nbsp;</td>
<td class="cellTop">4&nbsp;</td>
<td class="cellTop">5&nbsp;</td>
<td class="cellTop">6&nbsp;</td>
<td class="cellTop">1&nbsp;</td>
<td class="cellTop">2&nbsp;</td>
<td class="cellTop">3&nbsp;</td>
<td class="cellTop">4&nbsp;</td>
<td class="cellTop">5&nbsp;</td>
<td class="cellRight cellTop">6</td>
</tr>
<tr>
<td class="cellLeft">Message</td>
<td>D&nbsp;</td>
<td>D&nbsp;</td>
<td>L&nbsp;</td>
<td>R&nbsp;</td>
<td>M&nbsp;</td>
<td>E&nbsp;</td>
<td>R&nbsp;</td>
<td>G&nbsp;</td>
<td>L&nbsp;</td>
<td>M&nbsp;</td>
<td>U&nbsp;</td>
<td>J&nbsp;</td>
<td>T&nbsp;</td>
<td>L&nbsp;</td>
<td>L&nbsp;</td>
<td>C&nbsp;</td>
<td>H&nbsp;</td>
<td>E&nbsp;</td>
<td>R&nbsp;</td>
<td>S&nbsp;</td>
<td>L&nbsp;</td>
<td>S&nbsp;</td>
<td>O&nbsp;</td>
<td>E&nbsp;</td>
<td>E&nbsp;</td>
<td>S&nbsp;</td>
<td>M&nbsp;</td>
<td>E&nbsp;</td>
<td>J&nbsp;</td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Deciphered</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">N&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">U&nbsp;</td>
<td class="cellBottom">E&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">D&nbsp;</td>
<td class="cellBottom">E&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">B&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">L&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">E&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">I&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">E&nbsp;</td>
<td class="cellBottom">N&nbsp;</td>
<td class="cellBottom">E&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellBottom">I&nbsp;</td>
<td class="cellBottom">G&nbsp;</td>
<td class="cellBottom">A&nbsp;</td>
<td class="cellBottom">_&nbsp;</td>
<td class="cellRight cellBottom">R</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb70" href="#pb70" name=
"pb70">70</a>]</span></p>
<p class="par">Referring to our frequency tables as a check on
suppositions, we find everything agrees well enough if we assume the
first line to read:</p>
<div class="q">
<p class="par first xd21e152"><span class="tt"><span class=
"underline">U</span>NA<span class="underline">F</span>UE<span class=
"underline">RZ</span>A DE <span class=
"underline">C</span>ABAL<span class="underline">L</span>E<span class=
"underline">R</span>IA ENE<span class=
"underline">M</span>IGA</span></p>
</div>
<p class="par"></p>
<p class="par">We will now put the newly found letters in the table.
The letters previously found are in capitals and the new letters in
small letters. The addition of <span class="tt">D</span> <span class=
"tt">(=U</span>) to the first alphabet permits us to add all the
letters of the other alphabets to the first by the methods already
discussed. Each of the other letters may then be added to every
alphabet by these methods:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="xd21e7910 cellRight cellTop">
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ</td>
</tr>
<tr>
<td class="cellLeft">1st</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;T&nbsp;&nbsp;&nbsp;xhgoljqei&nbsp;msr&nbsp;&nbsp;d&nbsp;c&nbsp;u</td>
</tr>
<tr>
<td class="cellLeft">2d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;xhgOLjQEI&nbsp;MSr&nbsp;&nbsp;D&nbsp;C&nbsp;U</td>
</tr>
<tr>
<td class="cellLeft">3d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;xhgOLjQEI&nbsp;MSr&nbsp;&nbsp;D&nbsp;C&nbsp;U</td>
</tr>
<tr>
<td class="cellLeft">4th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;xhgOLjQEI&nbsp;MSr&nbsp;&nbsp;D&nbsp;C&nbsp;U</td>
</tr>
<tr>
<td class="cellLeft">5th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;xhgOLjQEI&nbsp;MSr&nbsp;&nbsp;D&nbsp;C&nbsp;U</td>
</tr>
<tr>
<td class="cellLeft cellBottom">6th</td>
<td class="xd21e7910 cellRight cellBottom">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;t&nbsp;&nbsp;&nbsp;xhgOLjQEI&nbsp;MSr&nbsp;&nbsp;D&nbsp;C&nbsp;U</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">One alphabet checks another in this way and we find
everything to fit so far. We will decipher a few words more of the
cipher message by the above alphabets and see if we can determine some
new letters.</p>
<div class="table">
<table>
<tr>
<td class="xd21e6306 cellLeft cellRight cellTop"><i>Alphabet</i></td>
</tr>
<tr>
<td class="cellLeft cellRight">
5612345612345612345612345612345612345612345612345612345612</td>
</tr>
<tr>
<td class="xd21e6306 cellLeft cellRight"><i>Message</i></td>
</tr>
<tr>
<td class="cellLeft cellRight">
JUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQ</td>
</tr>
<tr>
<td class="xd21e6306 cellLeft cellRight"><i>Deciphered</i></td>
</tr>
<tr>
<td class="cellLeft cellRight cellBottom">
PR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_ED</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Again referring to the frequency tables the first word
is evidently <span class="tt">PR<span class=
"underline">O</span>CEDEN<span class="underline">T</span>E</span>. We
have also <span class="tt">HA<span class="underline">L</span>LA</span>
and <span class="tt"><span class="underline">M</span>AR<span class=
"underline">C</span>HEUS<span class="underline">T</span>ED</span>. The
letter <span class="tt">B</span> may be determined from another cipher
group, <span class="tt">JF<span class="underline">B</span>SQDLD</span>
(56<span class="underline">1</span>23456) = <span class=
"tt">PO<span class="underline">S</span>ICION</span>. The letter
<span class="tt">N</span> may be determined from <span class=
"tt">BET<span class="underline">N</span>DQXUC</span> (123<span class=
"underline">4</span>56123) = <span class="tt">SER<span class=
"underline">R</span>ADERO</span>. The letters <span class="tt">F</span>
and <span class="tt">Y</span> may be determined from <span class=
"tt">JCPJOISL<span class="underline">Y</span>DUASIUP<span class=
"underline">F</span></span> (23456123<span class=
"underline">4</span>5612345<span class="underline">6</span>)=
<span class="pagenum">[<a id="pb71" href="#pb71" name=
"pb71">71</a>]</span><span class="tt">COMPANIA PARTIENDO</span>. The
completed alphabets, arranged as before, are:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="xd21e7910 cellRight cellTop">
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ</td>
</tr>
<tr>
<td class="cellLeft">1st</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
<tr>
<td class="cellLeft">2d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
<tr>
<td class="cellLeft">3d</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
<tr>
<td class="cellLeft">4th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
<tr>
<td class="cellLeft">5th</td>
<td class="xd21e7910 cellRight">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
<tr>
<td class="cellLeft cellBottom">6th</td>
<td class="xd21e7910 cellRight cellBottom">
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;TYVNXHGOLJQEIZMSRBADFCPU</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The key word is <span class="tt">TOLEDO</span> and the
completely deciphered message is:</p>
<div class="blockquote">
<p lang="es" class="par first">&ldquo;Una fuerza de caballeria enemiga
procedente de Aranjuez y Villaseca se halla en Azucaica. Marche usted
con su compania partiendo de la casa de la serradero por las alturas de
lo este y norte de Azucaica con el fin de reconocer su numero y clase
de fuerzas y en disposicion que se halla. (Q) Esta acantonada (Q) Se
hallan otras tropas detras de ella (Q). El resultado del reconocimiento
necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus
ordenes un ciclista (X) Fin.&rdquo;</p>
</div>
<p class="par"></p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Special Solution for Case 7</h3>
</div>
<div class="divBody">
<p class="par first">When a short message is enciphered with a long key
word, the methods of analysis already discussed may fail; first,
because there will be no recurring pairs to indicate the number of
alphabets used and, second, because there will be so few letters in
each alphabet that the methods of Case 6 will not be easily
applied.</p>
<p class="par">However, if we know or correctly assume one word,
preferably a fairly long one, in the cipher text, a solution is very
simple. For example, the following message is believed to refer to
re&euml;nforcements and to contain that word.</p>
<div class="table">
<table>
<tr>
<td class="xd21e10023 cellLeft cellTop">YANZV</td>
<td class="xd21e10023 cellTop">ZNLPP</td>
<td class="xd21e10023 cellTop">KQFXI</td>
<td class="cellRight cellTop">JBPWA</td>
</tr>
<tr>
<td class="xd21e10023 cellLeft cellBottom">NRUQP</td>
<td class="xd21e10023 cellBottom">EPLOM</td>
<td class="xd21e10023 cellBottom">CCWHM</td>
<td class="cellRight cellBottom">I</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb72" href="#pb72" name=
"pb72">72</a>]</span></p>
<p class="par">Let us assume that <span class=
"tt">REINFORCEMENTS</span> is the first word and that it is represented
by the cipher group <span class="tt">YANZVZNLPPKQFX</span>. We may put
the test in this tabular form, using a cipher disk and a Larrabee
cipher card to determine the value of <span class="tt">A</span> for
each letter under these two systems. Any other alphabets suspected may
be tried out at the same time.</p>
<p class="par">If</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">Y</td>
<td class="cellTop cellBottom">A</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">Z</td>
<td class="cellTop cellBottom">V</td>
<td class="cellTop cellBottom">Z</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">L</td>
<td class="cellTop cellBottom">P</td>
<td class="cellTop cellBottom">P</td>
<td class="cellTop cellBottom">K</td>
<td class="cellTop cellBottom">Q</td>
<td class="cellTop cellBottom">F</td>
<td class="cellRight cellTop cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">equals</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">R</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">I</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">F</td>
<td class="cellTop cellBottom">O</td>
<td class="cellTop cellBottom">R</td>
<td class="cellTop cellBottom">C</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">M</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">T</td>
<td class="cellRight cellTop cellBottom">S</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">then, with cipher disk, <span class="tt">A</span>
equals</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">P</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">R</td>
<td class="cellTop cellBottom">M</td>
<td class="cellTop cellBottom">A</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">T</td>
<td class="cellTop cellBottom">B</td>
<td class="cellTop cellBottom">O</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">Y</td>
<td class="cellRight cellTop cellBottom">P</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and, in Vigenere cipher, <span class="tt">A</span>
equals</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">H</td>
<td class="cellTop cellBottom">W</td>
<td class="cellTop cellBottom">F</td>
<td class="cellTop cellBottom">M</td>
<td class="cellTop cellBottom">Q</td>
<td class="cellTop cellBottom">L</td>
<td class="cellTop cellBottom">W</td>
<td class="cellTop cellBottom">J</td>
<td class="cellTop cellBottom">L</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">G</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">M</td>
<td class="cellRight cellTop cellBottom">F</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It is evident that the guess as to the appearance of the
word <span class="tt">REINFORCEMENTS</span> was correct, that it is the
first word of the message, that the cipher disk was used in preparing
the cipher and that the key words are <span class="tt">PERMANENT
BODY</span>.</p>
<p class="par">This is, of course, an especially favorable case and we
will take one less favorable to show how this method can be
applied.</p>
<p class="par">Two Mexican chieftains, A and B, have been communicating
with the following cipher alphabet:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">Plain text</td>
<td class="xd21e7910 cellRight cellTop">ABCDEFGHIJLMNOPQRSTUVXYZ</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Cipher</td>
<td class="xd21e7910 cellRight cellBottom">
PCJVRQZBAODFSUTMXIYHLGEN</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This alphabet has been determined from many radio
messages from A, the superior, to B, his sub-ordinate, who has a force
of about 2,000 men near the border. A uses the form ORDENO QUE instead
of the more familiar MANDO QUE in all his messages giving orders to B.
The following message is received from A by B&rsquo;s radio station
(and other listening stations) and about an hour <span class=
"pagenum">[<a id="pb73" href="#pb73" name="pb73">73</a>]</span>later
there is a good deal of noise and movement as if B&rsquo;s force were
breaking camp.</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">IIHAH</td>
<td class="cellTop">YDXRP</td>
<td class="cellTop">EGQGV</td>
<td class="cellTop">JJEEE</td>
<td class="cellRight cellTop">HOBGV</td>
</tr>
<tr>
<td class="cellLeft">GJCAG</td>
<td>XAESA</td>
<td>VVXLE</td>
<td>IILHM</td>
<td class="cellRight">PSQAG</td>
</tr>
<tr>
<td class="cellLeft cellBottom">BDGAV</td>
<td class="cellBottom">GSQAZ</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is a substitution cipher, but it is not Case 6
using the usual alphabet of the communications from A to B and, in
fact, is not Case 6 at all. The recurring pairs and triplets point to a
key word of ten letters and this would give us but six letters per
alphabet if it is Case 7.</p>
<p class="par">The preparations for a move lead us to believe that A
has given an order to B and he has, in that case, probably used the
expression ORDENO QUE in the message. We will try the first nine
letters of the message as in the other example, first preparing a
cipher disk or equivalent sliding arrangement having on it the alphabet
usually used between these chieftains or A-B cipher.</p>
<div class="table">
<table class="xd21e14892">
<tr>
<td colspan="3" class="xd21e14894 cellLeft cellRight cellTop"><b>Fixed
Cipher Alphabet</b></td>
</tr>
<tr>
<td colspan="3" class="xd21e14898 cellLeft cellRight"><span class=
"tt">PCJVRQZBAODFSUTMXIYHLGENPCJVRQZBAODFSUTMXIYHLGEN</span></td>
</tr>
<tr>
<td class="xd21e14902 cellLeft"></td>
<td class="xd21e14894"><span class=
"tt">ABCDEFGHIJLMNOPQRSTUVXYZ</span></td>
<td class="xd21e14902 cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="xd21e14912 cellBottom"><b>Sliding Plain Text
Alphabet</b></td>
</tr>
</table>
</div>
<p class="par"></p>
<div class="table">
<table>
<tr>
<td colspan="6" class="xd21e6306 cellLeft cellRight cellTop"><i>A-B
Cipher</i></td>
</tr>
<tr>
<td class="cellLeft">If</td>
<td>I</td>
<td>equals</td>
<td>O</td>
<td>then A equals</td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>I</td>
<td></td>
<td>R</td>
<td></td>
<td class="cellRight">C</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>H</td>
<td></td>
<td>D</td>
<td></td>
<td class="cellRight">X</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>A</td>
<td></td>
<td>E</td>
<td></td>
<td class="cellRight">R</td>
</tr>
<tr>
<td class="cellLeft"></td>
<td>H</td>
<td></td>
<td>N</td>
<td></td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">Y</td>
<td class="cellBottom"></td>
<td class="cellBottom">O</td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom">Q</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Clearly there is nothing here and the assumed words, if
they occur, are in the middle of the message. We may jump to the
combination <span class="tt">PEGQGV</span> at once since the preceding
letters do not make <span class="tt">ORDENO QUE</span>. We try this
without result and proceed to <span class="tt">EGQGVJ</span>,
<span class="tt">GQGVJJ</span>, <span class="tt">QGVJJE</span>,
<span class="tt">GVJJEE</span>, <span class="pagenum">[<a id="pb74"
href="#pb74" name="pb74">74</a>]</span><span class="tt">VJJEEE</span>,
<span class="tt">JJEEEH</span>, <span class="tt">JEEEHO</span>,
<span class="tt">EEEHOB</span>, <span class="tt">EEHOBG</span>,
<span class="tt">EHOBGV</span>, <span class="tt">HOBGVG</span>,
<span class="tt">OBGVGJ</span>, <span class="tt">BGVGJC</span>,
<span class="tt">GVGJCA</span>, <span class="tt">VGJCAG</span>, all
without result. This work requires less time than might be imagined and
is the kind of work which can be divided among a number of operators.
Now let us come to the next combination <span class="tt">GJCAGX</span>.
We add the next three letters, <span class="tt">AES</span>, against
<span class="tt">QUE</span>.</p>
<p class="par">If</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">G</td>
<td class="cellTop cellBottom">J</td>
<td class="cellTop cellBottom">C</td>
<td class="cellTop cellBottom">A</td>
<td class="cellTop cellBottom">G</td>
<td class="cellTop cellBottom">X</td>
<td class="cellTop cellBottom"></td>
<td class="cellTop cellBottom">A</td>
<td class="cellTop cellBottom">E</td>
<td class="cellRight cellTop cellBottom">S</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">equals</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">O</td>
<td class="cellTop cellBottom">R</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">O</td>
<td class="cellTop cellBottom"></td>
<td class="cellTop cellBottom">Q</td>
<td class="cellTop cellBottom">U</td>
<td class="cellRight cellTop cellBottom">E</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Then, in the A-B cipher, A equals</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">A</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">R</td>
<td class="cellTop cellBottom">O</td>
<td class="cellTop cellBottom">V</td>
<td class="cellTop cellBottom"></td>
<td class="cellTop cellBottom">I</td>
<td class="cellTop cellBottom">V</td>
<td class="cellRight cellTop cellBottom">A</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The key is found; <span class="tt">VIVA_ADERO</span> and
a trial of <span class="tt">M</span> in the blank space shows correct
results. This checks with our theory that a ten letter key word was
used and deciphering the message we have:</p>
<div class="blockquote">
<p class="par first">PARA EL ATAQUE CONTRA TORREON ORDENO QUE SUS
TROPAS MARCHEN ESTE NOCHE X.</p>
</div>
<p class="par"></p>
<p class="par">The reason for breaking camp is now evident.</p>
<p class="par">This method may be used, with some labor, on short words
like <span class="tt">THE</span>, <span class="tt">AND</span>, etc.
Parts of the key will appear whenever an assumed word is found in the
message and the whole key may be assembled if enough of the parts are
available. Even if only part of the key may be so recovered, it will
always lead to the ultimate solution of the cipher by trial of the
partially recovered key on the message letter by letter.</p>
<p class="par">As an example of recovery of a key by use of short
common words, let us refer to the message of Case <a href=
"#c7a">7-a</a>. There are twenty-four groups of three letters each in
this message and we will try them against <span class="tt">THE</span>,
<span class="tt">ARE</span> and <span class="tt">YOU</span>, assuming
that the Vigenere cipher is used. <span class="pagenum">[<a id="pb75"
href="#pb75" name="pb75">75</a>]</span></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">1</td>
<td class="cellTop">2</td>
<td class="cellTop">3</td>
<td class="cellTop">4</td>
<td class="cellTop">5</td>
<td class="cellTop">6</td>
<td class="cellTop">7</td>
<td class="cellTop">8</td>
<td class="cellTop">9</td>
<td class="cellTop">10</td>
<td class="cellTop">11</td>
<td class="cellRight cellTop">12</td>
</tr>
<tr>
<td class="cellLeft">If</td>
<td>OSB</td>
<td>VOI</td>
<td>GSW</td>
<td>CYY</td>
<td>ZSZ</td>
<td>BVJ</td>
<td>XLD</td>
<td>OSY</td>
<td>UVD</td>
<td>YJL</td>
<td>SQA</td>
<td class="cellRight">HSI</td>
</tr>
<tr>
<td class="cellLeft">equals</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td class="cellRight">THE</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td class="cellRight">ARE</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td class="cellRight">YOU</td>
</tr>
<tr>
<td class="cellLeft">then <span class="tt">A</span> equals</td>
<td>VLX</td>
<td>CHE</td>
<td>NLS</td>
<td>JRU</td>
<td>GLV</td>
<td>IOF</td>
<td>EEZ</td>
<td>VLU</td>
<td>BOZ</td>
<td><span class="underline">FCH</span></td>
<td>ZJW</td>
<td class="cellRight">OLE</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>OBX</td>
<td>VXE</td>
<td>GBS</td>
<td>CHU</td>
<td>ZBV</td>
<td><span class="underline">BEF</span></td>
<td>XUZ</td>
<td>OBU</td>
<td>UEZ</td>
<td>YSH</td>
<td>SZW</td>
<td class="cellRight"><span class="underline">HBE</span></td>
</tr>
<tr>
<td class="cellLeft cellBottom">or</td>
<td class="cellBottom">QEH</td>
<td class="cellBottom">XAO</td>
<td class="cellBottom">IEC</td>
<td class="cellBottom">EKE</td>
<td class="cellBottom"><span class="underline">BEF</span></td>
<td class="cellBottom">DHP</td>
<td class="cellBottom">ZXJ</td>
<td class="cellBottom">QEE</td>
<td class="cellBottom">WHJ</td>
<td class="cellBottom">AVR</td>
<td class="cellBottom">UCG</td>
<td class="cellRight cellBottom">JEO</td>
</tr>
</table>
</div>
<p class="par"></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">13</td>
<td class="cellTop">14</td>
<td class="cellTop">15</td>
<td class="cellTop">16</td>
<td class="cellTop">17</td>
<td class="cellTop">18</td>
<td class="cellTop">19</td>
<td class="cellTop">20</td>
<td class="cellTop">21</td>
<td class="cellTop">22</td>
<td class="cellTop">23</td>
<td class="cellRight cellTop">24</td>
</tr>
<tr>
<td class="cellLeft">If</td>
<td>BJV</td>
<td>SFX</td>
<td>DQB</td>
<td>AII</td>
<td>OHZ</td>
<td>IVX</td>
<td>JBF</td>
<td>ESF</td>
<td>JSC</td>
<td>NLU</td>
<td>CTW</td>
<td class="cellRight">CSM</td>
</tr>
<tr>
<td class="cellLeft">equals</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td>THE</td>
<td class="cellRight">THE</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td>ARE</td>
<td class="cellRight">ARE</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td>YOU</td>
<td class="cellRight">YOU</td>
</tr>
<tr>
<td class="cellLeft">then <span class="tt">A</span> equals</td>
<td>ICR</td>
<td>ZYT</td>
<td>KJX</td>
<td><span class="underline">HBE</span></td>
<td>VAV</td>
<td>POT</td>
<td>QUB</td>
<td>LLB</td>
<td>QLY</td>
<td>UEQ</td>
<td>JMS</td>
<td class="cellRight">JLI</td>
</tr>
<tr>
<td class="cellLeft">or</td>
<td>BSR</td>
<td>SOT</td>
<td>DZX</td>
<td>ARE</td>
<td>OQV</td>
<td>IET</td>
<td>JKB</td>
<td>EBB</td>
<td>JBY</td>
<td>NUQ</td>
<td>CCS</td>
<td class="cellRight">CBI</td>
</tr>
<tr>
<td class="cellLeft cellBottom">or</td>
<td class="cellBottom">DVB</td>
<td class="cellBottom">URD</td>
<td class="cellBottom"><span class="underline">FCH</span></td>
<td class="cellBottom">YUO</td>
<td class="cellBottom">QTF</td>
<td class="cellBottom">KHD</td>
<td class="cellBottom">LNL</td>
<td class="cellBottom">GEL</td>
<td class="cellBottom">LEI</td>
<td class="cellBottom">PXA</td>
<td class="cellBottom"><span class="underline">EFC</span></td>
<td class="cellRight cellBottom">EES</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">In column 5, we have, for <span class="tt">YOU</span>,
the key <span class="tt">BEF</span>; column 6 gives the same key for
<span class="tt">ARE</span>; column 10 gives the key <span class=
"tt">FCH</span> for <span class="tt">THE</span> and column 15 gives the
same key for <span class="tt">YOU</span>; column 12 gives the key
<span class="tt">HBE</span> for <span class="tt">ARE</span> and column
16 gives the same key for <span class="tt">THE</span>; column 23 gives
the key <span class="tt">EFC</span> for <span class="tt">YOU</span>.
The only possible key for the message is a five-letter one made up of
the letters <span class="tt">BEFCH</span> or <span class=
"tt">EFCHB</span> or <span class="tt">FCHBE</span> or <span class=
"tt">CHBEF</span> or <span class="tt">HBEFC</span>. If the key in this
case were a word, we would have no difficulty in determining it; as it
is, there is no real difficulty in the matter as we may now divide the
message into blocks of five letters and note that <span class=
"tt">ZSZ</span> (= <span class="tt">YOU</span>) form the 3d, 4th and
5th letters of a group. The corresponding key letters, <span class=
"tt">BEF</span>, are then the 3d, 4th and 5th letters of the key which
must be <span class="tt">CHBEF</span>.</p>
<p class="par">This special solution for Case 7 depends so largely on
the intuition of the operator in choice of a word that it is not, in
general, advisable to use it unless the message is very short and the
regular methods of analysis have been tried unsuccessfully. It is,
however, a wonderfully short cut in difficult cases where the other
methods fail. <span class="pagenum">[<a id="pb76" href="#pb76" name=
"pb76">76</a>]</span></p>
</div>
</div>
</div>
<div class="footnotes">
<hr class="fnsep">
<p class="par footnote"><span class="label"><a class="noteref" id=
"xd21e15272" href="#xd21e15272src" name="xd21e15272">1</a></span> The
method used is not the most satisfactory one for several reasons and a
better method is that of writing the message in multiples of the key
and enciphering the columns as already described.&nbsp;<a class=
"fnarrow" href="#xd21e15272src">&uarr;</a></p>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="main">Chapter VIII</h2>
</div>
<div class="divBody">
<p class="par xd21e21132"><span class="xd21e21132init">C</span>ase 8.
The Playfair cipher. This is the English military field cipher; as the
method is published in English military manuals and as it is a cipher
of proven reliability, it may be met with in general cipher work. The
Playfair cipher operates with a key word; two letters are substituted
for each two letters of the text.</p>
<p class="par">The Playfair cipher may be recognized by the following
points: (a) It is a substitution cipher, (b) it always contains an even
number of letters, (c) when the cipher is divided into groups of two
letters each, no group consists of the repetition of the same letter as
<span class="tt">SS</span> or <span class="tt">BB</span>, (d) there
will be recurrence of pairs throughout the message, following in a
general way, the frequency table of digraphs of pairs, (e) in short
messages there may be recurrence of cipher groups representing words or
even phrases, and these will always be found in long messages.</p>
<p class="par">In preparing a cipher by this method, a key word is
chosen by the correspondents. A large square, divided into twenty-five
smaller squares, is constructed as shown below and the letters of the
key word are written in, beginning at the upper left hand corner. If
any letter recurs in the key word, it is only used on the first
occurrence. The remaining letters of the alphabet are used to fill up
the square. It is customary to consider <span class="tt">I</span> and
<span class="tt">J</span> as one letter in this cipher and they are
written together in the same square.</p>
<p class="par">If the key word chosen is <span class=
"tt">LEAVENWORTH</span>, then the square would be constructed as
follows: <span class="pagenum">[<a id="pb77" href="#pb77" name=
"pb77">77</a>]</span></p>
<p class="par"></p>
<div class="table">
<table class="xd21e11940">
<tr>
<td class="xd21e21158 cellLeft cellTop">L</td>
<td class="xd21e21158 cellTop">E</td>
<td class="xd21e21158 cellTop">A</td>
<td class="xd21e21158 cellTop">V</td>
<td class="xd21e21158 cellTop">N</td>
<td class="cellRight cellTop"></td>
</tr>
<tr>
<td class="xd21e21158 cellLeft">W</td>
<td class="xd21e21158">O</td>
<td class="xd21e21158">R</td>
<td class="xd21e21158">T</td>
<td class="xd21e21158">H</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e21158 cellLeft">B</td>
<td class="xd21e21158">C</td>
<td class="xd21e21158">D</td>
<td class="xd21e21158">F</td>
<td class="xd21e21158">G</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e21158 cellLeft">IJ</td>
<td class="xd21e21158">K</td>
<td class="xd21e21158">M</td>
<td class="xd21e21158">P</td>
<td class="xd21e21158">Q</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="xd21e21158 cellLeft cellBottom">S</td>
<td class="xd21e21158 cellBottom">U</td>
<td class="xd21e21158 cellBottom">X</td>
<td class="xd21e21158 cellBottom">Y</td>
<td class="xd21e21158 cellBottom">Z</td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The text of the message to be sent is then divided up
into groups of two letters each, and equivalents are found for each
pair.</p>
<p class="par">Every pair of letters in the square must be: Either (1)
in the same vertical line. Thus in the above example each letter is
represented in cipher by that which stands next below it, and the
bottom letter by the top one of the same column; for instance,
<span class="tt">TY</span> is represented by <span class=
"tt">FV</span>.</p>
<p class="par">Or (2) in the same horizontal line. Each letter in this
case is represented by that which stands next on its right, and the
letter on the extreme right by that on the extreme left of the same
horizontal line with it; for instance <span class="tt">RH</span> is
represented by <span class="tt">TW</span>.</p>
<p class="par">Or (3) at opposite corners of a rectangle. Each letter
of the pair is represented by the letter in the other corner of the
rectangle in the same horizontal line with it; for instance
<span class="tt">TS</span> is represented by <span class=
"tt">WY</span>.</p>
<p class="par">If, on dividing the letters of the text into pairs, it
is found that a pair consists of the same letter repeated, a dummy
letter, as <span class="tt">X</span>, <span class="tt">Y</span>, or
<span class="tt">Z</span>, should be introduced to separate the similar
letters.</p>
<p class="par">If the message to be sent were &ldquo;The enemy moves at
dawn,&rdquo; it would be divided into pairs:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">TH</td>
<td class="cellTop">EX</td>
<td class="cellTop">EN</td>
<td class="cellTop">EM</td>
<td class="cellTop">YM</td>
<td class="cellTop">OV</td>
<td class="cellTop">ES</td>
<td class="cellTop">AT</td>
<td class="cellTop">DA</td>
<td class="cellRight cellTop">WN</td>
</tr>
<tr>
<td class="cellLeft cellBottom">and enciphered:</td>
<td class="cellBottom">HW</td>
<td class="cellBottom">AU</td>
<td class="cellBottom">AL</td>
<td class="cellBottom">AK</td>
<td class="cellBottom">XP</td>
<td class="cellBottom">TE</td>
<td class="cellBottom">LU</td>
<td class="cellBottom">VR</td>
<td class="cellBottom">MR</td>
<td class="cellRight cellBottom">HL</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">The message is then broken up into groups of five
letters for transmission.</p>
<p class="par">To decipher such a cryptogram, (knowing the key word),
the receiver divides it into pairs, and <span class="pagenum">[<a id=
"pb78" href="#pb78" name="pb78">78</a>]</span>from his table finds the
equivalent of these pairs, taking the letter immediately above each,
when they are in the same vertical line; those immediately on the left,
when in the same horizontal line; and those at opposite angles of the
rectangle when this is formed.</p>
<p class="par">It is evident, from the foregoing description, that any
letter of the plain text may be represented in cipher by one of five
letters, viz: The one next below it and the other four letters in the
same horizontal line with it in the square. Take, for example, the
letter <span class="tt">D</span> of the plain text, in combination with
each of the other letters of the alphabet. We have, using the key
<span class="tt">LEAVENWORTH</span>:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop">DA</td>
<td class="cellTop">DB</td>
<td class="cellTop">DC</td>
<td class="cellTop">DE</td>
<td class="cellTop">DF</td>
<td class="cellTop">DG</td>
<td class="cellTop">DH</td>
<td class="cellTop">DI</td>
<td class="cellTop">DK</td>
<td class="cellTop">DL</td>
<td class="cellTop">DM</td>
<td class="cellTop">DN</td>
<td class="cellTop">DO</td>
<td class="cellTop">DP</td>
<td class="cellTop">DQ</td>
<td class="cellTop">DR</td>
<td class="cellTop">DS</td>
<td class="cellTop">DT</td>
<td class="cellTop">DU</td>
<td class="cellTop">DV</td>
<td class="cellTop">DW</td>
<td class="cellTop">DX</td>
<td class="cellTop">DY</td>
<td class="cellRight cellTop">DZ</td>
</tr>
<tr>
<td class="cellLeft cellBottom">MR</td>
<td class="cellBottom">FC</td>
<td class="cellBottom">FD</td>
<td class="cellBottom">CA</td>
<td class="cellBottom">FG</td>
<td class="cellBottom">FB</td>
<td class="cellBottom">GR</td>
<td class="cellBottom">BM</td>
<td class="cellBottom">CM</td>
<td class="cellBottom">BA</td>
<td class="cellBottom">MX</td>
<td class="cellBottom">GA</td>
<td class="cellBottom">CR</td>
<td class="cellBottom">FM</td>
<td class="cellBottom">GM</td>
<td class="cellBottom">MD</td>
<td class="cellBottom">BX</td>
<td class="cellBottom">FR</td>
<td class="cellBottom">CX</td>
<td class="cellBottom">FA</td>
<td class="cellBottom">BR</td>
<td class="cellBottom">MA</td>
<td class="cellBottom">FX</td>
<td class="cellRight cellBottom">GX</td>
</tr>
</table>
</div>
<p class="par"></p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">This gives <span class="tt">D</span>
represented by</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">M</td>
<td class="cellRight cellTop"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">4</td>
<td class="cellBottom">4</td>
<td class="cellBottom">8</td>
<td class="cellBottom">4</td>
<td class="cellBottom">4</td>
<td class="cellRight cellBottom">times,</td>
</tr>
</table>
</div>
<p class="par"></p>
<div class="table">
<table>
<tr>
<td colspan="10" class="cellLeft cellRight cellTop">and, connected with
these five letters representing <span class="tt">D</span>,</td>
</tr>
<tr>
<td class="cellLeft">we have</td>
<td>A</td>
<td>R</td>
<td>D</td>
<td>M</td>
<td>X</td>
<td>B</td>
<td>C</td>
<td>G</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft cellBottom"></td>
<td class="cellBottom">5</td>
<td class="cellBottom">5</td>
<td class="cellBottom">2</td>
<td class="cellBottom">4</td>
<td class="cellBottom">5</td>
<td class="cellBottom">1</td>
<td class="cellBottom">1</td>
<td class="cellBottom">1</td>
<td class="cellRight cellBottom">times.</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Note that these letters are those of the vertical column
containing <span class="tt">D</span> plus the letters <span class=
"tt">B</span>, <span class="tt">C</span> and <span class="tt">G</span>,
of the horizontal line containing <span class="tt">D</span>.</p>
<p class="par">Lieut. Frank Moorman, U. S. Army, has developed a method
for determining the letters which make up the key word in a Playfair
cipher. In the first place, a key word necessarily contains vowels in
the approximate proportion of two vowels to three consonants and it is
also likely that a key word will contain other common letters. This key
word is placed in the first row or rows. Now if a table is made,
showing what letters in the cipher occur with every letter, it will be
found that the letters having the greatest number of other letters in
combination with them are very likely to be letters of the key
<span class="pagenum">[<a id="pb79" href="#pb79" name=
"pb79">79</a>]</span>word, or in other words, letters occurring in the
first or second lines. An example will make this clear:</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="blockquote">
<p class="par first"><span class="tt">DB FN EX TZ MF TO VB QB QT OB XA
OF PR TZ EQ RH QK QV DX OK AB PR QI EL TV KE EX XS FS BP WD BO BY BF RO
EA BO RH QK QV TX GU EL AB TH TR XN ON EA AY XH BO HN EX BS HR QB ZM SE
XP HF GZ UG KC BD PO EA AY XH BO XP HF KR QI AB PR QI EL BX FZ BI SE FX
PB RA PR QI WC BR XD YG TB QT EA AY XH BO HN EX BS HR QB PR QI EL BX BT
HB QB NF SI SE BX NU XP BU RB XB QR OX BA TB RH BP WD RP RO GU GX QR SE
ZY OX BA EL AX CW BY BA SX RK RO PR HB OP BD PI CN OX EM RP KR XT EL AX
CW EQ FZ SX EL RH RO PR HB UX DA SE XN ZN GU EL BX FS DG DB TB ZL VE RH
BO RQ.</span></p>
</div>
<p class="par"></p>
<p class="par">From this message, we make up the following table,
considering the letters of each pair: <span class="pagenum">[<a id=
"pb80" href="#pb80" name="pb80">80</a>]</span></p>
<p class="par xd21e152"><i>First Letters of Pairs</i></p>
<div class="table">
<table class="borderAll xd21e21551">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">K</td>
<td class="cellTop">L</td>
<td class="cellTop">M</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellTop">S</td>
<td class="cellTop">T</td>
<td class="cellTop">U</td>
<td class="cellTop">V</td>
<td class="cellTop">W</td>
<td class="cellTop">X</td>
<td class="cellTop">Y</td>
<td class="cellRight cellTop">Z</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td></td>
<td>3</td>
<td></td>
<td>1</td>
<td>4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>3</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td>1</td>
<td>4</td>
<td>1</td>
<td></td>
<td>3</td>
<td></td>
<td>1</td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>5</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td>5</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>2</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>8</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td></td>
<td>6</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td>4</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>7</td>
<td>2</td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">S</td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">T</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">U</td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">V</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">W</td>
<td></td>
<td></td>
<td>2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">X</td>
<td>1</td>
<td>5</td>
<td></td>
<td>1</td>
<td>4</td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>3</td>
<td></td>
<td></td>
<td></td>
<td>2</td>
<td>1</td>
<td>1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">Y</td>
<td></td>
<td>5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">2</td>
<td class="cellBottom">1</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom">2</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">From this table we pick out the letters <span class=
"tt">B</span>, <span class="tt">E</span>, <span class="tt">F</span>,
<span class="tt">O</span>, <span class="tt">R</span>, <span class=
"tt">T</span>, <span class="tt">X</span>, as tentative letters of the
key word on account of the variety of other letters with which they
occur. As there are but two vowels for seven letters, we will add
<span class="tt">A</span> to the list on account of its occurrences
with <span class="tt">B</span>, <span class="tt">D</span>, <span class=
"tt">E</span>, <span class="tt">R</span>, and <span class=
"tt">X</span>. This leaves the letters for the bottom lines of the
square as follows: <span class="pagenum">[<a id="pb81" href="#pb81"
name="pb81">81</a>]</span></p>
<div class="table">
<table class="borderAll">
<tr>
<td class="cellLeft cellTop">.</td>
<td class="cellTop">.</td>
<td class="cellTop">.</td>
<td class="cellTop">.</td>
<td class="cellRight cellTop">.</td>
</tr>
<tr>
<td class="cellLeft">.</td>
<td>.</td>
<td>.</td>
<td>C</td>
<td class="cellRight">D</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>H</td>
<td>IJ</td>
<td>K</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>N</td>
<td>P</td>
<td>Q</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">Y</td>
<td class="cellRight cellBottom">Z</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Referring to the table again we find the most frequent
combination to be <span class="tt">EL</span>, occurring 8 times, with
no occurrence of <span class="tt">LE</span>. Now, <span class=
"tt">TH</span> is the commonest pair in plain text, and <span class=
"tt">HT</span> is not common. The fact that <span class="tt">H</span>
occurs in the same horizontal line with <span class="tt">L</span> and
that <span class="tt">E</span> and <span class="tt">T</span> are
probably in the key, will lead us to put <span class="tt">E</span> in
the first line over <span class="tt">H</span> and <span class=
"tt">T</span> in the first line over <span class="tt">L</span>, so as
to make <span class="tt">EL</span> equal <span class=
"tt">TH</span>.</p>
<p class="par">The next most frequent combination is <span class=
"tt">PR</span> occurring 7 times, with <span class="tt">RP</span>
occurring twice. In the square as partially arranged, <span class=
"tt">PR</span> equals <span class="tt">M_</span> or <span class=
"tt">N_</span> or <span class="tt">Q_</span> or <span class=
"tt">I_</span>. We may eliminate all these except <span class=
"tt">N_</span>, and this <span class="tt">N_</span> could only be
<span class="tt">NO</span> or <span class="tt">NA</span>, so that we
will put, tentatively the <span class="tt">R</span> in the second line
over <span class="tt">H</span> and the <span class="tt">O</span> and
<span class="tt">A</span> in the same line over <span class=
"tt">IJ</span>. We have then:</p>
<div class="table">
<table class="borderAll">
<tr>
<td class="cellLeft cellTop">.</td>
<td class="cellTop">E</td>
<td class="cellTop">.</td>
<td class="cellTop">.</td>
<td class="cellRight cellTop">T</td>
</tr>
<tr>
<td class="cellLeft">.</td>
<td>R</td>
<td>AO</td>
<td>C</td>
<td class="cellRight">D</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>H</td>
<td>IJ</td>
<td>K</td>
<td class="cellRight">L</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>N</td>
<td>P</td>
<td>Q</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">Y</td>
<td class="cellRight cellBottom">Z</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Let us now check this by picking out the combinations
beginning with <span class="tt">EL</span> and seeing if the table will
solve them. We find, <span class="tt">ELTV</span>, <span class=
"tt">ELAB</span>, <span class="tt">ELBXFZ</span>, <span class=
"tt">ELBXBT</span>, <span class="tt">ELAXCWBY</span>, <span class=
"tt">ELAXCWEQ</span>, <span class="tt">ELRH</span>, <span class=
"tt">ELBXFS</span>. Now, on the assumption that the letter after
<span class="tt">EL</span> represents <span class="tt">E</span>, we
have it represented by <span class="tt">A</span> three times,
<span class="tt">B</span> three times, <span class="tt">R</span> once
and <span class="tt">T</span> once. This requires <span class=
"pagenum">[<a id="pb82" href="#pb82" name="pb82">82</a>]</span>that
<span class="tt">A</span> and <span class="tt">B</span> be put in the
same horizontal line with <span class="tt">E</span>, since <span class=
"tt">T</span> is already there, and <span class="tt">R</span> is
tentatively under <span class="tt">E</span>.</p>
<p class="par">The combination <span class="tt">ELTV</span> now equals
<span class="tt">THEZ</span>. If the <span class="tt">T</span> were
moved one place to the left, it would be <span class="tt">THEY</span>,
a more likely combination, but this requires the <span class=
"tt">L</span> to be moved one place to the left also, by putting
<span class="tt">I</span> or <span class="tt">K</span> in the key word
and taking out <span class="tt">O</span>, <span class="tt">R</span> or
<span class="tt">X</span> and returning it to its place in the
alphabetical sequence. The most frequent pairs containing <span class=
"tt">O</span> are <span class="tt">B O</span> six times, <span class=
"tt">R O</span> four times, and <span class="tt">O X</span> three
times. Now these pairs equal respectively <span class="tt">E N</span>,
<span class="tt">E S</span> and <span class="tt">H E</span>, if
<span class="tt">O</span> is put between <span class="tt">N</span> and
<span class="tt">P</span> in the fourth line. We will therefore cease
to consider it as a letter of the the key word. The combination
<span class="tt">ELAB</span> can only be <span class="tt">THE_</span>
on the assumption that <span class="tt">A</span> is the first letter to
the right of <span class="tt">E</span>. The combination <span class=
"tt">ELBX</span> occurs three times. If it represents <span class=
"tt">THE_</span>, the <span class="tt">B</span> must be the first
letter of the first line and the <span class="tt">X</span> must now be
placed under <span class="tt">E</span> where the <span class=
"tt">R</span> was tentatively put. We can get <span class=
"tt">THE_</span> out of <span class="tt">ELRH</span> by putting
<span class="tt">R</span> in the first line or leaving it where it is,
but the preponderance of the <span class="tt">BX</span> combination
should suggest the former alternative.</p>
<p class="par">A new square showing these changes will look like
this:</p>
<div class="table">
<table class="borderAll">
<tr>
<td class="cellLeft cellTop">B</td>
<td class="cellTop">E</td>
<td class="cellTop">A</td>
<td class="cellTop">T</td>
<td class="cellRight cellTop">R</td>
</tr>
<tr>
<td class="cellLeft">.</td>
<td>X</td>
<td>.</td>
<td>.</td>
<td class="cellRight">.</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>H</td>
<td>.</td>
<td>L</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">Y</td>
<td class="cellRight cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">As <span class="tt">I</span> put in the space under
<span class="tt">B</span> will give the word <span class=
"tt">BEATRIX</span> and as a vowel is clearly necessary there, we will
so use the <span class="tt">IJ</span> and leave <span class=
"tt">K</span> between <span class="tt">H</span> and <span class=
"tt">L</span>. This leaves <span class="tt">C</span>, <span class=
"tt">D</span> and <span class="tt">F</span> to be placed. It appeared
at <span class="pagenum">[<a id="pb83" href="#pb83" name=
"pb83">83</a>]</span>first that <span class="tt">F</span> was in the
key but if it is in the second line, in proximity to the letters of the
first line, it will give the same indications. Completing the square
then, we have</p>
<div class="table">
<table class="borderAll">
<tr>
<td class="cellLeft cellTop">B</td>
<td class="cellTop">E</td>
<td class="cellTop">A</td>
<td class="cellTop">T</td>
<td class="cellRight cellTop">R</td>
</tr>
<tr>
<td class="cellLeft">IJ</td>
<td>X</td>
<td>C</td>
<td>D</td>
<td class="cellRight">F</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>H</td>
<td>K</td>
<td>L</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td class="cellRight">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">Y</td>
<td class="cellRight cellBottom">Z</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">With this square, the message is deciphered without
difficulty.</p>
<div class="blockquote">
<p class="par first">&ldquo;It is very frequently neces(x)sary to
employ ciphers and they have for many centuries been employed in the
relations betwe(x)en governments, for com(x)munication betwe(x)en
com(x)manders and their subordinates and particularly betwe(x)en
governments and their agents in foreign countries; there are many cases
in history where the capture of a message not in cipher has made the
captors of the message victorious in their military
movements.&rdquo;</p>
</div>
<p class="par"></p>
<p class="par">It will be seen that the method of Lieut. Moorman
enabled us to pick out six letters of the key word out of eight letters
chosen tentatively. The reason for the appearance of <span class=
"tt">F</span> has already been noted; the letter <span class=
"tt">O</span> occurred with many other letters because it happened to
remain in the same line with <span class="tt">N</span> and <span class=
"tt">S</span> and to be under <span class="tt">H</span>. It thus was
likely to represent any of these three letters which occur very
frequently in any text.</p>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Two-character Substitution Ciphers</h3>
</div>
<div class="divBody">
<p class="par first"><span class="sc">Case</span>
9.&mdash;Two-character substitution ciphers. In ciphers of this type,
two letters, numerals, or conventional signs, are substituted for each
letter of the text. There are many ways of obtaining the characters
<span class="pagenum">[<a id="pb84" href="#pb84" name=
"pb84">84</a>]</span>to be substituted but, in general, these ciphers
may be considered as special varieties of Case 6 or Case 7. The ciphers
which come under this case are not well suited to telegraphic
correspondence because the cipher message will contain twice as many
letters as the plain text. However they are so used; an example is at
hand in which two numerals are substituted for each letter and this
makes transmission by telegraph very slow.</p>
<p class="par">Case 9 can be recognized by some or all of the following
points; the number of characters in the cipher is always an even
number; often only a few, say five to ten, of the letters of the
alphabet appear; either a frequency table for pairs of the cipher text
resembling the normal single letter frequency table can be made, or
groups of four letters will show a regular recurrence, from which the
cipher can be solved as in Case 7.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 9a.&mdash;</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="blockquote">
<p class="par first"><span class="tt">RNTGN RAAGR NARNA GTGRA TGAAN
NANGG RARAT NAANR NNNRN AAAGG AANGR NGGNN NRNAA AANRA TNANN NGGRN RNNRG
TTGRG TGGRN ARNTG NNART GGRNR GRNNT GTGAA NNARN ARNRT TGAGG GAAAA NANNA
RNAGA NGNAT NNNAT</span></p>
</div>
<p class="par"></p>
<p class="par">This message contains 160 letters and it will be noted
that the only letters used are <span class="tt">A</span>, <span class=
"tt">G</span>, <span class="tt">N</span>, <span class="tt">R</span> and
<span class="tt">T</span>.</p>
<p class="par">We may expect a simple two-letter substitution cipher at
once. It will simplify the work if we divide the cipher into groups of
two letters and then, if we find there are 26 or less recurring groups,
to assign an arbitrary letter to each group and work out the cipher by
the method of Case 6.</p>
<div class="blockquote">
<p class="par first"><span class="tt">RN TG NR AA GR NA RN AG TG RA TG
AA NN AN GG RA RA TN AA NR NN NR NA AA GG AA NG RN GG NN NR NA AA AN RA
TN AN NN GG RN RN NR GT TG RG TG GR NA RN TG NN AR TG GR NR GR NN TG TG
AA NN AR NA RN RT TG AG GG AA AA NA NN AR NA GA NG NA TN NN
AT</span></p>
</div>
<p class="par"><span class="pagenum">[<a id="pb85" href="#pb85" name=
"pb85">85</a>]</span></p>
<p class="par">With arbitrary letters substituted, we have</p>
<div class="blockquote">
<p class="par first"><span class="tt">A B C D E F A G B H B D I J K H H
L D C I C F D K D M A K I C F D J H L J I K A A C N B O B E F A B I P B
E C E B B D I P F A Q B G K D D F I P F R M F L I S</span></p>
</div>
<p class="par"></p>
<p class="par">Now, preparing a frequency table, with note of prefixes
and suffixes we have:</p>
<div class="table">
<table class="xd21e3010">
<thead>
<tr class="label">
<td class="cellHeadLeft cellHeadTop cellHeadBottom"></td>
<td colspan="2" class="cellHeadTop cellHeadBottom">
<i>Frequency</i></td>
<td class="cellHeadTop cellHeadBottom"><i>Prefix</i></td>
<td class="cellHeadRight cellHeadTop cellHeadBottom"><i>Suffix</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">A</td>
<td>7</td>
<td>1111111</td>
<td>FMKAFF</td>
<td class="cellRight">BGKACBQ</td>
</tr>
<tr>
<td class="cellLeft">B</td>
<td>10</td>
<td>1111111111</td>
<td>AGHNOAPIBQ</td>
<td class="cellRight">CHDOEIEBDG</td>
</tr>
<tr>
<td class="cellLeft">C</td>
<td>6</td>
<td>111111</td>
<td>BDIIAE</td>
<td class="cellRight">DIFFNE</td>
</tr>
<tr>
<td class="cellLeft">D</td>
<td>9</td>
<td>111111111</td>
<td>CBLFKFBKD</td>
<td class="cellRight">EICKMJIDF</td>
</tr>
<tr>
<td class="cellLeft">E</td>
<td>4</td>
<td>1111</td>
<td>DBBC</td>
<td class="cellRight">FFCI</td>
</tr>
<tr>
<td class="cellLeft">F</td>
<td>8</td>
<td>11111111</td>
<td>ECCEPDPM</td>
<td class="cellRight">ADDAAIRL</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>2</td>
<td>11</td>
<td>AB</td>
<td class="cellRight">BK</td>
</tr>
<tr>
<td class="cellLeft">H</td>
<td>4</td>
<td>1111</td>
<td>BKJH</td>
<td class="cellRight">BHLL</td>
</tr>
<tr>
<td class="cellLeft">I</td>
<td>9</td>
<td>111111111</td>
<td>DCKJBEDFL</td>
<td class="cellRight">JCCKPBPP</td>
</tr>
<tr>
<td class="cellLeft">J</td>
<td>3</td>
<td>111</td>
<td>IDL</td>
<td class="cellRight">KHI</td>
</tr>
<tr>
<td class="cellLeft">K</td>
<td>5</td>
<td>11111</td>
<td>JDAIG</td>
<td class="cellRight">HDIAD</td>
</tr>
<tr>
<td class="cellLeft">L</td>
<td>3</td>
<td>111</td>
<td>HHF</td>
<td class="cellRight">DJI</td>
</tr>
<tr>
<td class="cellLeft">M</td>
<td>2</td>
<td>11</td>
<td>DR</td>
<td class="cellRight">AF</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>1</td>
<td>1</td>
<td>C</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">O</td>
<td>1</td>
<td>1</td>
<td>B</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">P</td>
<td>3</td>
<td>111</td>
<td>III</td>
<td class="cellRight">BFF</td>
</tr>
<tr>
<td class="cellLeft">Q</td>
<td>1</td>
<td>1</td>
<td>A</td>
<td class="cellRight">B</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>1</td>
<td>1</td>
<td>F</td>
<td class="cellRight">M</td>
</tr>
<tr>
<td class="cellLeft cellBottom">S</td>
<td class="cellBottom">1</td>
<td class="cellBottom">1</td>
<td class="cellBottom">I</td>
<td class="cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">A brief study of this table and the distribution in the
cipher leads to the conclusion that <span class="tt">B</span>,
<span class="tt">F</span> and <span class="tt">C</span> are certainly
vowels and are, if the normal frequency holds, equal to <span class=
"tt">E</span>, <span class="tt">O</span>, and <span class="tt">A</span>
or <span class="tt">I</span>. Similarly <span class="tt">D</span> and
<span class="tt">I</span> are consonants and we may take them as
<span class="tt">N</span> and <span class="tt">T</span>. <span class=
"tt">I</span> is taken as <span class="tt">T</span> because of the
combination <span class="tt">IP</span> (=possibly <span class=
"tt">TH</span>) occurring three times. The next letter in order of
frequency is <span class="tt">A</span>; it is certainly a consonant and
may be taken as <span class="tt">R</span> on the basis of its
frequency. Let us now try these assumptions on the first two lines of
the message. We have</p>
<div class="table" id="t126">
<table>
<tr>
<td rowspan="2" class="cellLeft cellTop cellBottom">R</td>
<td rowspan="2" class="cellTop cellBottom">E</td>
<td class="cellTop">A</td>
<td rowspan="2" class="cellTop cellBottom">N</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">O</td>
<td rowspan="2" class="cellTop cellBottom">R</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">E</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">E</td>
<td rowspan="2" class="cellTop cellBottom">N</td>
<td rowspan="2" class="cellTop cellBottom">T</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">N</td>
<td class="cellTop">A</td>
<td rowspan="2" class="cellTop cellBottom">T</td>
<td class="cellTop">A</td>
<td rowspan="2" class="cellTop cellBottom">O</td>
<td rowspan="2" class="cellTop cellBottom">N</td>
<td rowspan="2" class="cellTop cellBottom">_</td>
<td rowspan="2" class="cellTop cellBottom">N</td>
<td rowspan="2" class="cellRight cellTop cellBottom">_</td>
</tr>
<tr>
<td class="cellBottom">I</td>
<td class="cellBottom">I</td>
<td class="cellBottom">I</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">This is clearly the word <span class=
"tt">REINFORCEMENTS</span> and, using the letters thus found, the rest
of the line becomes <span class="tt">AMMUNITIONAND</span>. We have then
the following letters determined:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">Arbitrary letters</td>
<td class="cellTop">A</td>
<td class="cellTop">B</td>
<td class="cellTop">C</td>
<td class="cellTop">D</td>
<td class="cellTop">E</td>
<td class="cellTop">F</td>
<td class="cellTop">G</td>
<td class="cellTop">H</td>
<td class="cellTop">I</td>
<td class="cellTop">J</td>
<td class="cellTop">K</td>
<td class="cellTop">L</td>
<td class="cellRight cellTop">M</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Plain Text</td>
<td class="cellBottom">R</td>
<td class="cellBottom">E</td>
<td class="cellBottom">I</td>
<td class="cellBottom">N</td>
<td class="cellBottom">F</td>
<td class="cellBottom">O</td>
<td class="cellBottom">C</td>
<td class="cellBottom">M</td>
<td class="cellBottom">T</td>
<td class="cellBottom">S</td>
<td class="cellBottom">A</td>
<td class="cellBottom">U</td>
<td class="cellRight cellBottom">D</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb86" href="#pb86" name=
"pb86">86</a>]</span></p>
<p class="par">If these be substituted we have for the message:</p>
<div class="blockquote">
<p class="par first"><span class="tt">REINFORCEMENTS AMMUNITION AND
RATIONS MUST ARRI_E _EFORE T_E FIFTEENT_ OR _E CANNOT _O_D
OUT_.</span></p>
</div>
<p class="par"></p>
<p class="par">From this the remainder of the letters are
determined:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">Arbitrary letters</td>
<td class="cellTop">N</td>
<td class="cellTop">O</td>
<td class="cellTop">P</td>
<td class="cellTop">Q</td>
<td class="cellTop">R</td>
<td class="cellRight cellTop">S</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Plain text</td>
<td class="cellBottom">V</td>
<td class="cellBottom">B</td>
<td class="cellBottom">H</td>
<td class="cellBottom">W</td>
<td class="cellBottom">L</td>
<td class="cellRight cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Now let us substitute the two-letter groups for the
arbitrary letters:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">Arbitrary letters</td>
<td class="cellTop">K</td>
<td class="cellTop">O</td>
<td class="cellTop">G</td>
<td class="cellTop">M</td>
<td class="cellTop">B</td>
<td class="cellTop">E</td>
<td class="cellTop">P</td>
<td class="cellTop">C</td>
<td class="cellTop">R</td>
<td class="cellTop">H</td>
<td class="cellTop">D</td>
<td class="cellTop">F</td>
<td class="cellTop">A</td>
<td class="cellTop">J</td>
<td class="cellTop">I</td>
<td class="cellTop">L</td>
<td class="cellTop">N</td>
<td class="cellTop">Q</td>
<td class="cellRight cellTop">S</td>
</tr>
<tr>
<td class="xd21e24143 xd21e24142 cellLeft">Two-letter groups</td>
<td class="xd21e24142">GG</td>
<td class="xd21e24142">RG</td>
<td class="xd21e24142">AG</td>
<td class="xd21e24142">NG</td>
<td class="xd21e24142">TG</td>
<td class="xd21e24142">GR</td>
<td class="xd21e24142">AR</td>
<td class="xd21e24142">NR</td>
<td class="xd21e24142">GA</td>
<td class="xd21e24142">RA</td>
<td class="xd21e24142">AA</td>
<td class="xd21e24142">NA</td>
<td class="xd21e24142">RN</td>
<td class="xd21e24142">AN</td>
<td class="xd21e24142">NN</td>
<td class="xd21e24142">TN</td>
<td class="xd21e24142">GT</td>
<td class="xd21e24142">RT</td>
<td class="xd21e24142 cellRight">AT</td>
</tr>
<tr>
<td class="cellLeft cellBottom">Plain text</td>
<td class="cellBottom">A</td>
<td class="cellBottom">B</td>
<td class="cellBottom">C</td>
<td class="cellBottom">D</td>
<td class="cellBottom">E</td>
<td class="cellBottom">F</td>
<td class="cellBottom">H</td>
<td class="cellBottom">I</td>
<td class="cellBottom">L</td>
<td class="cellBottom">M</td>
<td class="cellBottom">N</td>
<td class="cellBottom">O</td>
<td class="cellBottom">R</td>
<td class="cellBottom">S</td>
<td class="cellBottom">T</td>
<td class="cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellRight cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">It is evident that the cipher was prepared with the
letters of the word <span class="tt">GRANT</span> chosen by means of a
square of this kind:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">G</td>
<td class="cellTop">R</td>
<td class="cellTop">A</td>
<td class="cellTop">N</td>
<td class="cellRight cellTop">T</td>
</tr>
<tr>
<td class="cellLeft">G</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td class="cellRight">E</td>
</tr>
<tr>
<td class="cellLeft">R</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td class="cellRight">K</td>
</tr>
<tr>
<td class="cellLeft">A</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td class="cellRight">P</td>
</tr>
<tr>
<td class="cellLeft">N</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td>T</td>
<td class="cellRight">U</td>
</tr>
<tr>
<td class="cellLeft cellBottom">T</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">X</td>
<td class="cellBottom">Y</td>
<td class="cellRight cellBottom">Z</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">Thus <span class="tt">TG=E</span>, <span class=
"tt">AN=S</span>, etc., as we have already found.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 9-b</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop">1950492958</td>
<td class="cellTop">3123252815</td>
<td class="cellTop">4418452815</td>
<td class="cellRight cellTop">2048115041</td>
</tr>
<tr>
<td class="cellLeft">2252115345</td>
<td>5849134124</td>
<td>5028552526</td>
<td class="cellRight">5933195222</td>
</tr>
<tr>
<td class="cellLeft">5245113215</td>
<td>6215584143</td>
<td>2861361265</td>
<td class="cellRight">2945565015</td>
</tr>
<tr>
<td class="cellLeft">2342455850</td>
<td>6345542019</td>
<td>1550185311</td>
<td class="cellRight">2115415828</td>
</tr>
<tr>
<td class="cellLeft">1124174553</td>
<td>4554205950</td>
<td>2552454132</td>
<td class="cellRight">1533492048</td>
</tr>
<tr>
<td class="cellLeft cellBottom">5018152364</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">An examination of the groups of two numerals each which
make up this message, shows that we have 11 to 36 and 41 to 65 with
eleven groups missing. Now the 11 to 36 combination is a very familiar
one in numeral substitution ciphers (See Case 6-c) and it <span class=
"pagenum">[<a id="pb87" href="#pb87" name="pb87">87</a>]</span>will be
noted that 41 to 66 would give us a similar alphabet. Let us make a
frequency table in this form:</p>
<div class="table">
<table class="xd21e3010">
<thead>
<tr class="label">
<td class="cellHeadLeft cellHeadTop cellHeadBottom"><i>Group</i></td>
<td class="cellHeadTop cellHeadBottom"><i>Frequency</i></td>
<td class="cellHeadTop cellHeadBottom"><i>Group</i></td>
<td class="cellHeadRight cellHeadTop cellHeadBottom">
<i>Frequency</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">11</td>
<td>11111</td>
<td>41</td>
<td class="cellRight">11111</td>
</tr>
<tr>
<td class="cellLeft">12</td>
<td>1</td>
<td>42</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">13</td>
<td>1</td>
<td>43</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">14</td>
<td></td>
<td>44</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">15</td>
<td>111111111</td>
<td>45</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">16</td>
<td></td>
<td>46</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">17</td>
<td>1</td>
<td>47</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">18</td>
<td>111</td>
<td>48</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">19</td>
<td>111</td>
<td>49</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">20</td>
<td>1111</td>
<td>50</td>
<td class="cellRight">11111111</td>
</tr>
<tr>
<td class="cellLeft">21</td>
<td>1</td>
<td>51</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">22</td>
<td>11</td>
<td>52</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">23</td>
<td>111</td>
<td>53</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">24</td>
<td>11</td>
<td>54</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">25</td>
<td>111</td>
<td>55</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">26</td>
<td>1</td>
<td>56</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">27</td>
<td></td>
<td>57</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">28</td>
<td>11111</td>
<td>58</td>
<td class="cellRight">11111</td>
</tr>
<tr>
<td class="cellLeft">29</td>
<td>11</td>
<td>59</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">30</td>
<td></td>
<td>60</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">31</td>
<td>1</td>
<td>61</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">32</td>
<td>11</td>
<td>62</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">33</td>
<td>11</td>
<td>63</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">34</td>
<td></td>
<td>64</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">35</td>
<td></td>
<td>65</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft cellBottom">36</td>
<td class="cellBottom">1</td>
<td class="cellBottom">66</td>
<td class="cellRight cellBottom"></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">Each of these tables looks like the normal frequency
table except for the position of 20 and 50 which should represent
<span class="tt">T</span>, by all our rules, and should be apparently
30 and 60. But suppose we put the alphabet and corresponding numerals
in this form:</p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">1</td>
<td class="cellTop">2</td>
<td class="cellTop">3</td>
<td class="cellTop">4</td>
<td class="cellTop">5</td>
<td class="cellTop">6</td>
<td class="cellTop">7</td>
<td class="cellTop">8</td>
<td class="cellTop">9</td>
<td class="cellRight cellTop">0</td>
</tr>
<tr>
<td class="cellLeft">1 or 4</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td class="cellRight">J</td>
</tr>
<tr>
<td class="cellLeft">2 or 5</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft cellBottom">3 or 6</td>
<td class="cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">X</td>
<td class="cellBottom">Y</td>
<td class="cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb88" href="#pb88" name=
"pb88">88</a>]</span></p>
<p class="par">Then A=11 or 41, J=10 or 40 and T=20 or 50 as we found.
Using the above alphabet, the message may easily be read. Note that
this cipher is made up of ten characters only, the Arabic numerals.</p>
</div>
</div>
<div class="div2 section">
<div class="divBody">
<p class="par first"><span class="sc">Case</span> 9c&mdash;</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop">1156254676</td>
<td class="cellTop">2542294432</td>
<td class="cellTop">1949294015</td>
<td class="cellTop">1423217211</td>
<td class="cellRight cellTop">2979703115</td>
</tr>
<tr>
<td class="cellLeft">4924213511</td>
<td>7424147875</td>
<td>7646252444</td>
<td>5143254845</td>
<td class="cellRight">3179742533</td>
</tr>
<tr>
<td class="cellLeft">4055461512</td>
<td>7573227945</td>
<td>1627481511</td>
<td>7042351944</td>
<td class="cellRight">1378252149</td>
</tr>
<tr>
<td class="cellLeft">2514764553</td>
<td>1548342126</td>
<td>7215254075</td>
<td>1611257845</td>
<td class="cellRight">4642217415</td>
</tr>
<tr>
<td class="cellLeft">4952197929</td>
<td>7015242143</td>
<td>2925444933</td>
<td>1970187531</td>
<td class="cellRight">4079254829</td>
</tr>
<tr>
<td class="cellLeft cellBottom">4551491411</td>
<td class="cellBottom">7321171554</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">An examination of this message shows it to consist of
forty-four different two-figure groups running from 11 to 79. Let us
prepare a frequency table of these groups.</p>
<div class="table">
<table class="xd21e3010">
<thead>
<tr class="label">
<td class="cellHeadLeft cellHeadTop cellHeadBottom"><i>Group</i></td>
<td class="cellHeadRight cellHeadTop cellHeadBottom">
<i>Frequency</i></td>
</tr>
</thead>
<tbody>
<tr>
<td class="cellLeft">11</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">12</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">13</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">14</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">15</td>
<td class="cellRight">111111111</td>
</tr>
<tr>
<td class="cellLeft">16</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">17</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">18</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">19</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">20</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">21</td>
<td class="cellRight">1111111</td>
</tr>
<tr>
<td class="cellLeft">22</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">23</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">24</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">25</td>
<td class="cellRight">11111111111</td>
</tr>
<tr>
<td class="cellLeft">26</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">27</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">28</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">29</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">30</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">31</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">32</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">33</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">34</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">35</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">36</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">37</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">38</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">39</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">40</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">41</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">42</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">43</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">44</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">45</td>
<td class="cellRight">11111</td>
</tr>
<tr>
<td class="cellLeft">46</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">47</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">48</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">49</td>
<td class="cellRight">111111</td>
</tr>
<tr>
<td class="cellLeft">50</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">51</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">52</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">53</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">54</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">55</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">56</td>
<td class="cellRight">1</td>
</tr>
<tr>
<td class="cellLeft">57</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">58</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">59</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">70</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">71</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">72</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">73</td>
<td class="cellRight">11</td>
</tr>
<tr>
<td class="cellLeft">74</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">75</td>
<td class="cellRight">1111</td>
</tr>
<tr>
<td class="cellLeft">76</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft">77</td>
<td class="cellRight"></td>
</tr>
<tr>
<td class="cellLeft">78</td>
<td class="cellRight">111</td>
</tr>
<tr>
<td class="cellLeft cellBottom">79</td>
<td class="cellRight cellBottom">11111</td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">We at once note the resemblance between the frequency
tables for the groups 11 to 19 and 21 to <span class="pagenum">[<a id=
"pb89" href="#pb89" name="pb89">89</a>]</span>29; for the groups 30 to
36 and 50 to 56; and for the groups 40 to 49 and 70 to 79. Also the
groups 11 to 19 and 21 to 29 have a frequency fitting well with the
normal frequency table of the letters <span class="tt">A</span> to
<span class="tt">I</span>; the groups 41 to 49 and 71 to 79 have a
frequency fitting well with the normal frequency table of the letters
<span class="tt">K</span> to <span class="tt">S</span>; and the groups
31 to 36 and 51 to 56 have a frequency fitting well with the normal
frequency table of the letters <span class="tt">U</span> to
<span class="tt">Z</span>. We have <span class="tt">J</span> and
<span class="tt">T</span> unaccounted for, but note what occurred in
Case 9-b and that 40 and 70 would correspond well with <span class=
"tt">T</span> if they followed respectively 49 and 79. We may now make
up a cipher table as follows<span class="corr" id="xd21e25145" title=
"Source: .">:</span></p>
<div class="table">
<table class="xd21e3010">
<tr>
<td class="cellLeft cellTop"></td>
<td class="cellTop">1</td>
<td class="cellTop">2</td>
<td class="cellTop">3</td>
<td class="cellTop">4</td>
<td class="cellTop">5</td>
<td class="cellTop">6</td>
<td class="cellTop">7</td>
<td class="cellTop">8</td>
<td class="cellTop">9</td>
<td class="cellRight cellTop">0</td>
</tr>
<tr>
<td class="cellLeft">1 or 2</td>
<td>A</td>
<td>B</td>
<td>C</td>
<td>D</td>
<td>E</td>
<td>F</td>
<td>G</td>
<td>H</td>
<td>I</td>
<td class="cellRight">J</td>
</tr>
<tr>
<td class="cellLeft">4 or 7</td>
<td>K</td>
<td>L</td>
<td>M</td>
<td>N</td>
<td>O</td>
<td>P</td>
<td>Q</td>
<td>R</td>
<td>S</td>
<td class="cellRight">T</td>
</tr>
<tr>
<td class="cellLeft cellBottom">3 or 5</td>
<td class="cellBottom">U</td>
<td class="cellBottom">V</td>
<td class="cellBottom">W</td>
<td class="cellBottom">X</td>
<td class="cellBottom">Y</td>
<td class="cellBottom">Z</td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellBottom"></td>
<td class="cellRight cellBottom"></td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and this table will solve the cipher message.</p>
<p class="par">In ciphers coming under case 9-b and 9-c, it is not
uncommon to assign some of the unused numbers such as 85, 93, etc., to
whole words in common use or to names of persons or places. In case
such groups are found, the meaning must be guessed at from the context;
but if many messages in the same cipher are available, the meaning of
these groups will soon be obtained. The appearance of such odd groups
of figures in a message does not interfere materially with the
analysis, and it will be apparent at once on deciphering the message
that they represent whole words instead of letters. <span class=
"pagenum">[<a id="pb90" href="#pb90" name="pb90">90</a>]</span></p>
</div>
</div>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter IX</h2>
<h2 class="main">Other Substitution Methods</h2>
</div>
<div class="divBody">
<p class="par xd21e165"><span class="xd21e165init">T</span>he foregoing
cases by no means exhaust the possibilities of the substitution cipher
but they cover practically all methods which are satisfactory for
military purposes, having in mind conservation of time, the minimizing
of mental strain, and the requirements that complicated apparatus and
rules be avoided, and that the resulting cipher should be adapted to
telegraphic correspondence.</p>
<p class="par">A message may be re-enciphered two or more times using a
different key word each time or it may be enciphered by one method and
re-enciphered by another method, using the same or a different key
word. Complicated cipher systems requiring the memorizing of, or
reference to, numerous rules have been devised for special purposes.
Such systems usually fail utterly if there are any errors in
transmission and it will be seen later that such errors are very
common.</p>
<p class="par">There are several ingenious cipher machines by which
complicated ciphers can be formed, but if the apparatus is available
and fairly long messages are at hand for examination, it is usually
possible to solve them. Such machines are not, as a rule, simple and
small enough for field use; and it must always be remembered that a
machine cipher operates on certain mechanical cycles, which can be
determined if the machine is available.</p>
<p class="par">A book by Commandant Bazeries, entitled
&ldquo;<span lang="fr">Etude sur la Cryptographie
Militaire</span>,&rdquo; and a series of <span class="pagenum">[<a id=
"pb91" href="#pb91" name="pb91">91</a>]</span>articles by A. Collon,
entitled &ldquo;<span lang="fr">Etude sur la
Cryptographie</span>,&rdquo; which appeared in the <span lang=
"fr">Revue de L&rsquo;Arm&eacute;e Belge</span>, 1899&ndash;1902, give
illustrations and details of operation of several of these cipher
machines and the latter goes into the methods of deciphering messages
enciphered with them. These methods of analysis require long messages,
and as each one is adapted only to the product of a certain machine or
apparatus, it is not considered advisable to include a discussion of
them here. Those interested in such advanced cipher work must refer to
these and other European authors on the subject.</p>
<p class="par">The requirement that cipher messages should be adapted
to telegraphic transmission, practically excludes ciphers in which
three or more letters or whole words are substituted for each letter of
the plain text. Such ciphers might be used for the transmission of very
short messages but in no other case.</p>
<p class="par">The cipher of Case 7, with a key word or phrase longer
than one-fourth of the message, the cipher after the method of Case 7,
using a certain page of a book as a key, and the cipher with a running
key, where each letter of the cipher is the key for enciphering the
next letter, all look safe and desirable, theoretically, but,
practically, the work of enciphering and deciphering is hopelessly
slow, and errors in enciphering or transmission make deciphering very
difficult. Incidentally the first and second of these ciphers can be
solved by the special solution for Case 7, and the third can be solved
by trying each of the twenty-six letters of the alphabet as the first
key letter, and then continuing the work for five or six letters of the
cipher. When the proper primary key letter is found, the solution of
the next five or six letters of the cipher will make sense, and
thereafter the cipher offers no difficulty. <span class=
"pagenum">[<a id="pb92" href="#pb92" name="pb92">92</a>]</span></p>
<p class="par">There are numerous other methods of preparing what is
virtually a very long, or even an indefinitely long key from a short
key word, but all such cipher methods have the same practical
disadvantages of slowness of operation and difficulty in deciphering,
if errors of enciphering or transmission have been made.</p>
<p class="par">The ciphers of Napoleon were long series of numbers
representing letters, syllables and words. They were really codes; and
a code based on these principles, but using letters instead of
numerals, might be evolved very easily. The War Department Code, the
Western Union Code, and, in fact, all codes are nothing but specialized
substitution ciphers in which each code word represents a letter, word
or phrase of the plain text.</p>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Combined Transposition and Substitution Methods</h3>
</div>
<div class="divBody">
<p class="par first">It is evident that a message can be enciphered by
any transposition method, and the result enciphered again by any
substitution method, or vice versa. But this takes time and leads to
errors in the work, so that, if such a process is employed, the
substitution and transposition ciphers used are likely to be very
simple ones which can be operated with fair rapidity.</p>
<p class="par">On preliminary determination, a cipher prepared by such
a combination of methods will appear to be a substitution cipher to be
solved as such. The frequency table of the result will resemble the
normal frequency table, although the message will still be
unintelligible and we will know at once that it is a transposition
cipher for further solution.</p>
<p class="par">The substitution methods usually found in combination
ciphers are those of Case 4, 5 and 6, and the transposition method is
nearly always Case 1, and particularly the simple varieties of this
case like the <span class="pagenum">[<a id="pb93" href="#pb93" name=
"pb93">93</a>]</span>fence rail (Case 1-i), reversed writing or
vertical writing.</p>
<p class="par">A few examples will show some of the possible
combinations.</p>
<p class="par">The first line of the message of Case 4-a is:</p>
<p class="par xd21e152"><span class="tt">OBQFOBPBRP</span></p>
<p class="par">We might write it <span class="tt">BFBBPOQOPR</span>
(Case 1-i), or <span class="tt">PRBPBOFQBO</span> (Case 1, reversed
writing), or <span class="tt">OFQBOPRBPB</span> (Case 1, reversed by
groups of five).</p>
<p class="par">The first line of the message of Case 2-b is:</p>
<p class="par xd21e152"><span class="tt">SLCOF WEETN EBRDO ORVYM
FFEDI</span></p>
<p class="par">We might write it <span class="tt">TMDPG XFFUO FCSEP
PSWZN GGFEJ</span>, or <span class="tt">RKBNE VDDSM DAQCN NQUXL
EEDCH</span> (Case 4-a, going forward one letter or back one
letter).</p>
<p class="par">These examples give an idea of the use of combination
methods. It is very rare to find both complicated transposition and
substitution methods used in combination. If one is complicated, the
other will usually be very simple; and ordinarily both are simple, the
sender depending on the combination of the two to attain
indecipherability. It is evident how futile this idea is.</p>
</div>
</div>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Methods of Enciphering Numerals</h3>
</div>
<div class="divBody">
<p class="par first">It is frequently desirable to send numerals in the
body of a cipher message. Several cipher systems prescribe that all
numerals in the body of a message must be spelled out; and, while there
is no doubt but that this insures greater accuracy, it also greatly
increases the length of such messages. In most systems in which it is
permissible to send numerals, the following system is used. An
indicator, one of the little used letters and especially <span class=
"tt">X</span>, is interpolated before and after the numeral or numerals
to be enciphered, and then, for each numeral, a letter is substituted
using this or a similar table:</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">1</td>
<td class="cellTop">2</td>
<td class="cellTop">3</td>
<td class="cellTop">4</td>
<td class="cellTop">5</td>
<td class="cellTop">6</td>
<td class="cellTop">7</td>
<td class="cellTop">8</td>
<td class="cellTop">9</td>
<td class="cellRight cellTop">0</td>
</tr>
<tr>
<td class="cellLeft cellBottom">A</td>
<td class="cellBottom">B</td>
<td class="cellBottom">C</td>
<td class="cellBottom">D</td>
<td class="cellBottom">E</td>
<td class="cellBottom">F</td>
<td class="cellBottom">G</td>
<td class="cellBottom">H</td>
<td class="cellBottom">I</td>
<td class="cellRight cellBottom">J</td>
</tr>
</table>
</div>
<p class="par"><span class="pagenum">[<a id="pb94" href="#pb94" name=
"pb94">94</a>]</span></p>
<p class="par">The enciphering of the message then proceeds, dealing
with the indicator and substituted letters as if they were the letters
of a word. The decipherer arriving at an <span class="tt">X</span>, a
series of the letters of the above table and another <span class=
"tt">X</span>, casts out the <span class="tt">X</span>&rsquo;s and
substitutes numbers for the letters.</p>
<p class="par">Sometimes no indicator is used, but the system of
substitution of a certain letter for each numeral is followed. Again,
the indicator <span class="tt">NR</span> may be used instead of a
single letter.</p>
<p class="par">Conventional letters may also be substituted for special
characters like <span class="tt">?</span>, <span class="tt">$</span>,
<span class="tt">&rdquo;</span>, <span class="tt">-</span>, and periods
and commas, but this is rarely done except for the period and question
mark. The context will usually determine the meaning of such letters
when found. In this connection, the use of <span class="tt">X</span> to
represent end of a sentence and <span class="tt">Q</span> to represent
a question mark is quite common. <span class="pagenum">[<a id="pb95"
href="#pb95" name="pb95">95</a>]</span></p>
</div>
</div>
</div>
</div>
<div class="div1 chapter">
<div class="divHead">
<h2 class="label">Chapter X</h2>
<h2 class="main">Errors in Enciphering and Transmission</h2>
</div>
<div class="divBody">
<p class="par first">One of the most difficult tasks before the cipher
expert, is the correction of errors which creep into cipher texts in
the process of enciphering and transmission by telegraph or radio.</p>
<p class="par">In some cipher methods a mistake in enciphering one
letter, or the omission of one letter, will so mix up the deciphering
process that only one familiar with such errors can apply the necessary
corrections.</p>
<p class="par">The transmission of cipher text over the telegraph or by
radio is a slow process, and many fairly good operators cannot receive
such matter satisfactorily, because they listen for words and guess at
letters at times. The spaced letters in American Morse are the cause of
so many errors in code transmission that the War Department Code does
not employ any groups using them. In fact, this code is limited to the
letters</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop cellBottom">A</td>
<td class="cellTop cellBottom">B</td>
<td class="cellTop cellBottom">D</td>
<td class="cellTop cellBottom">E</td>
<td class="cellTop cellBottom">F</td>
<td class="cellTop cellBottom">G</td>
<td class="cellTop cellBottom">I</td>
<td class="cellTop cellBottom">K</td>
<td class="cellTop cellBottom">M</td>
<td class="cellTop cellBottom">N</td>
<td class="cellTop cellBottom">S</td>
<td class="cellTop cellBottom">T</td>
<td class="cellTop cellBottom">U</td>
<td class="cellRight cellTop cellBottom">X</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">so that there may be a minimum of such confusion.</p>
<p class="par">In cipher work it is necessary, under ordinary
circumstances, to use any or all of the letters of the alphabet. To
assist operators in keeping the text straight, it is customary to
divide cipher text into groups of four, five, six or ten letters, and
usually groups of five letters are used. The receiving operator may
then expect five letters per group, and if he receives more or less he
is sure that either he or the sending operator has made an error. This
division into groups of a constant number of letters eliminates word
forms and, in the mind of the non-expert, increases <span class=
"pagenum">[<a id="pb96" href="#pb96" name="pb96">96</a>]</span>the
difficulty of solving the cipher. But the increase in difficulty is
more apparent than real; particularly, as a cipher examiner habitually
finds himself dealing with ciphers without word forms, and the
occurrence of a cipher with word forms usually means that he has an
easy one to handle.</p>
<p class="par">Messages are occasionally encountered which consist
partly of plain text and partly of cipher. The cipher part may or may
not retain its word forms, but, when this method is used, it is clearly
impossible to have a fixed number of letters in each cipher group if
the word forms are not used. It is almost impossible to prevent errors
of transmission in such messages, and it often requires considerable
skill and labor to correct them.</p>
<p class="par">For those unfamiliar with the telegraph alphabets, they
are given below. Messages sent by commercial or military telegraphs or
buzzer lines will be transmitted with the American Morse alphabet.
Those sent by radio, visual signalling or submarine cable will be
transmitted by Continental Morse, known also as the International Code.
Messages may be transmitted by both alphabets in course of
transmission. For example, a cablegram from the Philippines to Nome,
Alaska, will be transmitted by Continental Morse (commercial cable)
from Manila to San Francisco, by American Morse (commercial land line)
from San Francisco to Seattle, by Continental Morse (military cable)
from Seattle to Valdez, by American Morse (military land line) from
Valdez to Nulato and by Continental Morse (military radio) from Nulato
to Nome.</p>
<p class="par">Prior to February, 1914, the Mexican government
telegraph lines used an alphabet differing slightly from the American
and Continental Morse. However, at that time, the Continental Morse
alphabet was prescribed for use on these lines and <span class=
"pagenum">[<a id="pb97" href="#pb97" name="pb97">97</a>]</span>it is
believed that the use of the old alphabet has entirely ceased on
Mexican lines. However, skilled American operators would have no
difficulty in picking up this alphabet if it were found to be in
use.</p>
<p class="par">Radio communication is, by International Convention,
invariably in Continental Morse.</p>
<div class="div2 section">
<div class="divHead">
<h3 class="main">Telegraph Alphabets</h3>
</div>
<div class="divBody">
<p class="par first"></p>
<div class="table">
<table class="xd21e3010">
<thead>
<tr class="label">
<td class=
"xd21e25488 xd21e7911 cellHeadLeft cellHeadTop cellHeadBottom">
Character</td>
<td class="xd21e25488 xd21e25486 cellHeadTop cellHeadBottom">American
Morse</td>
<td class=
"xd21e25488 xd21e25486 cellHeadRight cellHeadTop cellHeadBottom">
Continental Morse<br>
or International Code</td>
</tr>
</thead>
<tbody>
<tr>
<td class="xd21e7911 cellLeft">A</td>
<td class="xd21e25486">. -</td>
<td class="xd21e25486 cellRight">. -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">B</td>
<td class="xd21e25486">- . . .</td>
<td class="xd21e25486 cellRight">- . . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">C</td>
<td class="xd21e25486">. .&emsp;.</td>
<td class="xd21e25486 cellRight">- . - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">D</td>
<td class="xd21e25486">- . .</td>
<td class="xd21e25486 cellRight">- . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">E</td>
<td class="xd21e25486">.</td>
<td class="xd21e25486 cellRight">.</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">F</td>
<td class="xd21e25486">. - .</td>
<td class="xd21e25486 cellRight">. . - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">G</td>
<td class="xd21e25486">- - .</td>
<td class="xd21e25486 cellRight">- - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">H</td>
<td class="xd21e25486">. . . .</td>
<td class="xd21e25486 cellRight">. . . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">I</td>
<td class="xd21e25486">. .</td>
<td class="xd21e25486 cellRight">. .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">J</td>
<td class="xd21e25486">- . - .</td>
<td class="xd21e25486 cellRight">. - - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">K</td>
<td class="xd21e25486">- . -</td>
<td class="xd21e25486 cellRight">- . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">L</td>
<td class="xd21e25486">&mdash;</td>
<td class="xd21e25486 cellRight">. - . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">M</td>
<td class="xd21e25486">- -</td>
<td class="xd21e25486 cellRight">- -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">N</td>
<td class="xd21e25486">- .</td>
<td class="xd21e25486 cellRight">- .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">O</td>
<td class="xd21e25486">.&emsp;.</td>
<td class="xd21e25486 cellRight">- - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">P</td>
<td class="xd21e25486">. . . . .</td>
<td class="xd21e25486 cellRight">. - - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">Q</td>
<td class="xd21e25486">. . - .</td>
<td class="xd21e25486 cellRight">- - . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">R</td>
<td class="xd21e25486">.&emsp;. .</td>
<td class="xd21e25486 cellRight">. - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">S</td>
<td class="xd21e25486">. . .</td>
<td class="xd21e25486 cellRight">. . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">T</td>
<td class="xd21e25486">-</td>
<td class="xd21e25486 cellRight">-</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">U</td>
<td class="xd21e25486">. . -</td>
<td class="xd21e25486 cellRight">. . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">V</td>
<td class="xd21e25486">. . . -</td>
<td class="xd21e25486 cellRight">. . . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">W</td>
<td class="xd21e25486">. - -</td>
<td class="xd21e25486 cellRight">. - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">X</td>
<td class="xd21e25486">. - . .</td>
<td class="xd21e25486 cellRight">- . . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">Y</td>
<td class="xd21e25486">. .&emsp;. .</td>
<td class="xd21e25486 cellRight">- . - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">Z</td>
<td class="xd21e25486">. . .&emsp;.</td>
<td class="xd21e25486 cellRight">- - . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">1</td>
<td class="xd21e25486">. - - .</td>
<td class="xd21e25486 cellRight">. - - - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">2</td>
<td class="xd21e25486">. . - . .</td>
<td class="xd21e25486 cellRight">. . - - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">3</td>
<td class="xd21e25486">. . . - .</td>
<td class="xd21e25486 cellRight">. . . - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">4</td>
<td class="xd21e25486">. . . . -</td>
<td class="xd21e25486 cellRight">. . . . -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">5</td>
<td class="xd21e25486">- - -</td>
<td class="xd21e25486 cellRight">. . . . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">6</td>
<td class="xd21e25486">. . . . . .</td>
<td class="xd21e25486 cellRight">- . . . .<span class="pagenum">[<a id=
"pb98" href="#pb98" name="pb98">98</a>]</span></td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">7</td>
<td class="xd21e25486">- - . .</td>
<td class="xd21e25486 cellRight">- - . . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">8</td>
<td class="xd21e25486">- . . . .</td>
<td class="xd21e25486 cellRight">- - - . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">9</td>
<td class="xd21e25486">- . . -</td>
<td class="xd21e25486 cellRight">- - - - .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">0</td>
<td class="xd21e25486">&mdash;&mdash;</td>
<td class="xd21e25486 cellRight">- - - - -</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">Period</td>
<td class="xd21e25486">. . - - . .</td>
<td class="xd21e25486 cellRight"><span class="corr" id="xd21e25759"
title="Source: . .&emsp;. .&emsp;. .">. - . - . -</span></td>
</tr>
<tr>
<td class="xd21e7911 cellLeft">Question Mark</td>
<td class="xd21e25486">- . . - .</td>
<td class="xd21e25486 cellRight">. . - - . .</td>
</tr>
<tr>
<td class="xd21e7911 cellLeft cellBottom">Comma</td>
<td class="xd21e25486 cellBottom">. - . -</td>
<td class="xd21e25486 cellRight cellBottom"><span class="corr" id=
"xd21e25774" title="Source: . - . - . -">- - . . - -</span></td>
</tr>
</tbody>
</table>
</div>
<p class="par"></p>
<p class="par">The following example will show some of the errors that
creep into messages prepared with the cipher disk and transmitted by
radio:</p>
<p class="par xd21e152"><i>Message</i></p>
<div class="blockquote">
<p class="par first">Radio Douglas de El Paso, 2 H 71, twenty-fifth,
9:00 a.m., Govt. To C.O., Sixth Brigade, Douglas, Arizona:</p>
<p class="par"><span class="tt">JPRZI RDJSG XTRMJ USFPC RECLA BCPCB
OAXPK QEQKF PPZAE BKUTT JHWEU AHPZE EZOLT HKXPH KIHAV DRODN IAPZC LVUMP
KFUBV VTVNV EFVZV TLVQS BKAHQ NVKVF MGJTH OWBGN WWEPO LJKFP HEXKW CPDLZ
JWSQC JVKIG HTJHT EGAHA GDXXK BSPPK DIAVZ VQONC HOVDA VZQKW FNVON RPVGH
CUFPV SFPIE TOZOD WGYFE AWNJY KOEDW UMELD NOBUH MUPQL GYOPP ODBAB UFUUC
AEOJW RDIPK WMOKV OMICW CKPIH LUMSY YOSBG WOPHV PKOMO PHGER</span></p>
<p class="par xd21e12345">Smith.</p>
</div>
<p class="par"></p>
<p class="par">The key word is <span class="tt">ATCHISON</span>, the
cipher disk being used and the setting changed for every letter of the
message. The letter <span class="tt">X</span> indicates a period where
it is evidently not a letter of a word.</p>
<p class="par">Deciphering the message with this key and method we
have:</p>
<div class="blockquote">
<p class="par first"><span class="tt">RELIA BLEIN FOR<span class=
"underline">GF</span> TIONF ROMCA SASGR ANDES RECEI <span class=
"underline">L</span>EDHE RETHA TAMOU NTEDD ETACH M<span class=
"underline">SK</span>TL EFTTH ERELA STNIG HTTOE SCORT SHYMP ENTOF ARMSA
NDAMM UNITI ONTOB ESMUG GLEDA CR<span class="underline">JX</span>S
BORDE RNEXT FRIDA YNIGH TATAP OINTT WELVE MI<span class="underline">ENX
FKOSB</span></span></p>
</div>
<p class="par"></p>
<p class="par">Beyond this point the message, if we continue the
deciphering process, is unintelligible. The sense fails at the first
<span class="tt">P</span> of the cipher group <span class=
"tt">BSPPK</span>. We have translated <span class="tt">B</span> as
<span class="tt">M</span> with disk <span class="tt">A</span> to
<span class="tt">N</span> and <span class="tt">S</span> as <span class=
"tt">I</span> with disk <span class="tt">A</span> to <span class=
"tt">A</span>. The last words that make sense <span class=
"pagenum">[<a id="pb99" href="#pb99" name="pb99">99</a>]</span>are
<span class="tt">A POINT TWELVE MI</span>; clearly the rest of the last
word is <span class="tt">LES</span> and this is represented by
<span class="tt">PPK</span>. Putting <span class="tt">P=L</span> then
<span class="tt">A=A</span> and putting <span class="tt">P=E</span>
then <span class="tt">A=T</span>. In other words, the encipherer forgot
to change his disk setting, <span class="tt">A</span> to <span class=
"tt">A</span>, after enciphering <span class="tt">I</span> into
<span class="tt">S</span> and enciphered <span class="tt">L</span> into
<span class="tt">P</span> with the same setting, <span class=
"tt">A</span> to <span class="tt">A</span>. Continuing the deciphering
on this basis, we have:</p>
<div class="blockquote">
<p class="par first"><span class="tt">&nbsp;&nbsp;LES EASTO FDOUG LAS.T
HISIS INYOU RDIST RICT. WILLY OUTAK ENECE SSAR<span class=
"underline">V</span> STEPS TOPRE VENTT HISSH IPMEN TFROM GOING
<span class="underline">SKZRX</span> LEADE ROFSM UGGLE RSSA<span class=
"underline">L</span> DTOBE JUANH ERNAN DEZOF NACO.</span></p>
</div>
<p class="par"></p>
<p class="par">The minor errors underlined above are not difficult to
correct except the sixth word in the eighth line. They will be taken up
however for analysis of cause of error.</p>
<p class="par">Line 1, <span class="tt"><span class=
"underline">GF</span></span> should be <span class="tt">MA</span>.
Putting the latter into cipher we find the letters of the cipher should
have been <span class="tt">GO</span> instead of <span class=
"tt">MJ</span>. This is clearly a telegrapher&rsquo;s error,
<span class="tt">--. ---</span> becoming <span class="tt">--
.---</span></p>
<p class="par">Line 2, <span class="tt"><span class=
"underline">L</span></span> should be <span class="tt">V</span>. The
corresponding cipher letter should be <span class="tt">F</span> instead
of <span class="tt">P</span>. This is an error of the encipherer in
copying.</p>
<p class="par">Line 2, <span class="tt"><span class=
"underline">SK</span></span> should be <span class="tt">EN</span>. The
corresponding cipher letters should be <span class="tt">YU</span>
instead of <span class="tt">KX</span>. Another telegrapher&rsquo;s
error, <span class="tt">-.-- ..-</span> becoming <span class="tt">-.-
-..-</span></p>
<p class="par">Line 3, <span class="tt"><span class=
"underline">Y</span></span> should be <span class="tt">I</span>. The
corresponding cipher letter should be <span class="tt">L</span> instead
of <span class="tt">V</span>. Another error in copying by the
encipherer.</p>
<p class="par">Line 4, <span class="tt"><span class=
"underline">JX</span></span> should be <span class="tt">OS</span>. The
corresponding cipher letters should be <span class="tt">FK</span>
instead of <span class="tt">KF</span>; an error on the part of the
encipherer in copying.</p>
<p class="par">Line 7, <span class="tt"><span class=
"underline">V</span></span> should be <span class="tt">Y</span>. A
mistake in copying.</p>
<p class="par">Line 8, <span class="tt"><span class=
"underline">SKZRX</span></span>. If we take <span class="tt">X</span>
as a period, then this line might be <span class="tt">OVER</span>, the
<span class="tt">R</span> being correct and <span class=
"pagenum">[<a id="pb100" href="#pb100" name="pb100">100</a>]</span>SKZ
being in question. The corresponding cipher letters are <span class=
"tt">AEO</span> and if we encipher <span class="tt">OVE</span> we get
<span class="tt">ETJ</span>. Here again we have a telegrapher&rsquo;s
error, <span class="tt">. - .---</span> becoming <span class="tt">.- .
---</span></p>
<p class="par">Line 9, <span class="tt"><span class=
"underline">L</span></span> should be <span class="tt">I</span>. The
corresponding cipher letter should be <span class="tt">K</span> instead
of <span class="tt">H</span>; an error in copying by the
encipherer.</p>
<p class="par">The errors by the encipherer above noted are fairly
common ones. These and similar errors are usually found when a cipher
message, prepared as a rough draft by the encipherer, is copied by a
clerk and a careful check of the copy is not made. The letters mistaken
depend, of course, on the encipherer&rsquo;s hand writing or printing.
Other errors, besides those noted, are the confusion of <span class=
"tt">C</span>, <span class="tt">G</span>, and <span class=
"tt">Q</span>; <span class="tt">I</span>, and <span class=
"tt">J</span>; <span class="tt">B</span> and <span class="tt">R</span>,
etc.</p>
<p class="par">The error by the encipherer, in not changing his disk
setting for one letter and thus throwing out the whole process of
deciphering, would not have occurred had he put the message into eight
columns or a multiple thereof and enciphered each column with one disk
setting. This latter method is also very much faster.</p>
<p class="par">Telegraphers&rsquo; errors in cipher transmission are
common and often very confusing. Note should be taken as to whether
Continental or American Morse was used for transmission. An analysis
along the lines indicated will usually develop the error and
correction. If not, a repetition should be demanded, calling attention,
if possible, to the particular groups that are not clear.</p>
<p class="par">The deciphered and corrected message is:</p>
<div class="blockquote">
<p class="par first">&ldquo;Reliable information from Casas Grandes
received here that a mounted detachment left there last night to escort
shipment of arms and ammunition to be smuggled across border next
Friday night, at a point twelve miles east of Douglas. This is in
<span class="pagenum">[<a id="pb101" href="#pb101" name=
"pb101">101</a>]</span>your district. Will you take necessary steps to
prevent this shipment going over? Leader of smugglers said to be Juan
Hernandez of Naco.&rdquo;</p>
</div>
<p class="par"></p>
<p class="par">Another remarkable example of errors in transmission by
American Morse is the following: A message, partly in cipher and partly
in plain text, contained the cipher words</p>
<p class="par xd21e152"><span class="tt">GA GTXIEIT EIDISXQ</span></p>
<p class="par">This, deciphered as far as possible by the alphabet
determined by analysis of the rest of the cipher, read</p>
<p class="par xd21e152"><span class="tt">SU SME_Y_M Y_O_GES</span></p>
<p class="par">It was finally decided that the context required a
single word like <span class="tt">SUSPENDIO</span> or <span class=
"tt">SUSPENDIOLES</span> for this cipher group. An examination along
this line showed that the cipher words should have been</p>
<div class="table">
<table>
<tr>
<td class="cellLeft cellTop">received</td>
<td class="cellTop">G</td>
<td class="cellTop">A</td>
<td class="cellTop">G</td>
<td class="cellTop">L</td>
<td class="cellTop">X</td>
<td class="cellTop">C</td>
<td class="cellTop">U</td>
<td class="cellTop">R</td>
<td class="cellTop">D</td>
<td class="cellTop">P</td>
<td class="cellTop">X</td>
<td class="cellRight cellTop">G</td>
</tr>
<tr>
<td class="cellLeft cellBottom">and were received</td>
<td class="cellBottom">G</td>
<td class="cellBottom">A</td>
<td class="cellBottom">G</td>
<td class="cellBottom">T</td>
<td class="cellBottom">X</td>
<td class="cellBottom">IE</td>
<td class="cellBottom">IT</td>
<td class="cellBottom">EI</td>
<td class="cellBottom">D</td>
<td class="cellBottom">IS</td>
<td class="cellBottom">X</td>
<td class="cellRight cellBottom">Q</td>
</tr>
</table>
</div>
<p class="par"></p>
<p class="par">and that there were five errors in transmission in these
three cipher groups alone.</p>
</div>
</div>
</div>
</div>
</div>
<div class="back">
<div class="transcribernote">
<h2 class="main">Colophon</h2>
<h3 class="main">Availability</h3>
<p class="par first">This eBook is for the use of anyone anywhere at no
cost and with almost no restrictions whatsoever. You may copy it, give
it away or re-use it under the terms of the <a class="exlink xd21e41"
title="External link" href="http://www.gutenberg.org/license" rel=
"license">Project Gutenberg License</a> included with this eBook or
online at <a class="exlink xd21e41" title="External link" href=
"http://www.gutenberg.org/" rel="home">www.gutenberg.org</a>.</p>
<p class="par">This eBook is produced by the Online Distributed
Proofreading Team at <a class="exlink xd21e41" title="External link"
href="http://www.pgdp.net/">www.pgdp.net</a>.</p>
<p class="par">Scans for this book are available from the Internet
Archive (copy <a class="seclink xd21e41" title="External link" href=
"https://archive.org/details/manualforsolutio00hittrich">1</a>).</p>
<p>Library of Congress Classification: UB290 .H5.</p>
<p>Related Library of Congress catalog page: <a class="catlink" href=
"http://lccn.loc.gov/war16000058">war16000058</a>.</p>
<p>Related Open Library catalog page (for source): <a class="catlink"
href="https://openlibrary.org/books/OL7044123M">OL7044123M</a>.</p>
<p>Related Open Library catalog page (for work): <a class="catlink"
href="https://openlibrary.org/works/OL92027W">OL92027W</a>.</p>
<h3 class="main">Encoding</h3>
<span class="bibl">Library of Congress Subject
Headings</span><span class="bibl">Library of Congress
Classification</span>
<h3 class="main">Revision History</h3>
<ul>
<li>2011-12-15 Started.</li>
</ul>
<h3 class="main">External References</h3>
<p>This Project Gutenberg eBook contains external references. These
links may not work for you.</p>
<h3 class="main">Corrections</h3>
<p>The following corrections have been applied to the text:</p>
<table class="correctiontable" summary=
"Overview of corrections applied to the text.">
<tr>
<th>Page</th>
<th>Source</th>
<th>Correction</th>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e220">1</a></td>
<td class="width40 bottom">messages</td>
<td class="width40 bottom">message</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e6299">17</a></td>
<td class="width40 bottom">[<i>Not in source</i>]</td>
<td class="width40 bottom">,</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e6715">22</a></td>
<td class="width40 bottom">begining</td>
<td class="width40 bottom">beginning</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e6976">27</a></td>
<td class="width40 bottom">b</td>
<td class="width40 bottom">d</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e7419">28</a></td>
<td class="width40 bottom">of</td>
<td class="width40 bottom">or</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e10500">37</a></td>
<td class="width40 bottom">Kirckhoff&rsquo;s</td>
<td class="width40 bottom">Kerckhoffs&rsquo;</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e11606">44</a></td>
<td class="width40 bottom">preceeding</td>
<td class="width40 bottom">preceding</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e12747">49</a></td>
<td class="width40 bottom">WE</td>
<td class="width40 bottom">We</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e13053">51</a></td>
<td class="width40 bottom">identfied</td>
<td class="width40 bottom">identified</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e16744">63</a></td>
<td class="width40 bottom">[<i>Not in source</i>]</td>
<td class="width40 bottom">.</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e18132">66</a></td>
<td class="width40 bottom">[<i>Not in source</i>]</td>
<td class="width40 bottom">)</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e18964">67</a></td>
<td class="width40 bottom">0</td>
<td class="width40 bottom">2</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e19119">67</a></td>
<td class="width40 bottom">[<i>Not in source</i>]</td>
<td class="width40 bottom">1</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e25145">89</a></td>
<td class="width40 bottom">.</td>
<td class="width40 bottom">:</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e25759">98</a></td>
<td class="width40 bottom">. .&emsp;. .&emsp;. .</td>
<td class="width40 bottom">. - . - . -</td>
</tr>
<tr>
<td class="width20"><a class="pageref" href="#xd21e25774">98</a></td>
<td class="width40 bottom">. - . - . -</td>
<td class="width40 bottom">- - . . - -</td>
</tr>
</table>
</div>
</div>

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