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                                 MANUAL
                          FOR THE SOLUTION OF
                            MILITARY CIPHERS


                                   BY
                              PARKER HITT
                     Captain of Infantry, U. S. A.


                                PRESS OF
                        THE ARMY SERVICE SCHOOLS
                        Fort Leavenworth, Kansas

                                  1916








                        MANUAL FOR THE SOLUTION
                          OF MILITARY CIPHERS

                                   BY
                              PARKER HITT
                Captain of Infantry, United States Army


INTRODUCTION


The 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.

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.

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.

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' 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.

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.

Kerckhoffs has stated that a military cipher should fulfill the
following requirements:


    1st. The system should be materially, if not mathematically,
         indecipherable.
    2d.  It should cause no inconvenience if the apparatus and methods
         fall into the hands of the enemy.
    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.
    4th. The system should be applicable to telegraphic correspondence.
    5th. The apparatus should be easily carried and a single person
         should be able to operate it.
    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.


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.

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 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.

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
Abbé Tritheme, 1499, are the basis of most of the modern substitution
ciphers.

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.

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.








CHAPTER I

EQUIPMENT FOR CIPHER WORK


Success 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.

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.

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.

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
message contains a particular word, often leads to its solution.

As to luck, there is the old miner's proverb: "Gold is where you
find it."

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.

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.

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's antenna is sufficient, and the station
instruments can be easily carried in a suit case. Three thoroughly
competent operators should be provided, so that the station can be
"listening in" during the entire twenty-four hours.

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.

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.

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.








CHAPTER II

PRINCIPLES OF MECHANISM OF A WRITTEN LANGUAGE


With 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 A, B, C, D, E, 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.

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.

Again there is a fixed ratio of occurrence of 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.

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.

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.




Data for Solution of Ciphers in English

Table I.--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.


             10,000 Letters        200 Letters

         A              778        16   1111111111111111
         B              141         3   111
         C              296         6   111111
         D              402         8   11111111
         E             1277        26   11111111111111111111111111
         F              197         4   1111
         G              174         3   111
         H              595        12   111111111111
         I              667        13   1111111111111
         J               51         1   1
         K               74         2   11
         L              372         7   1111111
         M              288         6   111111
         N              686        14   11111111111111
         O              807        16   1111111111111111
         P              223         4   1111
         Q                8
         R              651        13   1111111111111
         S              622        12   111111111111
         T              855        17   11111111111111111
         U              308         6   111111
         V              112         2   11
         W              176         3   111
         X               27
         Y              196         4   1111
         Z               17

Vowels AEIOU = 38.37%; consonants LNRST = 31.86%; consonants JKQXZ
= 1.77%.

The vowels may be safely taken as 40%, consonants LNRST as 30% and
consonants JKQXZ as 2%.

Order of letters: 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.



Table II.--Frequency table for telegraph messages, English text. This
table varies slightly from the standard frequency table because the
common word "the" is rarely used in telegrams and there is a tendency
to use longer and less common words in preparing telegraph messages.


             10,000 Letters        200 Letters

         A              813        16   1111111111111111
         B              149         3   111
         C              306         6   111111
         D              417         8   11111111
         E             1319        26   11111111111111111111111111
         F              205         4   1111
         G              201         4   1111
         H              386         8   11111111
         I              711        14   11111111111111
         J               42         1   1
         K               88         2   11
         L              392         8   11111111
         M              273         6   111111
         N              718        14   11111111111111
         O              844        17   11111111111111111
         P              243         5   11111
         Q               38         1   1
         R              677        14   11111111111111
         S              656        13   1111111111111
         T              634        13   1111111111111
         U              321         6   111111
         V              136         3   111
         W              166         3   111
         X               51         1   1
         Y              208         4   1111
         Z                6


In this table the vowels AEIOU = 40.08%, consonants LNRST = 30.77%
and consonants JKQXZ = 2.25%.

Orders of letters: 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.



Table III.--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 AH once
and HA twenty-six times.


    A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T   U   V   W   X   Y   Z

A        1   7  10  22  3   2   26   4  2   2    7   8  11   2  9       13  12   9       2  4   1   12
B    5           1   2               1           1   1   1   2               2   1   3               1
C    6       1   1  14  2           11                  11   3           2   3   1   1      1        1
D    6          12  30  1            2           4      30   1           4   1   1   1      1        3
E       11  14  16  12  2   6   33  10  2   6   18  14  12   1  7       36  11  12   2  16  5        1  1
F    3           2   8  2   1        2           2   1   3  25               3   1   1               1
G    4           1   3               2                  11   2           3                           1
H    1      11   2   4  1   4                    1       2   1  1        2  10  50          3        2
I    2   1   4  12   6  5   1   12   1      5    9   8  12   1  3       12  13  22   2   3  6        1  1
J        1
K    1       1       2                                                   2   1       1
L   14   6   2   1   6  1   1    1   6           9       3   6  3        3   2   3   5
M    7           3  13  2        2   3               4   1  10           4   1   1                   2
N   38           3  25      2    1  31      3        2   2  39           4   3      11      2
O    1   1  12   4   8  8   3   12  18  2        4   7   8   3  7       13  15  22       2  6   1    5
P    2           1   8               1           2   4   2   3  2        1   8   1   4          3    1
Q                    2                                   1   1               1
R   16   1   3   3  40  3   6    2   6           1   2   1  25  8        2   2   8  11               2
S   16   1       3  25  1   2       17      1    2   1  12   7  2        9  11   6  11      1        6
T   25   1   3  12  13  5   2    3  20           2   1  24   8  2       16  20  11   6      2   2    7
U    1   2   1   6   1  3   2    2      3        3   1      17  1   5    3   5   5              1
V    3   1           5               5                       3           2           5               1
W    1           2   8      1    1               1   1   2   4               2   3                   3
X    1               4               2                       1                       1
Y    3   2       2   4      1    1               8   1   2      1        3   1   7
Z    1                               1                   1

    A   B   C   D   E   F   G   H   I   J   K   L   M   N   O   P   Q   R   S   T   U   V   W   X   Y   Z



Table IV.--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).


                      TH   50   AT   25   ST   20
                      ER   40   EN   25   IO   18
                      ON   39   ES   25   LE   18
                      AN   38   OF   25   IS   17
                      RE   36   OR   25   OU   17
                      HE   33   NT   24   AR   16
                      IN   31   EA   22   AS   16
                      ED   30   TI   22   DE   16
                      ND   30   TO   22   RT   16
                      HA   26   IT   20   VE   16



Table V.--Table of recurrence of groups of three letters to be expected
in a count of 10,000 letters of English text.


                     THE   89   TIO   33   EDT   27
                     AND   54   FOR   33   TIS   25
                     THA   47   NDE   31   OFT   23
                     ENT   39   HAS   28   STH   21
                     ION   36   NCE   27   MEN   20



Table VI.--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 Q, X and Z are rare as initials
and B, I, J, Q, V, X and Z are rare as finals.


Letters  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
Initial  9  6  6  5  2  4  2  3  3  1  1  2  4  2 10  2  -  4  5 17  2  -  7  -  3  -
Final    1  -  - 10 17  6  4  2  -  -  1  6  1  9  4  1  -  8  9 11  1  -  1  -  8  -


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
Y when a vowel) is as follows:


                  A,   19.5%   E,   32.0%   I,   16.7%
                  O,   20.2%   U,   8.0%    Y,   3.6%


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.




Data for the Solution of Ciphers in Spanish

The Spanish language is written with the following alphabet:


                A  B  C  CH  D  E  F  G  H  I  J  L  LL
              M  N  Ñ  O  P  Q  R  RR  S  T  U  V  X  Y  Z


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, CH, LL and RR and they do not appear as such in
any specimens of Spanish or Mexican cipher examined. Accented vowels
and Ñ are also not found and we may, in general, say that a cipher
whose text is Spanish will be prepared with the following alphabet:


            A B C D E F G H I J L M N O P Q R S T U V X Y Z


and the receiver must supply the accents and the tilde over the N to
conform to the general sense.

However, many Mexican cipher alphabets contain the letters K and
W. This is particularly true of the ciphers in use by secret service
agents who must be prepared to handle words like NEW YORK, WILSON
and WASHINGTON. The letters K and W will, however, have a negligible
frequency except in short messages where words like these occur more
than once.

In this connection, if a cipher contains Mexican geographical names
like CHIHUAHUA, MEXICO, MUZQUIZ, the letters H, X and Z will have a
somewhat exaggerated frequency.

In Spanish, the letter Q is always followed by U and the U is always
followed by one of the other vowels, A, E, I or O. As QUE or QUI
occurs not infrequently in Spanish text, particularly in telegraphic
correspondence, it is well worth noting that, if a Q occurs in a
transposition cipher, we must connect it with U and another vowel. The
clue to several transposition ciphers has been found from this simple
relation.


Table VII.--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.


        10,000 Letters   200 Letters

    A             1352            27    111111111111111111111111111
    B              102             2    11
    C              474             9    111111111
    D              524            10    1111111111
    E             1402            28    1111111111111111111111111111
    F               91             2    11
    G              137             3    111
    H              102             2    11
    I              606            12    111111111111
    J               41             1    1
    L              517            10    1111111111
    M              300             6    111111
    N              619            12    111111111111
    O              818            16    1111111111111111
    P              257             5    11111
    Q               87             2    11
    R              751            15    111111111111111
    S              724            14    11111111111111
    T              422             8    11111111
    U              387             7    1111111
    V               85             2    11
    X                6
    Y              103             2    11
    Z               42             1    1


In this table the vowels AEIOU = 45.65%; consonants LNRST = 30.33%;
consonants JKQXZ = 1.76%.

Order of letters:

           E A O R S N I D L C T U M P G Y (BH) F Q V Z J X.


Table VIII.--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 AI
twice and IA twenty-three times.



     A   B    C    D    E   F   G    H    I   J    L    M    N    O    P    Q    R    S    T    U   V   X   Y   Z

A    9   4   19   11    5       6   17   23       54   18    9    3   20        29   11   21    8   6       2   5   A
B    6                                    3             1         4                                                 B
C   24        6    6   24                 5        3         8    8              9    5         2           2       C
D   31                 29                 3                 19   13             10    9                     4       D
E   12   2    6   59   10       1    5    7   2   12   18   22    4    9        38   25   28   25   3       3       E
F    4                  4                          4         3                        3                     1       F
G    2                  4                 8                  4                                                  2   G
H    2       12        10                                                             2                     1       H
I    2       23   16        5   2                  3   11   13                   6   10    5        3               I
J    3                  2                                    1                                                      J
L   21   3    6        39   3   3         7       21         5    6             12    2         2                   L
M   12                  6                 5        1         6   15              7    2         6           1       M
N   32                 46       2         8                      32                            12           2       N
O            26   22    2   6   3    4    9       16    2    8        20        15    7   11                        O
P   13                  3                 2        4    9    2    7              4   11                             P
Q   11   5                                         1         2                   3         1                        Q
R   40                 27   2             4        4             36    3        11        17    3                   R
S   39                 52                10                  7   14              2             14           3       S
T    5                 13                 4        4        18    5              6   30                             T
U    2        4    2    6   3   4             5         2    6         4   17        15    2                1       U
V    2                  2                          2              2                   2                     2       V
X                                                                                                                   X
Y    5                  6                                         2                   5         2               2   Y
Z    1                  2                                    1                   4              2                   Z

     A   B    C    D    E   F   G    H    I   J    L    M    N    O    P    Q    R    S    T    U   V   X   Y   Z



Table IX.--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.


                      DE   59   ON   32   AC   24
                      LA   54   AD   31   EC   24
                      ES   52   ST   30   CI   23
                      EN   46   ED   29   IA   23
                      AR   40   RA   29   DO   22
                      AS   39   TE   28   NE   22
                      EL   39   ER   27   AL   21
                      RE   38   CO   26   LL   21
                      OR   36   SE   25   PA   20
                      AN   32   UE   25   PO   20




Alphabetic Frequency Tables

(Truesdell)

Frequency of occurrence in 1,000 letters of text:


            Letter   French   German   Italian   Portuguese
            A            80       52       117          140
            B             6       18         6            6
            C            33       31        45           34
            D            40       51        31           40
            E           197      173       126          142
            F             9       21        10           12
            G             7       42        17           10
            H             6       41         6           10
            I            65       81       114           59
            J             3        1       [1]            5
            K           [1]       10       [1]
            L            49       28        72           32
            M            31       20        30           46
            N            79      120        66           48
            O            57       28        93          110
            P            32        8        30           28
            Q            12      [1]         3           16
            R            74       69        64           64
            S            66       57        49           88
            T            65       60        60           43
            U            62       51        29           46
            V            21        9        20           15
            W           [1]       15
            X             3      [1]       [1]            1
            Y             2      [1]       [1]            1
            Z             1       14        12            4




Order of Frequency


French

    E A N R S I U O L D C P M V Q F G B J Y Z
              T                       H X


German

    E N I R T S A D G H C L F M B W Z K V P J Q X Y
                  U       O


Italian

    E A I O L N R T S C D M U V G Z F B Q
                        P           H


Portuguese

    E A O S R I N M T D C L P Q V F G B J Z X Y
                  U                 H




Graphic Frequency Tables

Frequency of occurrence in 200 letters of text.


French

            A   16  1111111111111111
            B    2  11
            C    6  111111
            D   10  1111111111
            E   39  111111111111111111111111111111111111111
            F    2  11
            G    1  1
            H    1  1
            I   13  1111111111111
            J    1  1
            K
            L   10  1111111111
            M    6  111111
            N   16  1111111111111111
            O   11  11111111111
            P    6  111111
            Q    2  11
            R   15  111111111111111
            S   13  1111111111111
            T   13  1111111111111
            U   12  111111111111
            V    4  1111
            W
            X    1  1
            Y
            Z



Italian

            A   23  11111111111111111111111
            B    1  1
            C    9  111111111
            D    6  111111
            E   25  1111111111111111111111111
            F    2  11
            G    3  111
            H    1  1
            I   23  11111111111111111111111
            L   14  11111111111111
            M    6  111111
            N   13  1111111111111
            O   19  1111111111111111111
            P    6  111111
            Q
            R   13  1111111111111
            S   10  1111111111
            T   12  111111111111
            U    6  111111
            V    4  1111
            X
            Y
            Z    2  11



German

            A   10  1111111111
            B    4  1111
            C    6  111111
            D   10  1111111111
            E   32  11111111111111111111111111111111
            F    4  1111
            G    8  11111111
            H    8  11111111
            I   16  1111111111111111
            J
            K    2  11
            L    6  111111
            M    4  1111
            N   24  111111111111111111111111
            O    6  111111
            P    2  11
            Q
            R   14  11111111111111
            S   11  11111111111
            T   12  111111111111
            U   10  1111111111
            V    2  11
            W    3  111
            X
            Y
            Z    3  111



Portuguese

            A   28  1111111111111111111111111111
            B    1  1
            C    7  1111111
            D    8  11111111
            E   28  1111111111111111111111111111
            F    2  11
            G    2  11
            H    2  11
            I   12  111111111111
            J    1  1
            L    6  111111
            M    9  111111111
            N   10  1111111111
            O   22  1111111111111111111111
            P    6  111111
            Q    3  111
            R   13  1111111111111
            S   18  111111111111111111
            T    9  111111111
            U    9  111111111
            V    3  111
            X
            Y
            Z    1  1








CHAPTER III

TECHNIQUE OF CIPHER EXAMINATION


In 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.

The preamble, "place from," 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, "place from," etc., are in an operators' cipher
and are distinct from the body of the message. As these operators'
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's cipher and then to decipher the parts of
the messages enciphered with it.

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,
such a table will give the best evidence for this purpose.

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.

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.

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.

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 "From," "At," "To," "At," "Date,"
are for the information concerning sender and addressee of the cipher
and are to be obtained from the message. In case an operators' cipher
has been used, these parts of the message will have to be deciphered
before the blanks can be filled in.



                  Intelligence Section, General Staff
                             1st Field Army

                       -------------------------------------------------
                               Place,                      Date

                      Record of Cipher Examination

This cipher obtained by               Office No. -----------------------

                                      Received ------------- -----------
----------------------------------                 (Date)       (Hour)

----------------------------------    From -----------------------------

at -------------------------------    At -------------------------------

on ---------------- --------------    To -------------------------------
       (date)           (hour)
                                      At -------------------------------
How being transmitted when obtained.
(Underscore means used and enter      Date -----------------------------
data on sending and receiving
stations).                            Probable language of text --------

                Sending    Receiving          { Transposition ----------
                Station    Station            {
                                              { ------------------------
Radio                                 Class   {
Telephone                                     { Substitution -----------
Telegraph                                     {
Buzzer                                        { ------------------------
Helio
Lantern                               Case -----------------------------
Flag
Cyclist        from        to         Remarks:
Foot Messenger  ,,         ,,
Mtd. Messenger  ,,         ,,

How obtained. (Underscore means
used). Captured before delivery       Solution completed --------- ------
to addressee. Captured after                               (date)  (hour)
delivery to addressee. Intercepted,
not received by addressee. Copied,    Language of text ------------------
but received by addressee.
                                      Key, (if determined) --------------
Remarks:
                                      -----------------------------------

                                      Type ---------- File No. ----------

                                      -----------------------------------

                                      -----------------------------------
                                                    Examiner.



The probable language of the text is assumed from the preceding
data and, if necessary, from internal evidence. Thus a cipher from
a Mexican source and not containing K or W is probably in Spanish.

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.

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 AEIOU,
LNRST, and JKQXZ, while the examining officer is looking over the
cipher for possible recurring groups of letters and underlining them
when found.

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 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.

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 Q and try to connect it with U and another
vowel. The stenographer may be set to work putting the cipher into
rectangles of different dimensions. The clerk'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.

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 4, 5 or 6 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--for example, the most common letter occurring
not over three or four times as often as the least common letter--we
may at once eliminate the first three cases 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
Case 7, or some more complicated case, should be chosen.

If something more complicated than Case 7 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.

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.

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.

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.

Periodically, say once a week or even daily at the beginning 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.








CHAPTER IV

CLASSES OF CIPHERS


There are, in general, two classes of ciphers. These are the
transposition cipher and the substitution cipher.

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.

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).

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.

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.

We can now lay down the rules for determining whether any given cipher
belongs to the substitution class or to the transposition class.

Count the number of letters in the message, the number of vowels,
AEIOU, the number of the consonants, LNRST, and the number of the
consonants, JKQXZ.

If the text is English and the cipher is a transposition cipher,
this proportion will hold; vowels AEIOU constitute 40% of the whole;
consonants LNRST, 30% and consonants JKQXZ, 3%.

If the text be Spanish the proportions for a transposition cipher
will be: vowels AEIOU 45%, consonants LNRST, 30%; consonants JKQXZ, 2%.

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 K, X,
Z 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.

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 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
A, E, N, O and T 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.

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.








CHAPTER V

EXAMINATION OF TRANSPOSITION CIPHERS


After 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.



Case 1.--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.

Taking the message:


            A B C D E F G H I J K L M N O P Q R S T U V W X


of twenty-four letters and assuming a rectangle of six letters
horizontally, and four letters vertically, we may have:


(a) Simple Horizontal:

         A B C D E F   F E D C B A   S T U V W X   X W V U T S
         G H I J K L   L K J I H G   M N O P Q R   R Q P O N M
         M N O P Q R   R Q P O N M   G H I J K L   L K J I H G
         S T U V W X   X W V U T S   A B C D E F   F E D C B A


(b) Simple Vertical:

         A E I M Q U   D H L P T X   U Q M I E A   X T P L H D
         B F J N R V   C G K O S W   V R N J F B   W S O K G C
         C G K O S W   B F J N R V   W S O K G C   V R N J F B
         D H L P T X   A E I M Q U   X T P L H D   U Q M I E A


(c) Alternate Horizontal:

         A B C D E F   F E D C B A   X W V U T S   S T U V W X
         L K J I H G   G H I J K L   M N O P Q R   R Q P O N M
         M N O P Q R   R Q P O N M   L K J I H G   G H I J K L
         X W V U T S   S T U V W X   A B C D E F   F E D C B A


(d) Alternate Vertical:

         A H I P Q X   D E L M T U   X Q P I H A   U T M L E D
         B G J O R W   C F K N S V   W R O J G B   V S N K F C
         C F K N S V   B G J O R W   V S N K F C   W R O J G B
         D E L M T U   A H I P Q X   U T M L E D   X Q P I H A


(e) Simple Diagonal:

         A B D G K O   G K O S V X   O K G D B A   X V S O K G
         C E H L P S   D H L P T W   S P L H E C   W T P L H D
         F I M Q T V   B E I M Q U   V T Q M I F   U Q M I E B
         J N R U W X   A C F J N R   X W U R N J   R N J F C A

         A C F J N R   J N R U W X   R N J F C A   X W U R N J
         B E I M Q U   F I M Q T V   U Q M I E B   V T Q M I F
         D H L P T W   C E H L P S   W T P L H D   S P L H E C
         G K O S V X   A B D G K O   X V S O K G   O K G D B A


(f) Alternate Diagonal:

         A B F G N O   G N O U V X   O N G F B A   X V U O N G
         C E H M P U   F H M P T W   U P M H E C   W T P M H F
         D I L Q T V   B E I L Q S   V T Q L I D   S Q L I E B
         J K R S W X   A C D J K R   X W S R K J   R K J D C A

         A C D J K R   J K R S W X   R K J D C A   X W S R K J
         B E I L Q S   D I L Q T V   S Q L I E B   V T Q L I D
         F H M P T W   C E H M P U   W T P M H F   U P M H E C
         G N O U V X   A B F G N O   X V U O N G   O N G F B A


(g) Spiral, clockwise:

         A B C D E F   L M N O P A   I J K L M N   D E F G H I
         P Q R S T G   K V W X Q B   H U V W X O   C R S T U J
         O X W V U H   J U T S R C   G T S R Q P   B Q X W V K
         N M L K J I   I H G F E D   F E D C B A   A P O N M L


(h) Spiral, counter clockwise:

         A P O N M L   N M L K J I   I H G F E D   F E D C B A
         B Q X W V K   O X W V U H   J U T S R C   G T S R Q P
         C R S T U J   P Q R S T G   K V W X Q B   H U V W X O
         D E F G H I   A B C D E F   L M N O P A   I J K L M N


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.




Message


                         ILVGIOIAEITSRNMANHMNG


This message contains eight vowels or 38% out of twenty-one letters,
and the letters LNRST occur 7 times or 33%, the letters XQJKZ 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:


                             I L V G I O I
                             A E I T S R N
                             M A N H M N G


and reading down each column in succession (Case 1-b) reveals the
message to be "I am leaving this morning."




Message

M S I B R   O R S E E   V U E E M   C O R E R   E L I D E   T O E P Q
E N R E R   N S E R Y   E C O L L   E R E U S   P L U R C   E L O A J
A E H U H   P F A S O   N N O A A   E P I U A   P P E A C   U Q A R U
O P O E I   I R R M I   A F D A A   R Q U B O   Z A E G E   R S F S X


There are 120 letters in this message with 57 vowels or 47% vowels,
and the letters LNRST occur 31 times or 26% of the whole.

Non-occurrence of K and W and vowel proportion leads us to the
assumption that it is a transposition cipher of a Spanish text. The
factors of 120 are 5 × 3 × 2 × 2 × 2. We may then have one rectangle
of 4 × 30 or one of 5 × 24 or two of 5 × 12, or three of 5 × 8, or
four of 5 × 6, or five of 3 × 8, or ten of 3 × 4, or twenty of 3 ×
2. The message being in a rectangle of 4 × 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 × 24, thus:


M  S  I  B  R  O  R  S  E  E  V  U  E  E  M  C  O  R  E  R  E  L  I  D
E  T  O  E  P  Q  E  N  R  E  R  N  S  E  R  Y  E  C  O  L  L  E  R  E
U  S  P  L  U  R  C  E  L  O  A  J  A  E  H  U  H  P  F  A  S  O  N  N
O  A  A  E  P  I  U  A  P  P  E  A  C  U  Q  A  R  U  O  P  O  E  I  I
R  R  M  I  A  F  D  A  A  R  Q  U  B  O  Z  A  E  G  E  R  S  F  S  X


Here an inspection shows this to be Case 1-f, alternate diagonal,
and the text to be "ME SITUO SOBRE PARRAL PORQUE ME PRESENCIA FUE
REVELADA POR U"; here the sense breaks but note that U is the twelfth
letter of the line and continue as if the rectangle were 5 × 12 and
we have "NA PAREJA QU." Now inspect the second rectangle of 5 × 12
in the same way and the sense continues "E SE ME ACERCO Y HUBO QUE
RECHAZAR POR EL FUEGO ALLI ESRERO ORDENES FINISX".

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.

The following ciphers come under Case 1:




Case 1-i.--The rail fence cipher, useful as an operators' cipher but
permits of no variation and is therefore read almost as easily as
straight text when the method is known. The message:


                      HOSTILE CAVALRY HAS RETIRED


is written:


                         O T L C V L Y A R T R D
                        H S I E A A R H S E I E


and is sent:


                     OTLCV LYART RDHSI EAARH SEIEX




Case 1-j.

Message


                   S S O H S   T P F O R   I E E A E
                   T Q N E T   F A I X E   G L F D R
                   A U L R N   O S R X L   H A T R O


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.

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.




Reversed Writing.--(Special case of Case 1-a).

LEAVING TONIGHT is enciphered THGINOT GNIVAEL or it may be reversed
by words, thus GNIVAEL THGINOT or by groups of five letters, thus
IVAEL NOTGN XTHGI.




Vertical Writing.--(Special case of Case 1-b). Same message is
enciphered,


                  LT
                  EO
                  AN
                  VI   and is sent, LTEOA NVIIG NHGTX.
                  IG
                  NH
                  GT




Case 2.--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.




Case 2-a.

Message


     HIIGF   TNGHI   NTCVN   IEIOT   CYIFY   LHAEA   ESNBA   EEEEN
     RWGBN   YDELR   OAESG   RNEBO   VNLDA   ICAOA   LCNDT   IRGVA
     CDOIE   SEREC   DVPEI   AFIFL   RINEH   ETT


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 × 9 or 9 × 12 letters. Put
into this form we have:


                          Vowels                         Vowels

H I I G F T N G H I N T        3     H I I G F T N G H        2
C V N I E I O T C Y I F        5     I N T C V N I E I        4
Y L H A E A E S N B A E        6     O T C Y I F Y L H        2
E E E N R W G B N Y D E        4     A E A E S N B A E        6
L R O A E S G R N E B O        5     E E E N R W G B N        3
V N L D A I C A O A L C        5     Y D E L R O A E S        4
N D T I R G V A C D O I        4     G R N E B O V N L        2
E S E R E C D V P E I A        6     D A I C A O A L C        5
F I F L R I N E H E T T        4     N D T I R G V A C        2
                                     D O I E S E R E C        5
                                     D V P E I A F I F        4
                                     L R I N E H E T T        3


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.


            1   2   3   4   5   6   7   8   9   10   11   12

            H   I   I   G   F   T   N   G   H   I    N    T
            C   V   N   I   E   I   O   T   C   Y    I    F
            Y   L   H   A   E   A   E   S   N   B    A    E
            E   E   E   N   R   W   G   B   N   Y    D    E
            L   R   O   A   E   S   G   R   N   E    B    O
            V   N   L   D   A   I   C   A   O   A    L    C
            N   D   T   I   R   G   V   A   C   D    O    I
            E   S   E   R   E   C   D   V   P   E    I    A
            F   I   F   L   R   I   N   E   H   E    T    T


These combinations appear among others:


                         1   6   2   4   5   2

                         H   T   I   G   F   I
                         C   I   V   I   E   V
                         Y   A   L   A   E   L
                         E   W   E   N   R   E
                         L   S   R   A   E   R
                         V   I   N   D   A   N
                         N   G   D   I   R   D
                         E   C   S   R   E   S
                         F   I   I   L   R   I


The word FIGHT stares at us from the first line; let us arrange the
columns thus:


                         5   2   4   1   6   3

                         F   I   G   H   T   I
                         E   V   I   C   I   N
                         E   L   A   Y   A   H
                         R   E   N   E   W   E
                         E   R   A   L   S   O
                         A   N   D   V   I   L
                         R   D   I   N   G   T
                         E   S   R   E   C   E
                         R   I   L   F   I   F


We have the words FIGHTI(NG), VICIN(ITY), RENEWE(D), ANDVIL(LA),
RDINGT(O), RECE(IVED). 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


                              M E X I C O
                              4 2 6 3 1 5


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.

Actually, this cipher was solved because the word VILLA was suspected
and all the necessary letters were found in line six of the arrangement
in twelve columns. The order 1, 6, 3, 11, 8 was tried and gave
this result.


                           1   6   3   11   8

                           H   T   I   N    G
                           C   I   N   I    T
                           Y   A   H   A    S
                           E   W   E   D    B
                           L   S   O   B    R
                           V   I   L   L    A
                           N   G   T   O    A
                           E   C   E   I    V
                           F   I   F   T    E


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.




Case 2-b.

Message


                 SLCOF   WEETN   EBRDO   ORVYM   FFEDI
                 NMTEC   ROIAR   PERHO   ESETS   RFBHL
                 TENAH   OPTAU   SOMTL   RTETT   ASCBH
                 NIODC   RENEN   AAPRD   LACYE   ECIIE
                 SGUFN


This is a transposition cipher, English text, and contains 105
letters. The factors of 105 are 5 × 3 × 7 so that we must investigate
the following rectangles; 5 × 21, 15 × 7, three of 5 × 7, five of 3 ×
7 and seven of 5 × 3.


21 × 5                                                                                   Vowels
        S   L   C   O   F   W   E   E   T   N   E   B   R   D   O   O   R   V   Y   M   F   6
        F   E   D   I   N   M   T   E   C   R   O   I   A   R   P   E   R   H   O   E   S   9
        E   T   S   R   F   B   H   L   T   E   N   A   H   O   P   T   A   U   S   O   M   7
        T   L   R   T   E   T   T   A   S   C   B   H   N   I   O   D   C   R   E   N   E   6
        N   A   A   P   R   D   L   A   C   Y   E   E   C   I   I   E   S   G   U   F   N   9
Vowels  1   2   1   2   1   0   1   4   0   1   3   3   1   3   3   3   1   1   3   2   1


The vowel count of the columns of the rectangle 5 × 21 is very
satisfactory. Let us consider it as three blocks of 5 × 7 each,
since we must do this ultimately, and make a vowel count of columns
for these blocks.


                5 × 21                     Vowels
                         S   L   C   O   F   1
                         W   E   E   T   N   2
                         E   B   R   D   O   2
                         O   R   V   Y   M   1
                         F   F   E   D   I   2
                         N   M   T   E   C   1
                         R   O   I   A   R   3
                         P   E   R   H   O   2
                         E   S   E   T   S   2
                         R   F   B   H   L   0
                         T   E   N   A   H   2
                         O   P   T   A   U   3
                         S   O   M   T   L   1
                         R   T   E   T   T   1
                         A   S   C   B   H   1
                         N   I   O   D   C   2
                         R   E   N   E   N   2
                         A   A   P   R   D   2
                         L   A   C   Y   E   2
                         E   C   I   I   E   4
                         S   G   U   F   N   1
                Vowels   7   9   8   7   6


                                             Column

                                        1   2   3   4   5
               Vowels, 1st block        2   2   3   2   2
               Vowels, 2d block         2   3   2   2   2
               Vowels, 3d block         3   4   3   2   2


This is also excellent, so we will try three blocks 5 × 7 and see
if rearrangement of horizontal lines will give results reading the
columns vertically.


                 1   S L C O F   P E R H O   A S C B H
                 2   W E E T N   E S E T S   N I O D C
                 3   E B R D O   R F B H L   R E N E N
                 4   O R V Y M   T E N A H   A A P R D
                 5   F F E D I   O P T A U   L A C Y E
                 6   N M T E C   S O M T L   E C I I E
                 7   R O I A R   R T E T T   S G U F N


Among other combinations are:


                 3   E B R D O   R F B H L   R E N E N
                 2   W E E T N   E S E T S   N I O D C
                 1   S L C O F   P E R H O   A S C B H

                 5   F F E D I   O P T A U   L A C Y E
                 7   R O I A R   R T E T T   S G U F N


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.




Case 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.




Message

                 WVGAE   EGENL   TFTOH   TEIEF   RBTSE
                 INENG   ONWRM   GXIXN   GOITN   ROMRO
                 ESPAL   HNEAC   UDNNH   DERME


This is a transposition cipher, English text and the number of letters,
70, leads us to try rectangles of 10 × 7 and 7 × 10.


                               Vowels                   Vowels

         W V G A E E G E N L        4   W V G A E E G        3
         T F T O H T E I E F        3   E N L T F T O        2
         R B T S E I N E N G        3   H T E I E F R        3
         O N W R M G X I X N        2   B T S E I N E        3
         G O I T N R O M R O        4   N G O N W R M        1
         E S P A L H N E A C        4   G X I X N G O        2
         U D N N H D E R M E        3   I T N R O M R        2
                                        O E S P A L H        3
                                        N E A C U D N        3
                                        N H D E R M E        2


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.


                   1   2   3   4   5   6   7   8   9   10

               1   W   V   G   A   E   E   G   E   N   L
               2   T   F   T   O   H   T   E   I   E   F
               3   R   B   T   S   E   I   N   E   N   G
               4   O   N   W   R   M   G   X   I   X   N
               5   G   O   I   T   N   R   O   M   R   O
               6   E   S   P   A   L   H   N   E   A   C
               7   U   D   N   N   H   D   E   R   M   E


Among other combinations we have these:


                   3   5   1   4   2   8   10   6   9   7

               1   G   E   W   A   V   E   L    E   N   G
               2   T   H   T   O   F   I   F    T   E   E
               3   T   E   R   S   B   E   G    I   N   N
               4   W   M   O   R   N   I   N    G   X   X
               5   I   N   G   T   O   M   O    R   R   O
               6   P   L   E   A   S   E   C    H   A   N
               7   N   H   U   N   D   R   E    D   M   E


A very casual inspection of the lines shows that they should be
rearranged in order 6, 1, 2, 7, 3, 5, 4, as follows:


                   3   5   1   4   2   8   10   6   9   7

               6   P   L   E   A   S   E   C    H   A   N
               1   G   E   W   A   V   E   L    E   N   G
               2   T   H   T   O   F   I   F    T   E   E
               7   N   H   U   N   D   R   E    D   M   E
               3   T   E   R   S   B   E   G    I   N   N
               5   I   N   G   T   O   M   O    R   R   O
               4   W   M   O   R   N   I   N    G   X   X


Although of no particular importance, it may be stated that the
column key in this case was GRAND and the line key was CENTRAL,
both used as in enciphering Case 2-a.




Case 3. 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.

"To encipher the message 'MOVE DAYLIGHT. ENEMY APPROACHING FROM
NORTH. PRISONERS SAY STRENGTH ONE HUNDRED THOUSAND. MEET HIM AS
PLANNED.' arrange as follows:


              MOVE          STRENGTH   PLANNED   SAY
              DAYLIGHT      ONE        AS        PRISONERS
              ENEMY         HUNDRED    HIM       NORTH
              APPROACHING   THOUSAND   MEET      FROM


Here the route is down the first column, up the fourth, down the
second and up the third."

This cipher was often complicated by the introduction of nulls for
every fifth word. Thus the above message might be sent:


    MOVE STRENGTH PLANNED SAY NEVER DAYLIGHT ONE AS PRISONERS LEAVING
    ENEMY HUNDRED HIM NORTH UNCHANGED APPROACHING THOUSAND MEET
    FROM COME.


The words in italics are nulls and not a part of the message and the
receiver eliminates them before arranging his message in columns to
get the sense of it.

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,--as to march,
to sail, to encamp, to attack, to retreat,--were represented by
other words.

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.




General Remarks on Transposition Ciphers

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 Kerckhoffs' requirements as
to indecipherability, safety when apparatus and method fall into the
hands of the enemy, and dependability on a readily changeable key word.

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.

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
by complicated rules, will, on analysis, be seen to be very simple.

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 EHT,
LLIW, ROF, DNA, etc., should be appreciated immediately as common
words written backward.

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.

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.








CHAPTER VI

EXAMINATION OF SUBSTITUTION CIPHERS


When 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.

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:

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.

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.

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.




Case 4-a.

Message


           OBQFO BPBRP QBAML OBHIF PILFQ FJBOX OFLNR BIXOZ EL


From the recurrence of B, F and O, 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:


                          O B Q F O B P B R P
                          P C R G P C Q C S Q
                          Q D S H Q D R D T R
                          R E T I R E S E U S


The word RETIRESE 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
USTED POR EL MISMO ITINERARIO QUE MARCHO. The message was enciphered
using an alphabet where A = X, B = Y, C = Z, D = A, etc. noting that
as this message is in Spanish the letters K and W do not appear in
the alphabet.




Case 4-b.

Message

           HUJZH UIUPN OZYTS VQXMI SMOMX MQHUD UMREI SESJU AG

This is a message in Spanish. We will handle it as in case 4-a,
setting down the whole message.


    HUJZHUIU   PNOZY   TSV   QX    MISMO   MXMQHUDUMR   EIS   ESJUAG
    IVLAIVJV   QOPAZ   UTX   RY    A=A     NYNRIVEVNS   FJT   FTLVBH
    JXMBJXLX   RPQBA   VUY   SZ            OZOSJXFXOT   GLU   GUMXCI
    LYNCLYMY   SQRCB   XVZ   TA            PAPTLYGYPU   HMV   HVNYDJ
    MZODMZNZ   TRSDC   YXA   UB            QBQUMZHZQV   INX   IXOZEL
    NAPENAOA   USTED   ZYB   VC            RCRVNAIARX   JOY   JYPAFM
    OBQFOBPB   A=U     AZC   XD            SDSXOBJBSY   LPZ   LZQBGN
    PCRGPCQC           BAD   YE            TETYPCLCTZ   MQA   MARCHO
    QDSHQDRD           CBE   ZF            UFUZQDMDUA   NRB   A=S
    RETIRESE           DCF   AG            VGVARENEVB   OSC
    A=Q                EDG   BH            XHXBSFOFXC   PTD
                       FEH   CI            YIYCTGPGYD   QUE
                       GFI   DJ            ZJZDUHQHZE   A=O
                       HGJ   EL            ALAEVIRIAF
                       IHL   A=M           BMBFXJSJBG
                       JIM                 CNCGYLTLCH
                       LJN                 DODHZMUMDI
                       MLO                 EPEIANVNEJ
                       NMP                 FQFJBOXOFL
                       ONQ                 GRGLCPYPGM
                       POR                 HSHMDQZQHN
                       A=E                 ITINERARIO
                                           A=D


Here each word of the message comes out on a different line, and
noting in each case the letter corresponding to A, we have the word
QUEMADOS which is the key. The cipher alphabet changed with each word
of the message.

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.

Note in using case 4 that if we are deciphering a Spanish message
we use the alphabet without K or W as a rule, altho if the letters
K or W appear in the cipher it is evidence that the regular English
alphabet is used.




Case 5-a.

Message


    DNWLW MXYQJ ANRSA RLPTE CABCQ RLNEC LMIWL XZQTT QIWRY ZWNSM
    BKNWR YMAPL ASDAN


This message contains K and W and therefore we expect the English
alphabet to be used. The frequency of occurrence of A, L, N, R and
W has lead us to examine it under case 4 but without result. Let us
set down the first two words and decipher them with a cipher disk
set A to A and then proceed as in case 4.


               Cipher message    DNWLWMXYQJ
               Deciphered A to   A            XNEPEODCKR
                                 B            YOFQFPEDLS
                                 C            ZPGRGQFEMT
                                 D            AQHSHRGFNU
                                 E            BRITISHGOV


The message is thus found to be enciphered with a cipher disk set
A to E and the text is: BRITISH GOVERNMENT PLACED CONTRACTS WITH
FOLLOWING FIRMS DURING SEPTEMBER.




Case 5-b.

Same as case 4-b except that the cipher message must be deciphered
by means of a cipher disk set A to A 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 case 4-b.

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 form is here presented in order to compare with it the
frequency table for the message discussed in case 4-a.


Standard Spanish                                Table for Message
frequency table                                 Case 4-a

A   111111111111111111111111111         27      A   1            1
B   11                                   2      B   1111111      7
C   111111111                            9      C
D   1111111111                          10      D
E   1111111111111111111111111111        28      E   1            1
F   11                                   2      F   11111        5
G   111                                  3      G
H   11                                   2      H   1            1
I   111111111111                        12      I   111          3
J   1                                    1      J   1            1
L   1111111111                          10      L   111          3
M   111111                               6      M   1            1
N   111111111111                        12      N   1            1
O   1111111111111111                    16      O   111111       6
P   11111                                5      P   111          3
Q   11                                   2      Q   111          3
R   111111111111111                     15      R   11           2
S   11111111111111                      14      S
T   11111111                             8      T
U   1111111                              7      U
V   11                                   2      V
X                                               X   11           2
Y   11                                   2      Y
Z   1                                    1      Z   1            1


Our first assumption might be that B = A and F = E but it is evident
at once that in that case, S, T, U and V (equal to R, S, T and U)
do not occur and a message even this short without R, S, T or U is
practically impossible. By trying B = E 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 coördinate 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
case 6-a is of this character. An examination of the frequency table
given under that case shows that it bears no graphic resemblance to the
standard table. However, as will be seen in case 7-b, 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.




General Remarks

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.




Case 6-a.

Message

    QDBYP BXHYS OXPCP YSHCS EDRBS ZPTPB BSCSB PSHSZ AJHCD OSEXV HPODA
    PBPSZ BSVXY XSHCD


This message was received from a source which makes us sure it is in
Spanish. The occurrence of B, H, P and S 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 preceding and following
letter. This latter proceeding takes little longer than the preparation
of an ordinary frequency table and gives most valuable information.


        Frequency Table

                                    Prefix         Suffix

        A   11                  2   ZD             JP
        B   11111111            8   DPRPBSPZ       YXSBSPPS
        C   11111               5   PHSHH          PSSDD
        D   11111               5   QECOC          BROA
        E   11                  2   SS             DX
        F
        G
        H   111111              6   XSSJVS         YCSCPC
        I
        J   1                   1   A              H
        L
        M
        N
        O   111                 3   SDP            XSD
        P   111111111           9   YXCZTBHAB      BCYTBSOBS
        Q   1                   1                  D
        R   1                   1   D              B
        S   111111111111       12   YYCBBCPHOPBX   OHEZCBHZEZVH
        T   1                   1   P              P
        U
        V   11                  2   XS             HX
        X   11111               5   BOEVY          HPVYS
        Y   1111                4   BHPX           PSSX
        Z   111                 3   SSS            PAB


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.

We may assume that P and S are probably A and E, both on account of
the frequency with which they occur and the variety of their prefixes
and suffixes. If this is so, then B and H, are probably consonants
and may represent R and N respectively. D and X are then vowels by
the same method of analysis. Noting that HC occurs three times and
taking H as N we conclude that C is probably T. Substitute these
values in the last three words of the message because the letters
assumed occur rather frequently there.


                            PBPSZBSVXYXSHCD

                                    I I   I
                            ARAE_RE_ _ ENT
                                    O O   O


Now Z is always prefixed by S and may be L. Taking X=I and D=O,
(they are certainly vowels), V=G and Y=M, we have


                           ARA EL REGIMIENTO


Substituting these values in the rest of the message we have


              Q   DBYPBXH   YSOXPCP   YSHCSED   RBSZPTPB
              _   ORMARIN   ME_IATA   MENTE_O   _RELA_AR

                  BSCSB     PSHSZ     AJHCD     OSEXVHPODA
                  RETER     AENEL     __NTO     _E_IGNA_O_


We may now take Q=F, O=D, E=S, R=B, T=C, A=P and J=U and the message
is complete. We are assisted in our last assumption by noting that
S=E and E=S, 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.


Ordinary   A B C D E  F   G  H  I   J   L   M   N  O P Q R S T U V X Y Z
Cipher     P R T O S (Q) (V) N (X) (U) (Z) (Y) (H) D A F B E C J G I M L


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.----




Case 6-b.

Message


    Lt. J. B. Smith, Royal Flying Corps, Calais, France.

                 DACFT   RRBHA   MOOUE   AENOI   ZTIET
                 ASMOS   EOHIE   YOCKF   NOHOE   NOUTH
                 OMEAH   NILGO   OSAHU   OHOUE   APCHS
                 TLNDA   CFTEN   INTWN   BAFOH   GROHT
                 AEIOH   ABRIS   ODACF   TRREN   OSTSM
                 AYBIS   DFTEN   EFAPH   OSMNI   ZTIEA
                 HLILL   TWSOU   GDENO   UTHOM   EAHBH
                 AMOOU   EAYOE   QISUU   OLEHA   DENOE
                 NHOOQ   OBBOR   TSLHO   BAHEO   UBHOB
                 IHTSW   ENOHO   PAHIH   ITUAS   BIHTL

                                                Graham-White.


The address and signature indicate that this message is in English.

There are 250 letters in the cipher; the vowels AEIOU occur 109 times
or 43.6%, the letters LNRST occur 62 times or 24.8%, and the letters
KQVXZ occur 5 times or 2%. The proportion in the case of the vowels
is somewhat too large and, in the case of the letters LRNST, it is
too small. It is then questionable whether this is a transposition
cipher altho, at first glance it might appear to be one.

On examination for parts of possible words we are at once struck by
the occurrence at irregular intervals of recurring groups, viz:


                   DACFTRR   ENO            BHAMOOUEA
                   DACFTEN   ENOUTHOMEAH    BHAMOOUEA
                             ENO
                   DACFTRR   DENOUTHOMEAH   IZTIE
                   FTEN      DENO           IZTIE
                             ENO


This is a strong indication that the cipher is a substitution cipher,
so, to make an examination a frequency table will be constructed.


    Frequency Table

    A    B    C   D   E    F   G   H    I    J   K   L   M
    23   11   7   6   24   7   3   26   16   0   1   8   8

    N    O    P   Q   R   S    T    U    V   W   X   Y   Z
    15   36   3   2   8   14   17   11   1   3   0   3   2


Superficially, this looks like a normal frequency table, but O is
the dominant letter, followed by H, E, A, T, I, N, S, in the order
named. It is certainly Case 6 if it is a substitution cipher at all.

Let us see what can be done by assuming O=E; the triplet ENO, occurring
six times might well be THE and E=T and N=H. A glance at the frequency
table shows this to be reasonable. Now substitute these letters in some
likely groups. FNOHOENO becomes _HE_ETHE; FTEN becomes _TH; ENOENHO
becomes THETH_E; ENOHO becomes THE_E. A bit of study will show that
F=W, T=I and H=R and the frequency table bears this out except that
H(=R) seems to occur too frequently. The recurring groups containing
DAC (see above) occur in such a way that we may be sure DAC is one
word, FTRR is another and FTEN(=WITH) is a third. Now FTRR becomes
WI__, which can only be completed by a double letter. LL fills the
bill and we may say R=L. As DAC starts the message and is followed
by FTRR (=WILL) it is reasonable to try DAC=YOU. Looking up DAC in
the frequency table it is evident that we strain nothing by this
assumption. We now have:


                 Letters of cipher    ONTAHECFD
                 Letters of message   EHIORTUWY


Now take the group ENOUTHOMEAH which occurs twice. This
becomes THE_IRE_TOR and if we substitute U=D and M=C we have THE
DIRECTOR. Next the group (FTRR)BHAMOOUEA becomes (WILL) _ROCEEDTO
and the context gives word with missing letter as PROCEED, from
which B=P. Next the group (ENO) IZTIETASMOSEOHIEYOCK(FNOHO) becomes
(THE)__I_TIO_CE_TER_T_EU_(WHERE) and the group (FTEN)EFAPHOSMNIZTIEAHL
becomes (WITH)TWO_RE_CH__I_TOR_. The substitution of A for I, V for
Z, N for S and F for P makes the latter group read (WITH TWO FRENCH
AVIATORS and the former read (THE)AVIATION CENTER AT _EU_(WHERE).

Now the word YOCK = (_EU_) is the name of a place, evidently. We
find another group containing Y, viz: ENOSTSMAYBISD which becomes
THENINCO_PANY so that evidently we should substitute M for Y. The
other occurrence of Y (=M) is in the group EAYOEQISU which becomes
TOMET_AND. A reasonable knowledge of geography gives us the words
MEUX and METZ so that X should be substituted for K and Z for Q.

We now have sufficient letters for a complete deciphering of the
message.


             Letters of cipher    ABCDEFGHIKLMNOPQRSTUVWYZ
             Letters of message   OPUYTW_RAXSCHEFZLNID__MV


The message deciphers:


    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.


The substitution of B for G, G for W and K for V 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.

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.




Case 6-c.--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:


                 "??2&   45x15   )"8&#   &&1x4   %&4&%
                 6x?&"   8&*x4   6°*°&   %"4&"


By arbitrary substitution of letters this is made


                 ABBCD   EFGHF   IJKDL   DDHGE   MDEDM
                 NGBDA   KDOGE   NPOPD   MAEDA


This message is now in convenient shape to handle as Case 6-a and on
solution is found to read:


         ALL PERSONS HAVE BEEN ORDERED TO LEAVE FORTIFIED AREA.


In the same way the message


    1723 3223 2825 1828 3630 2336 1423 2827 2324 3120 2317 3123
    3036 2120 2415 3029 1512 2831 1721 2715 2811 2715 1923 3030
    1215 1130 2128 3623


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:


       AB   CB   DE   FD   GH   BG   IB   DJ   BK   LM   BA   LB
       HG   NM   OP   HQ   PR   DL   AN   JP   DS   JP   TB   HH
       RP   SH   ND   GB


and this message is also in shape to handle as Case 6-a. It reads,
on solution,


    SEVEN HUNDRED MEN LEFT YESTERDAY FOR POINTS ON LOWER RIO GRANDE.








CHAPTER VII


We 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.

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.

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, "All radio messages must hereafter be put
in cipher," with the key Grant, using the Vigenere cipher alphabets
given below. Each of these alphabets is identified by the first or left
hand letter which represents A of the text. We thus will use in turn
the alphabets beginning with G, with R, with A, with N, and with T.


                 G   R   A   N   T   G   R   A   N   T

                 A   L   L   R   A   D   I   O   M   E
                 S   S   A   G   E   S   M   U   S   T
                 H   E   R   E   A   F   T   E   R   B
                 E   P   U   T   I   N   C   I   P   H
                 E   R


Using the alphabet indicated by G, we get


                                 G   J
                                 Y   Y
                                 N   L
                                 K   T
                                 K


Continuing for the other alphabets, we get


                 G   C   L   E   T   J   Z   O   Z   X
                 Y   J   A   T   X   Y   D   U   F   M
                 N   V   R   R   T   L   K   E   E   U
                 K   G   U   G   B   T   T   I   C   A
                 K   I


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.

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:


A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z
B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A
C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B
D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C
E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D
F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E
G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F
H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G
I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H
J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I
K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J
L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K
M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L
N  O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M
O  P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N
P  Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O
Q  R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P
R  S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q
S  T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R
T  U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S
U  V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T
V  W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U
W  X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V
X  Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W
Y  Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X
Z  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y


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 BAD, the second,
first and fourth alphabets are used in turn and the word WILL is
enciphered XIOM.

The Larrabee cipher is merely a slightly different arrangement of
the Vigenere cipher and is printed on a card in this form:


                ----------------------------------
                A       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        abcdefghijklmnopqrstuvwxyz
                ----------------------------------
                B       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        bcdefghijklmnopqrstuvwxyza
                ----------------------------------
                C       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        cdefghijklmnopqrstuvwxyzab
                ----------------------------------
                etc.
                ----------------------------------
                Y       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        yzabcdefghijklmnopqrstuvwx
                ----------------------------------
                Z       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        zabcdefghijklmnopqrstuvwxy
                ----------------------------------


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.

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 A is set
to the letter of the key word.


                     Fixed Alphabet of Text
    |                                                     |
    |ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ |
    +-----------------------------------------------------+
         |  ABCDEFGHIJKLMNOPQRSTUVWXYZ               |
         |                                           |
         |       Movable Alphabet of Cipher          |
         +-------------------------------------------+


As shown here, A of the fixed or text alphabet coincides with T
of the movable cipher alphabet. This is the setting where T is the
letter of the key word in use. The lower movable alphabet is moved
for each letter of the message and the A 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 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 A of the
fixed alphabet is obtained by rotating the disk.

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:


                      Fixed Alphabet
    |                                                      |
    | ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ |
    +------------------------------------------------------+
          |  ZYXWVUTSRQPONMLKJIHGFEDCBA              |
          |                                          |
          |             Movable Alphabet             |
          +------------------------------------------+


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 A = G then G = A. This
is not true of the Vigenere cipher.

It is perfectly feasible to substitute a card for the U. S. Army
cipher disk. It would have this form:


                          ABCDEFGHIJKLMNOPQRSTUVWXYZ
                      1   AZYXWVUTSRQPONMLKJIHGFEDCB
                      2   BAZYXWVUTSRQPONMLKJIHGFEDC
                      3   CBAZYXWVUTSRQPONMLKJIHGFED
                   etc.
                     25   YXWVUTSRQPONMLKJIHGFEDCBAZ
                     26   ZYXWVUTSRQPONMLKJIHGFEDCBA


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.

One of the ciphers of Porta was prepared with a card of this kind:


                 -----------------------------
                 AB              ABCDEFGHIJKLM
                                 NOPQRSTUVWXYZ
                 -----------------------------
                 CD              ABCDEFGHIJKLM
                                 ZNOPQRSTUVWXY
                 -----------------------------
                 EF              ABCDEFGHIJKLM
                                 YZABCDEFGHIJK
                 -----------------------------
                 etc.
                 -----------------------------
                 WX              ABCDEFGHIJKLM
                                 PQRSTUVWXYZNO
                 -----------------------------
                 YZ              ABCDEFGHIJKLM
                                 OPQRSTUVWXYZN
                 -----------------------------


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 BAD to encipher WILL
we would get JVXY. Note that with either B or A as the key letter,
the first alphabet would be used.

A combination of the Vigenere and Porta ciphers is this:


                ----------------------------------
                A       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        ABCDEFGHIJKLMNOPQRSTUVWXYZ
                ----------------------------------
                BC      ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        BCDEFGHIJKLMNOPQRSTUVWXYZA
                ----------------------------------
                DE      ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        CDEFGHIJKLMNOPQRSTUVWXYZAB
                ----------------------------------
                etc.
                ----------------------------------
                VW      ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        LMNOPQRSTUVWXYZABCDEFGHIJK
                ----------------------------------
                XY      ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        MNOPQRSTUVWXYZABCDEFGHIJKL
                ----------------------------------
                Z       ABCDEFGHIJKLMNOPQRSTUVWXYZ
                        NOPQRSTUVWXYZABCDEFGHIJKLM
                ----------------------------------


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.

This cipher can also be operated by a fixed and sliding alphabet.


                     Fixed Alphabet of Text:
    |                                                      |
    | ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ |
    +------------------------------------------------------+
          | ABCDEFGHIJKLMNOPQRSTUVWXYZ               |
          |                                          |
          |        Sliding Alphabet of Cipher        |
          |                  Index                   |
          +------------------------------------------+
            BDFHJLNPRTVX
           A            Z      Letters of Key.
            CEGIKMOQSUWY


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.

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 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.

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. [2]

"--This simple disk can be used with a cipher word or, preferably,
cipher words, known only to the correspondents.... Using the key word
'disk' to encipher the message 'Artillery commander will order all
guns withdrawn,' we will proceed as follows: Write out the message
to be enciphered and above it write the key word ... letter over
letter, thus:


            |    |    |    |    |    |    |    |    |    |
        DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DISK|DIS
        ARTI|LLER|YCOM|MAND|ERWI|LLOR|DERA|LLGU|NSWI|THDR|AWN
            |    |    |    |    |    |    |    |    |    |
        DRZC|SXOT|FGEY|RIFH|ZRWC|SXET|AEBK|SXMQ|QQWC|XBPT|DMP
            |    |    |    |    |    |    |    |    |    |


"Now bring the 'a' of the upper disk under the first letter of the
key word on the lower disk, in this case 'D'. The first letter of
the message to be enciphered is 'A': 'd' is found to be the letter
connected with 'A', and it is put down as the first cipher letter. The
letter 'a' is then brought under 'I' which is the second letter of the
key word. 'R' is to be enciphered and 'r' 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 'D', so continue
until all letters of the message have been enciphered. Divided into
groups of five letters, it will be as follows:


         "DRZCS XOTFG EYRIF HZRWC SXETA EBKSX MQQQW CKBPT DMF."


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);


                     CSX--CSX   16 = 4×4
                      SX--SX    16 = 4×4
                      SX--SX     8 = 2×4
                      WC--WC    16 = 4×4


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.

A later and more extensive example (Case 7-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 CSX in the above example. The
number of alphabets having been determined each alphabet is handled
by the methods of Case 6 already discussed.




Case 7-a.--The following message appeared in the "personal" column
of a London paper:


    "M. B. Will deposit £27 14s 5d tomorrow,"


and the next day we find this one:


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.


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 W 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 AEIOU number 90 and the letters JKQXZ number 78. It is thus
a substitution cipher (20% of 473=94.6).

Recurring words and similar groups are AIIWG, AII; BKSM, BKAI; CT,
CTWY, CTW; DLMMJXL, DL; ESF, ESBP; FJNVX, FJHVSI; NPSI, NPUXQG; OSB,
OSY, ROSB; OL, OL; PORTELOGJ, PO; SQ, SQA; TP, TP; TLBWTPZ, TLFNS,
TLFTWMC; UVZUA, UVD, UV; XMKUL, XMKUHW; YJL, YJVTI.




Frequency Table for the Message

A   B   C   D  E   F   G   H   I   J   K   L   M   N   O   P   Q   R  S   T   U   V   W   X   Y   Z
15  13  15  8  13  20  16  16  30  21  13  27  14  19  15  26  13  9  33  30  17  12  19  20  19  11


This clearly eliminates Cases 4, 5 and 6.

Referring to the recurring words and groups above noted, we figure
the number of letters between each.

                AII    ...   AII     45   =   3×3×5
                BK     ...   BK     345   =   23×3×5
                CT     ...   CT     403       No factors
                CTW    ...   CTW     60   =   2×2×3×5
                DL     ...   DL      75   =   3×5×5
                ES     ...   ES      14   =   2×7
                FJ     ...   FJ     187       No factors
                NP     ...   NP      14   =   2×7
                OL     ...   OL     120   =   2×2×2×3×5
                OS     ...   OS     220   =   11×2×2×5
                OSB    ...   OSB    465   =   31×3×5
                PO     ...   PO     105   =   7×3×5
                SQ     ...   SQ     250   =   2×5×5×5
                TLF    ...   TLF     80   =   2×2×2×2×5
                TP     ...   TP     405   =   3×3×3×3×5
                UV     ...   UV     115   =   23×5
                XMKU   ...   XMKU   120   =   2×2×2×3×5
                UV     ...   UV      73       No factors
                YJ     ...   YJ      85   =   17×5


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:


Frequency Tables

Colum 1        Column 2                 Column 3       Column 4               Column 5

A  11          A  111111111             A  1           A  1                   A  11
B              B  111                   B  111         B                      B  1111111
C  1111111     C  1                     C  111         C  1111                C
D  11          D  11                    D  1           D                      D  111
E  1111        E                        E  11          E  1111111             E
F  111         F                        F  111111111   F  111                 F  11111
G  111111111   G                        G  111         G  11                  G  11
H  111         H  11111                 H  111         H  111                 H  11
I  11          I  11                    I  1111111     I  11111111111111111   I  11
J  11111       J  1                     J  111111      J                      J  111111111
K  111111      K  11111                 K              K  1                   K  1
L              L  1111111111111111111   L  11          L  11111               L  1
M              M                        M  1111111     M  1111                M  111
N  1111111     N  111                   N  1111        N                      N  11111
O  11111       O                        O  111111111   O  1                   O
P  1111111     P  1111111               P  11111111    P  1111                P
Q  11111       Q                        Q              Q  11                  Q  111111
R              R  1                     R  1           R  111111              R  1
S              S  11111111              S  111111      S  111111111111        S  1111111
T  1111111     T  111                   T  11111       T  1                   T  11111111111111
U  1111111     U  111                   U  111111      U                      U  1
V  11111       V                        V  11          V  11111               V
W  111         W  1111                  W              W  11111               W  1111111
X  11          X                        X  1111        X  11111111            X  111111
Y  1111        Y  11111                 Y              Y  111                 Y  1111111
Z              Z  11111                 Z  111         Z                      Z  111


In the table for Column 1, the letter G occurs 9 times. Let us
consider it tentatively as E. Then if the cipher alphabet runs
regularly and in the direction of the regular alphabet, C (7 times)=A
and the cipher alphabet bears a close resemblance to the regular
frequency table. Note TUV (=RST) occurring respectively 7, 7, and 5
times and the non-occurrence of B, L, M, R, S, Z, (=Z, J, K, P, Q,
and X respectively.)

In the next table, L occurs 19 times and taking it for E with the
alphabet running in the same way, A=H. The first word of our message,
CT, thus becomes AM when deciphered with these two alphabets and the
first two letters of the key are C H.

Similarly in the third table we may take either F or O for E, but a
casual examination shows that the former is correct and A=B (even if
we were looking for a vowel for the next letter of the keyword).

In the fourth table, I is clearly E and A=E. The fifth table shows
T=14 and J=9. If we take T=E we find that we would have many letters
which should not occur. On the other hand, if we take J=E then
T=O and in view of the many E'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, OSB, which
deciphers NOW. Using these alphabets to decipher the whole message,
we find it to read:


    "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 tamper with
    your correspondence but later on when hue and cry have died down
    will let you know all."


The key to this message is CHBEF 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 "personal"
which appeared in the same paper the day before reading:


    "M. B. Will deposit £27 14s 5d tomorrow."




Case 7-b.

Message

             DDLRM   ERGLM   UJTLL   CHERS   LSOEE   SMEJU
             ZJIMU   DAEES   DUTDB   GUGPN   RCHOB   EQEIE
             OOACD   EIOOG   COLJL   PDUVM   IGIYX   QQTOT
             DJCPJ   OISLY   DUASI   UPFNE   AECOB   OESHO
             BETND   QXUCY   LUQOY   EHYDU   LXPEQ   FIXZE
             PDCNZ   ENELQ   MJTSQ   ECFIE   ARNDN   ETSCF
             IFQSE   TDDNP   UUZHQ   CDTXQ   IRMER   GLXBE
             IQRXJ   FBSQD   LDSVI   XUMTB   AEQEB   YLECO
             IYCUD   QTPYS   VOQBL   ULYRO   YHEFM   OYMUY
             ROYMU   EQBLV   UBREY   GHYTQ   CMUBR   EQTOF
             VSDDU   DAFFS   CEBSV   TIOYE   TCLQX   DVNLQ
             XYTSI   MZULX   BAXQR   ECVTD   ETGOB   CCUYF
             TTNXL   UNEFS   IVIJR   ZHSBY   LLTSI


On the preliminary determination, we have the following count of
letters out of a total of 385:


                A         8   L        23   J         9
                E        38   N        11   Q        22
                I        19   R        14   V         9
                O        21   S        20   X        13
                U        24   T        21   Z         6

                Total   110   Total    89   Total    59
                        28%           23%           15%


Every letter except K and W 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 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, HOBE, OYMU, RMERGL and
UBRE show, without question, that six alphabets were used. It is not
necessary, as a rule, to make a complete list like the following:


AE     74=2×37          IE     110=2×5×11          RE       50=2×5×5
AE     120=2×2×2×3×5    IM     302=2×151           RMERGL   198=2×3×3×11
BE     88=2×2×2×11      IO     250=2×5×5×5         SC       132=2×2×3×11
CD     132=2×2×3×11     IX     78=2×3×13           SD       262=2×131
CFI    12=2×2×3         LY     158=2×79            SI       230=2×5×23
CH     36=2×2×3×3       JT     150=2×3×5×5         SI       34=2×17
CO     42=2×3×7         LL     367 No factors      SI       264=2×2×2×3×11
CO     126=2×3×3×7      LQ     164=2×2×41          SI       12=2×2×3
CU     114=2×3×19       LQX    6=2×3               SL       78=2×3×13
DD     186=2×3×31       LU     124=2×2×31          SQ       54=2×3×3×3
DD     116=2×2×29       LU     110=2×5×11          SV       27=3×3×3
DE     285=5×57         LU     234=2×3×3×13        SV       63=3×3×7
DL     218=2×109        LX     66=2×3×11           SV       90=2×3×3×5
DN     14=2×7           LXB    132=2×2×3×11        TD       47 No factors
DQ     120=2×2×2×3×5    LY     158=2×79            TD       165=3×5×11
DU     36=2×2×3×3       ME     22=2×11             TD       96=2×2×2×2×2×3
DU     24=2×2×2×3       MU     24=2×2×2×3          TN       239 No factors
DU     38=2×19          MU     240=2×2×2×2×3×5     TS       14=2×7
DU     165=3×5×11       MU     18=2×3×3            TS       156=2×2×3×13
EA     30=2×3×5         ND     47 No factors       TSI      50=2×5×5
EB     78=2×3×13        NE     48=2×2×2×2×3        UBRE     12=2×2×3
EC     180=2×2×3×3×5    NE     18=2×3×3            UD       60=2×2×3×5
ECO    126=2×3×3×7      NE     192=2×2×2×2×2×2×3   UDA      270=2×3×3×3×5
EES    14=2×7           OB     6=2×3               UL       114=2×3×19
EF     105=3×5×7        OB     234=2×3×3×13        ULX      198=2×3×3×11
EI     8=2×2×2          OE     93=3×31             UY       89 No factors
EI     152=2×2×2×19     OI     144=2×2×2×2×3×3     UZ       162=2×3×3×3×3
EQ     88=2×2×2×11      OO     7 No factors        VI       148=2×2×37
EQ     264=2×2×2×3×11   OY     6=2×3               VT       33=3×11
EQ     44=2×2×11        OY     46=2×23             XQ       114=2×3×19
EQE    176=2×2×2×2×11   OYMU   6=2×3               XQ       144=2×2×2×2×3×3
ER     12=2×2×3         PD     75=3×5×5            XU       99=3×3×11
ES     78=2×3×13        QBL    24=2×2×2×3          YE       184=2×2×2×23
ET     135=3×3×5        QC     95=5×19             YL       106=2×53
ET     9=3×3            QE     108=2×2×3×3×3       YL       144=2×2×2×2×3×3
ET     54=2×3×3×3       QE     68=2×2×17           YM       6=2×3
ET     31 No factors    QR     132=2×2×3×11        YRO      12=2×2×3
HE     245=5×7×7        QTO    210=2×3×5×7         ZE       6=2×3
HOBE   66=2×3×11        QX     198=2×3×3×11        ZH       183=3×61


Out of one hundred and one recurring pairs we have fifty with the
factors 2×3=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 HAVANA 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.

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 numbers after "Prefix" and "Suffix" refer to the
alphabet to which these belong, for convenience in future reference.


    Frequency Tables

    First Alphabet

    Letter                   Prefix (6)       Suffix (2)

    A  111               3   DUD              ESF
    B  11111111          8   OOOFEEOS         EOESYSCY
    C                    0
    D  1111              4   TYT              DJUD
    E  1                 1   E                S
    F                    0
    G                    0
    H                    0
    I  11111111          8   EOFFEOVS         OSEFQYJ
    J                    0
    L  1                 1   O                J
    M  1                 1   F                O
    N  1111              4   FEDU             EEEE
    O  1                 1   E                O
    P  11                2   GE               ND
    Q  1111              4   UEOE             OFBB
    R  1111111           7   EEEYYBB          GSGOOEE
    S  1                 1   D                V
    T  11111111          8   JUJMQYVF         LDSBPQDT
    U                    0
    V  11                2   UF               MS
    X  111111            6   YQTQQA           QUQDYQ
    Y  1                 1   O                E
    Z  111               3   UUM              JHU


    Second Alphabet

    Letter                   Prefix (1)       Suffix (3)

    A                    0
    B  111               3   TQQ              ALL
    C  1                 1   B                C
    D  111111            6   DTPDXT           LBCNVE
    E  11111111111 1     1   ABNBNINRRYN      EOATLATYQTF
    F  111               3   QIA              IQF
    G  11                2   RR               LL
    H  1                 1   Z                O
    I                    0
    J  1111              4   ZLDI             ILCR
    L  1                 1   T                L
    M  1                 1   V                I
    N  1                 1   P                R
    O  1111111           7   OIBQRMR          AOEYYYY
    P  1                 1   T                Y
    Q  11111             5   XXITX            OIRCR
    R                    0
    S  11111111          8   REIATBVB         LMLIQQDV
    T  1                 1   T                N
    U  111               3   XDZ              CLL
    V  1                 1   S                I
    X                    0
    Y  1111              4   BIXB             LCTL
    Z                    0


    Third Alphabet

    Letter                   Prefix (2)       Suffix (4)

    A  1111              4   OEEB             CERE
    B  1                 1   D                G
    C  111111            6   JUDYQC           PYNUMU
    D  1                 1   S                D
    E  111               3   EOD              SST
    F  11                2   FE               SS
    G                    0
    H                    0
    I  111111            6   JMSFQV           MGUXRX
    J                    0
    L  11111111111111   14   DGLSJSUEGYBBUY   RMCSPYXQXEUVXL
    M  1                 1   S                E
    N  11                2   DT               PX
    O  1                 1   O                G
    P                    0
    Q  1111111           7   EQSFHSE          ETESCDT
    R  1111              4   NQQJ             CXEZ
    S                    0
    T  1111              4   EEEY             NSCS
    U                    0
    V  11                2   SD               TN
    X                    0
    Y  111111            6   OPOOOE           ESHMMG
    Z                    0


    Fourth Alphabet

    Letter                   Prefix (3)       Suffix (5)

    A                    0
    B                    0
    C  11111             5   LRAQT            HHDDL
    D  11                2   QD               LU
    E  11111111          8   MQAYQALR         JICHCQCC
    F                    0
    G  1111              4   BOIY             UCIH
    H  1                 1   Y                E
    I                    0
    J                    0
    L  1                 1   L                T
    M  11111             5   LIYYC            UUUUU
    N  111               3   TCV              DZL
    O                    0
    P  111               3   LCN              DJU
    Q  1                 1   L                M
    R  111               3   LAI              MNM
    S  111111111         9   LEETQYFTF        ODHCEVCII
    T  1111              4   QQVE             OOIG
    U  1111              4   ICLC             PDLY
    V  1                 1   L                U
    X  1111111           7   LILRILN          PZBUBL
    Y  11                2   LC               DLJ
    Z  1                 1   R                H


    Fifth Alphabet

    Letter                   Prefix (4)       Suffix (6)

    A                    0
    B  11                2   XX               EA
    C  1111111           7   GDDSDSD          OOFFOEV
    D  111111            6   SCPYNCU          UEUUQTQ
    E  11                2   SH               TP
    F                    0
    G  1                 1   U                T
    H  111111            6   CCSDGZ           EOOYYS
    I  11111             5   EGTSS            EYOMV
    J  111               3   EPX              UOP
    L  111111            6   YDUCNX           UDYQQU
    M  111               3   RQR              EJE
    N  1                 1   R                D
    O  111               3   STT              ETF
    P  11                2   UX               FE
    Q  1                 1   E                E
    R                    0
    S                    0
    T  1                 1   L                S
    U  1111111111       10   MMGPXMMVMD       JDGUMYEBBD
    V  1                 1   S                O
    X                    0
    Y  1                 1   U                F
    Z  11                2   XN               EE


    Sixth Alphabet

    Letter                   Prefix (5)       Suffix (1)

    A  1                 1   B                X
    B  11                2   UU               RR
    C                    0
    D  1111              4   UNLU             ANSA
    E  1111111111111    13   MHOIDPZZMBQUC    RREOIQPNRIBQB
    F  1111111           7   PCCJEOC          NIIBMVT
    G  1                 1   U                P
    H                    0
    I                    0
    J  11                2   UM               TT
    L                    0
    M  11                2   UI               TZ
    N                    0
    O  111111111         9   HCJCHCVIG        BLIBBIQYB
    P                    0
    Q  1111              4   DDLL             XTXX
    R                    0
    S  11                2   HT               BI
    T  111               3   OED              DDX
    U  1111111           7   JDDDLUL          ZTVAQZN
    V  11                2   CI               TI
    X  1                 0   I
    Y  11111             5   IHLUH            XDRRT
    Z                    0


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 A is probably represented by a vowel in these two
alphabets and probably equals A or O, because these two letters are
such common finals in Spanish.

1st Alphabet. Probable vowels T, X; probable common consonants, B, I,
N, R. We conclude this because of the frequency of occurrence of T and
X and the variety of their prefixes and suffixes. On the other hand, B,
I, N, and R have for prefixes and suffixes, in a majority of cases, E,
F, O and S which are the probable vowels in the 2d and 6th alphabets.

2d and 6th Alphabets.--Probable vowels E, F, O, S; probable common
consonants, D, J, Q, U, Y.

3d Alphabet.--Probable vowels C, I, L; probable common consonants A,
Q, T, Y.

4th Alphabet.--Probable vowels, E, G, S, T; probable common consonants,
C, M, N, P, U, X.

5th Alphabet.--Probable vowels, D, L, U; probable common consonants,
C, H, I.

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:


    |               Fixed Alphabet of Text                 |
    |   ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ   |
    +------------------------------------------------------+
         |          PCJVRQZBAODFSUTMXIYHLGEN        |
         |         Movable Alphabet of Cipher        |
         +-------------------------------------------+


Here A of the plain text is enciphered by S and the other letters come
as they will. If we move the cipher alphabet one space to the left,
A will be enciphered by U and the whole sequence of the alphabet will
be changed.

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:


                   ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
    1st Alphabet                          t   x
    2d                                    ol qei ms  d c u
    3d                                   ol qei ms  d c u
    4th                               ol qei ms  d c u
    5th                                   d c u      ol qei  ms
    6th                                   ol qei ms  d c  u


In the 1st alphabet, T and X are placed as A and E respectively on the
basis of frequency. In the 2d and 6th alphabets, O and E are placed as
A and E respectively on the basis of frequency. In the 4th alphabet,
E and S are placed as A and E, and in the 5th, D, U and L are placed
as A, E and O for the same reason. We now have an excess of E's and
a deficiency of A's, which will be corrected if, in the 3d alphabet,
we place L, I and C as A, E and O respectively. As a check, this
gives us TOLEDO as the key word.

In the second alphabet, O is four letters to the left of E; we may
place O four letters to the left of E in the fourth and it comes under
V. Note that in the fourth frequency table O (=V) does not occur. In
the same way in the fourth alphabet, S is four letters to the right
of E; placing it in the same position with respect to E in the second
and sixth, we have S under I. We have already noted that S probably
represents a vowel in these two alphabets. In this way, we may add
D and U to the third alphabet from their position in the fifth with
respect to L and we may add I and O to the fifth from their position
in the third with respect to L. In every case we check results from
the frequency tables and find nothing unlikely in the results.

Now in the second and sixth, let us try Q, D and U as D, N and R
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 L to the
second, third, fourth and sixth from its position with reference to
D and U in the fifth. M is probably D 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.

Let us try these letters on the first line of the message and see if
some other letters will be self-evident.


Alphabet     1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
Message      D D L R M E R G L M U J T L L C H E R S L S O E E S M E J U
Deciphered   _ N A _ U E _ _ A D E _ A B A L _ E _ I A E N E _ I G A _ R


Referring to our frequency tables as a check on suppositions, we find
everything agrees well enough if we assume the first line to read:


                    UNAFUERZA DE CABALLERIA ENEMIGA


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 D (=U) 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:


               ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
         1st                           T   xhgoljqei msr  d c u
         2d                     t   xhgOLjQEI MSr  D C U
         3d                    t   xhgOLjQEI MSr  D C U
         4th                t   xhgOLjQEI MSr  D C U
         5th        t   xhgOLjQEI MSr  D C U
         6th                    t   xhgOLjQEI MSr  D C U


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.


Alphabet   5612345612345612345612345612345612345612345612345612345612
Message    JUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQ
Deciphered PR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_ED


Again referring to the frequency tables the first word is
evidently PROCEDENTE. We have also HALLA and MARCHEUSTED. The
letter B may be determined from another cipher group, JFBSQDLD
(56123456) =POSICION. The letter N may be determined from BETNDQXUC
(123456123) =SERRADERO. The letters F and Y may be determined from
JCPJOISLYDUASIUPF (23456123456123456)= COMPANIA PARTIENDO. The
completed alphabets, arranged as before, are:


               ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
         1st                           TYVNXHGOLJQEIZMSRBADFCPU
         2d                     TYVNXHGOLJQEIZMSRBADFCPU
         3d                    TYVNXHGOLJQEIZMSRBADFCPU
         4th                TYVNXHGOLJQEIZMSRBADFCPU
         5th        TYVNXHGOLJQEIZMSRBADFCPU
         6th                    TYVNXHGOLJQEIZMSRBADFCPU


The key word is TOLEDO and the completely deciphered message is:


    "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."




Special Solution for Case 7

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.

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 reënforcements and to
contain that word.


                     YANZV   ZNLPP   KQFXI   JBPWA
                     NRUQP   EPLOM   CCWHM   I


Let us assume that REINFORCEMENTS is the first word and that it is
represented by the cipher group YANZVZNLPPKQFX. We may put the test in
this tabular form, using a cipher disk and a Larrabee cipher card to
determine the value of A for each letter under these two systems. Any
other alphabets suspected may be tried out at the same time.

If


         Y   A   N   Z   V   Z   N   L   P   P   K   Q   F   X


equals


         R   E   I   N   F   O   R   C   E   M   E   N   T   S


then, with cipher disk, A equals


         P   E   R   M   A   N   E   N   T   B   O   D   Y   P


and, in Vigenere cipher, A equals


         H   W   F   M   Q   L   W   J   L   D   G   D   M   F


It is evident that the guess as to the appearance of the word
REINFORCEMENTS 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 PERMANENT BODY.

This is, of course, an especially favorable case and we will take
one less favorable to show how this method can be applied.

Two Mexican chieftains, A and B, have been communicating with the
following cipher alphabet:


                 Plain text   ABCDEFGHIJLMNOPQRSTUVXYZ
                 Cipher       PCJVRQZBAODFSUTMXIYHLGEN


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's radio station (and  other
listening stations) and about an hour later there is a good deal of
noise and movement as if B's force were breaking camp.


                 IIHAH   YDXRP   EGQGV   JJEEE   HOBGV
                 GJCAG   XAESA   VVXLE   IILHM   PSQAG
                 BDGAV   GSQAZ


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.

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.


    |                 Fixed Cipher Alphabet                |
    |   PCJVRQZBAODFSUTMXIYHLGENPCJVRQZBAODFSUTMXIYHLGEN   |
    +------------------------------------------------------+
          |         ABCDEFGHIJLMNOPQRSTUVXYZ         |
          |       Sliding Plain Text Alphabet        |
          +------------------------------------------+


                A-B Cipher

                If  I  equals  O  then A equals  R
                    I          R                 C
                    H          D                 X
                    A          E                 R
                    H          N                 B
                    Y          O                 Q


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 PEGQGV at
once since the preceding letters do not make ORDENO QUE. We try this
without result and proceed to EGQGVJ, GQGVJJ, QGVJJE, GVJJEE, VJJEEE,
JJEEEH, JEEEHO, EEEHOB, EEHOBG, EHOBGV, HOBGVG, OBGVGJ, BGVGJC, GVGJCA,
VGJCAG, 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 GJCAGX. We add
the next three letters, AES, against QUE.

If

                  G   J   C   A   G   X      A   E   S

equals

                  O   R   D   E   N   O      Q   U   E

Then, in the A-B cipher, A equals

                  A   D   E   R   O   V      I   V   A

The key is found; VIVA_ADERO and a trial of M 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:


    PARA EL ATAQUE CONTRA TORREON ORDENO QUE SUS TROPAS MARCHEN ESTE
    NOCHE X.


The reason for breaking camp is now evident.

This method may be used, with some labor, on short words like THE, AND,
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.

As an example of recovery of a key by use of short common words, let
us refer to the message of Case 7-a. There are twenty-four groups of
three letters each in this message and we will try them against THE,
ARE and YOU, assuming that the Vigenere cipher is used.


                  1    2    3    4    5    6    7    8    9   10   11   12

If              OSB  VOI  GSW  CYY  ZSZ  BVJ  XLD  OSY  UVD  YJL  SQA  HSI
equals          THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE
or              ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE
or              YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU
then A equals   VLX  CHE  NLS  JRU  GLV  IOF  EEZ  VLU  BOZ  FCH  ZJW  OLE
or              OBX  VXE  GBS  CHU  ZBV  BEF  XUZ  OBU  UEZ  YSH  SZW  HBE
or              QEH  XAO  IEC  EKE  BEF  DHP  ZXJ  QEE  WHJ  AVR  UCG  JEO

                 13   14   15   16   17   18   19   20   21   22   23   24

If              BJV  SFX  DQB  AII  OHZ  IVX  JBF  ESF  JSC  NLU  CTW  CSM
equals          THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE  THE
or              ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE  ARE
or              YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU  YOU
then A equals   ICR  ZYT  KJX  HBE  VAV  POT  QUB  LLB  QLY  UEQ  JMS  JLI
or              BSR  SOT  DZX  ARE  OQV  IET  JKB  EBB  JBY  NUQ  CCS  CBI
or              DVB  URD  FCH  YUO  QTF  KHD  LNL  GEL  LEI  PXA  EFC  EES


In column 5, we have, for YOU, the key BEF; column 6 gives the same key
for ARE; column 10 gives the key FCH for THE and column 15 gives the
same key for YOU; column 12 gives the key HBE for ARE and column 16
gives the same key for THE; column 23 gives the key EFC for YOU. The
only possible key for the message is a five-letter one made up of the
letters BEFCH or EFCHB or FCHBE or CHBEF or HBEFC. 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 ZSZ (=YOU) form the
3d, 4th and 5th letters of a group. The corresponding key letters, BEF,
are then the 3d, 4th and 5th letters of the key which must be CHBEF.

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.








CHAPTER VIII


Case 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.

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 SS
or BB, (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.

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 I and J as one letter in this cipher and
they are written together in the same square.

If the key word chosen is LEAVENWORTH, then the square would be
constructed as follows:


                           L    E   A   V   N
                           W    O   R   T   H
                           B    C   D   F   G
                           IJ   K   M   P   Q
                           S    U   X   Y   Z


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.

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, TY is represented by FV.

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 RH is represented by TW.

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 TS is represented by WY.

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 X,
Y, or Z, should be introduced to separate the similar letters.

If the message to be sent were "The enemy moves at dawn," it would
be divided into pairs:


                     TH   EX   EN   EM   YM   OV   ES   AT   DA   WN
   and enciphered:   HW   AU   AL   AK   XP   TE   LU   VR   MR   HL


The message is then broken up into groups of five letters for
transmission.

To decipher such a cryptogram, (knowing the key word), the receiver
divides it into pairs, and 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.

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
D of the plain text, in combination with each of the other letters
of the alphabet. We have, using the key LEAVENWORTH:


DA DB DC DE DF DG DH DI DK DL DM DN DO DP DQ DR DS DT DU DV DW DX DY DZ
MR FC FD CA FG FB GR BM CM BA MX GA CR FM GM MD BX FR CX FA BR MA FX GX


This gives D represented by   B   C   F   G   M
                              4   4   8   4   4   times,

and, connected with these five letters representing D,
we have                          A   R   D   M   X   B   C   G
                                 5   5   2   4   5   1   1   1   times.

Note that these letters are those of the vertical column containing
D plus the letters B, C and G, of the horizontal line containing D.

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 word,
or in other words, letters occurring in the first or second lines. An
example will make this clear:


Message

    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.


From this message, we make up the following table, considering the
letters of each pair:


First Letters of Pairs

    A  B  C  D  E  F  G  H  I  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

A      3     1  4                                   1                 1
B   3        2           3                 1  1  4  1     3     1     1
C                              1                                   1
D      2                                                           2  1
E                              1                       5        1
F      1                 2           1  1  1
G            1                                      1        1           1
H                                                   5     1           3
I      1                                      1  5     1
K                                          1     2  1
L               8                                                           1
M               1                                                           1
N         1        1     2                 1                          2     1
O      6                                      1     4     1
P      2                                   1        2                 3
Q               2
R      1                 2     2              7  2        1
S      2           2                                                  1
T      1                                         2                    1
U      1              3                 1
V                                                2
W         2
X   1  5     1  4  1  1                    3           2  1  1
Y      5                                                                    1
Z                  2  1                                   2


From this table we pick out the letters B, E, F, O, R, T, X, 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 A to the list on account of its occurrences with
B, D, E, R, and X. This leaves the letters for the bottom lines of
the square as follows:


                       +----+----+----+----+----+
                       |  . |  . |  . |  . |  . |
                       +----+----+----+----+----+
                       |  . |  . |  . |  C |  D |
                       +----+----+----+----+----+
                       |  G |  H  | IJ|  K |  L |
                       +----+----+----+----+----+
                       |  M |  N |  P |  Q |  S |
                       +----+----+----+----+----+
                       |  U |  V  | W |  Y |  Z |
                       +----+----+----+----+----+


Referring to the table again we find the most frequent combination to
be EL, occurring 8 times, with no occurrence of LE. Now, TH is the
commonest pair in plain text, and HT is not common. The fact that
H occurs in the same horizontal line with L and that E and T are
probably in the key, will lead us to put E in the first line over H
and T in the first line over L, so as to make EL equal TH.

The next most frequent combination is PR occurring 7 times, with RP
occurring twice. In the square as partially arranged, PR equals M_
or N_ or Q_ or I_. We may eliminate all these except N_, and this N_
could only be NO or NA, so that we will put, tentatively the R in
the second line over H and the O and A in the same line over IJ. We
have then:


                       +----+----+----+----+----+
                       |  . |  E |  . | .  |  T |
                       +----+----+----+----+----+
                       |  . |  R | AO |  C |  D |
                       +----+----+----+----+----+
                       |  G |  H | IJ |  K |  L |
                       +----+----+----+----+----+
                       |  M |  N | P  |  Q |  S |
                       +----+----+----+----+----+
                       |  U |  V |  W |  Y |  Z |
                       +----+----+----+----+----+


Let us now check this by picking out the combinations beginning with EL
and seeing if the table will solve them. We find, ELTV, ELAB, ELBXFZ,
ELBXBT, ELAXCWBY, ELAXCWEQ, ELRH, ELBXFS. Now, on the assumption that
the letter after EL represents E, we have it represented by A three
times, B three times, R once and T once. This requires that A and B
be put in the same horizontal line with E, since T is already there,
and R is tentatively under E.

The combination ELTV now equals THEZ. If the T were moved one place
to the left, it would be THEY, a more likely combination, but this
requires the L to be moved one place to the left also, by putting I
or K in the key word and taking out O, R or X and returning it to its
place in the alphabetical sequence. The most frequent pairs containing
O are B O six times, R O four times, and O X three times. Now these
pairs equal respectively E N, E S and H E, if O is put between N
and P in the fourth line. We will therefore cease to consider it
as a letter of the the key word. The combination ELAB can only be
THE_ on the assumption that A is the first letter to the right of
E. The combination ELBX occurs three times. If it represents THE_,
the B must be the first letter of the first line and the X must now
be placed under E where the R was tentatively put. We can get THE_
out of ELRH by putting R in the first line or leaving it where it
is, but the preponderance of the BX combination should suggest the
former alternative.

A new square showing these changes will look like this:


                       +----+----+----+----+----+
                       |  B |  E |  A |  T |  R |
                       +----+----+----+----+----+
                       |  . |  X |  . |  . |  . |
                       +----+----+----+----+----+
                       |  G |  H |  . |  L |  M |
                       +----+----+----+----+----+
                       |  N |  O | P  |  Q |  S |
                       +----+----+----+----+----+
                       |  U |  V |  W |  Y |  Z |
                       +----+----+----+----+----+


As I put in the space under B will give the word BEATRIX and as a
vowel is clearly necessary there, we will so use the IJ and leave
K between H and L. This leaves C, D and F to be placed. It appeared
at first that F 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


                       +----+----+----+----+----+
                       |  B |  E |  A |  T |  R |
                       +----+----+----+----+----+
                       | IJ |  X |  C |  D |  F |
                       +----+----+----+----+----+
                       |  G |  H |  K |  L |  M |
                       +----+----+----+----+----+
                       |  N |  O | P  |  Q |  S |
                       +----+----+----+----+----+
                       |  U |  V |  W |  Y |  Z |
                       +----+----+----+----+----+


With this square, the message is deciphered without difficulty.

    "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."

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 F has already been noted;
the letter O occurred with many other letters because it happened
to remain in the same line with N and S and to be under H. It thus
was likely to represent any of these three letters which occur very
frequently in any text.




Two-character Substitution Ciphers

Case 9.--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
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.

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.




Case 9a.--

Message


    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


This message contains 160 letters and it will be noted that the only
letters used are A, G, N, R and T.

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.


    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


With arbitrary letters substituted, we have


    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


Now, preparing a frequency table, with note of prefixes and suffixes
we have:


                   Frequency         Prefix       Suffix

            A       7   1111111      FMKAFF       BGKACBQ
            B      10   1111111111   AGHNOAPIBQ   CHDOEIEBDG
            C       6   111111       BDIIAE       DIFFNE
            D       9   111111111    CBLFKFBKD    EICKMJIDF
            E       4   1111         DBBC         FFCI
            F       8   11111111     ECCEPDPM     ADDAAIRL
            G       2   11           AB           BK
            H       4   1111         BKJH         BHLL
            I       9   111111111    DCKJBEDFL    JCCKPBPP
            J       3   111          IDL          KHI
            K       5   11111        JDAIG        HDIAD
            L       3   111          HHF          DJI
            M       2   11           DR           AF
            N       1   1            C            B
            O       1   1            B            B
            P       3   111          III          BFF
            Q       1   1            A            B
            R       1   1            F            M
            S       1   1            I


A brief study of this table and the distribution in the cipher leads
to the conclusion that B, F and C are certainly vowels and are, if
the normal frequency holds, equal to E, O, and A or I. Similarly D
and I are consonants and we may take them as N and T. I is taken as T
because of the combination IP (=possibly TH) occurring three times. The
next letter in order of frequency is A; it is certainly a consonant
and may be taken as R on the basis of its frequency. Let us now try
these assumptions on the first two lines of the message. We have


            A                                 A   A
        R E   N _ O R _ E _ E N T _ _ _ _ _ N   T   O N _ N _
            I                                 I   I


This is clearly the word REINFORCEMENTS and, using the letters thus
found, the rest of the line becomes AMMUNITIONAND. We have then the
following letters determined:


Arbitrary letters   A   B   C   D   E   F   G   H   I   J   K   L   M
Plain Text          R   E   I   N   F   O   C   M   T   S   A   U   D


If these be substituted we have for the message:

    REINFORCEMENTS AMMUNITION AND RATIONS MUST ARRI_E _EFORE T_E
    FIFTEENT_ OR _E CANNOT _O_D OUT_.

From this the remainder of the letters are determined:


               Arbitrary letters   N   O   P   Q   R   S
               Plain text          V   B   H   W   L   X


Now let us substitute the two-letter groups for the arbitrary letters:


Arbitrary letters   K  O  G  M  B  E  P  C  R  H  D  F  A  J  I  L  N  Q  S
Two-letter groups   GG RG AG NG TG GR AR NR GA RA AA NA RN AN NN TN GT RT AT
Plain text          A  B  C  D  E  F  H  I  L  M  N  O  R  S  T  U  V  W  X


It is evident that the cipher was prepared with the letters of the
word GRANT chosen by means of a square of this kind:


                             G   R   A   N   T
                         G   A   B   C   D   E
                         R   F   G   H   I   K
                         A   L   M   N   O   P
                         N   Q   R   S   T   U
                         T   V   W   X   Y   Z


Thus TG=E, AN=S, etc., as we have already found.




Case 9-b

Message


           1950492958   3123252815   4418452815   2048115041
           2252115345   5849134124   5028552526   5933195222
           5245113215   6215584143   2861361265   2945565015
           2342455850   6345542019   1550185311   2115415828
           1124174553   4554205950   2552454132   1533492048
           5018152364


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 will be noted that 41 to
66 would give us a similar alphabet. Let us make a frequency table
in this form:


             Group   Frequency   Group   Frequency

              11     11111        41     11111
              12     1            42     1
              13     1            43     1
              14                  44     1
              15     111111111    45     111111111
              16                  46
              17     1            47
              18     111          48     11
              19     111          49     111
              20     1111         50     11111111
              21     1            51
              22     11           52     1111
              23     111          53     111
              24     11           54     11
              25     111          55     1
              26     1            56     1
              27                  57
              28     11111        58     11111
              29     11           59     11
              30                  60
              31     1            61     1
              32     11           62     1
              33     11           63     1
              34                  64     1
              35                  65     1
              36     1            66


Each of these tables looks like the normal frequency table except for
the position of 20 and 50 which should represent T, by all our rules,
and should be apparently 30 and 60. But suppose we put the alphabet
and corresponding numerals in this form:


                      1   2   3   4   5   6   7   8   9   0

             1 or 4   A   B   C   D   E   F   G   H   I   J
             2 or 5   K   L   M   N   O   P   Q   R   S   T
             3 or 6   U   V   W   X   Y   Z


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.




Case 9c--

Message


     1156254676   2542294432   1949294015   1423217211   2979703115
     4924213511   7424147875   7646252444   5143254845   3179742533
     4055461512   7573227945   1627481511   7042351944   1378252149
     2514764553   1548342126   7215254075   1611257845   4642217415
     4952197929   7015242143   2925444933   1970187531   4079254829
     4551491411   7321171554


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.


                      Group    Frequency

                       11      111111
                       12      1
                       13      1
                       14      1111
                       15      111111111
                       16      11
                       17      1
                       18      1
                       19      1111
                       20
                       21      1111111
                       22      1
                       23      1
                       24      1111
                       25      11111111111
                       26      1
                       27      1
                       28
                       29      111111
                       30
                       31      111
                       32      1
                       33      11
                       34      1
                       35      11
                       36
                       37
                       38
                       39
                       40      1111
                       41
                       42      111
                       43      11
                       44      1111
                       45      11111
                       46      1111
                       47
                       48      1111
                       49      111111
                       50
                       51      11
                       52      1
                       53      1
                       54      1
                       55      1
                       56      1
                       57
                       58
                       59
                       70      1111
                       71
                       72      11
                       73      11
                       74      111
                       75      1111
                       76      111
                       77
                       78      111
                       79      11111


We at once note the resemblance between the frequency tables for the
groups 11 to 19 and 21 to 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 A to I; the groups 41 to 49 and 71 to 79 have a
frequency fitting well with the normal frequency table of the letters
K to S; and the groups 31 to 36 and 51 to 56 have a frequency fitting
well with the normal frequency table of the letters U to Z. We have
J and T unaccounted for, but note what occurred in Case 9-b and that
40 and 70 would correspond well with T if they followed respectively
49 and 79. We may now make up a cipher table as follows:


                      1   2   3   4   5   6   7   8   9   0

             1 or 2   A   B   C   D   E   F   G   H   I   J
             4 or 7   K   L   M   N   O   P   Q   R   S   T
             3 or 5   U   V   W   X   Y   Z


and this table will solve the cipher message.

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.








CHAPTER IX

OTHER SUBSTITUTION METHODS


The 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.

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.

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.

A book by Commandant Bazeries, entitled "Etude sur la Cryptographie
Militaire," and a series of articles by A. Collon, entitled "Etude
sur la Cryptographie," which appeared in the Revue de L'Armée Belge,
1899-1902, 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.

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.

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.

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.

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.




Combined Transposition and Substitution Methods

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.

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.

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 fence rail (Case 1-i), reversed writing or vertical writing.

A few examples will show some of the possible combinations.

The first line of the message of Case 4-a is:


                               OBQFOBPBRP


We might write it BFBBPOQOPR (Case 1-i), or PRBPBOFQBO (Case 1,
reversed writing), or OFQBOPRBPB (Case 1, reversed by groups of five).

The first line of the message of Case 2-b is:


                     SLCOF WEETN EBRDO ORVYM FFEDI


We might write it TMDPG XFFUO FCSEP PSWZN GGFEJ, or RKBNE VDDSM DAQCN
NQUXL EEDCH (Case 4-a, going forward one letter or back one letter).


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.




Methods of Enciphering Numerals

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 X, 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:


                 1   2   3   4   5   6   7   8   9   0
                 A   B   C   D   E   F   G   H   I   J


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 X, a series of the letters of the
above table and another X, casts out the X's and substitutes numbers
for the letters.

Sometimes no indicator is used, but the system of substitution of a
certain letter for each numeral is followed. Again, the indicator NR
may be used instead of a single letter.

Conventional letters may also be substituted for special characters
like ?, $, ", -, 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 X to represent end of a sentence and Q to represent a question
mark is quite common.








CHAPTER X

ERRORS IN ENCIPHERING AND TRANSMISSION


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.

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.

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


         A   B   D   E   F   G   I   K   M   N   S   T   U   X


so that there may be a minimum of such confusion.

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 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.

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.

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.

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 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.

Radio communication is, by International Convention, invariably in
Continental Morse.


Telegraph Alphabets

    Character       American Morse   Continental Morse
                                     or International Code

    A               . -              . -
    B               - . . .          - . . .
    C               . .  .           - . - .
    D               - . .            - . .
    E               .                .
    F               . - .            . . - .
    G               - - .            - - .
    H               . . . .          . . . .
    I               . .              . .
    J               - . - .          . - - -
    K               - . -            - . -
    L               --               . - . .
    M               - -              - -
    N               - .              - .
    O               .  .             - - -
    P               . . . . .        . - - .
    Q               . . - .          - - . -
    R               .  . .           . - .
    S               . . .            . . .
    T               -                -
    U               . . -            . . -
    V               . . . -          . . . -
    W               . - -            . - -
    X               . - . .          - . . -
    Y               . .  . .         - . - -
    Z               . . .  .         - - . .
    1               . - - .          . - - - -
    2               . . - . .        . . - - -
    3               . . . - .        . . . - -
    4               . . . . -        . . . . -
    5               - - -            . . . . .
    6               . . . . . .      - . . . .
    7               - - . .          - - . . .
    8               - . . . .        - - - . .
    9               - . . -          - - - - .
    0               ----             - - - - -
    Period          . . - - . .      . - . - . -
    Question Mark   - . . - .        . . - - . .
    Comma           . - . -          - - . . - -


The following example will show some of the errors that creep into
messages prepared with the cipher disk and transmitted by radio:




Message


    Radio Douglas de El Paso, 2 H 71, twenty-fifth, 9:00 a.m.,
    Govt. To C.O., Sixth Brigade, Douglas, Arizona:

    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

                                                                Smith.


The key word is ATCHISON, the cipher disk being used and the setting
changed for every letter of the message. The letter X indicates a
period where it is evidently not a letter of a word.

Deciphering the message with this key and method we have:


    RELIA BLEIN FORGF TIONF ROMCA SASGR ANDES RECEI LEDHE RETHA TAMOU
    NTEDD ETACH MSKTL EFTTH ERELA STNIG HTTOE SCORT SHYMP ENTOF ARMSA
    NDAMM UNITI ONTOB ESMUG GLEDA CRJXS BORDE RNEXT FRIDA YNIGH TATAP
    OINTT WELVE MIENX FKOSB


Beyond this point the message, if we continue the deciphering process,
is unintelligible. The sense fails at the first P of the cipher group
BSPPK. We have translated B as M with disk A to N and S as I with
disk A to A. The last words that make sense are A POINT TWELVE MI;
clearly the rest of the last word is LES and this is represented by
PPK. Putting P=L then A=A and putting P=E then A=T. In other words,
the encipherer forgot to change his disk setting, A to A, after
enciphering I into S and enciphered L into P with the same setting,
A to A. Continuing the deciphering on this basis, we have:


      LES EASTO FDOUG LAS.T HISIS INYOU RDIST RICT. WILLY OUTAK ENECE
    SSARV STEPS TOPRE VENTT HISSH IPMEN TFROM GOING SKZRX LEADE ROFSM
    UGGLE RSSAL DTOBE JUANH ERNAN DEZOF NACO.


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.

Line 1, GF should be MA. Putting the latter into cipher we find the
letters of the cipher should have been GO instead of MJ. This is
clearly a telegrapher's error, --. --- becoming -- .---

Line 2, L should be V. The corresponding cipher letter should be F
instead of P. This is an error of the encipherer in copying.

Line 2, SK should be EN. The corresponding cipher letters should be YU
instead of KX. Another telegrapher's error, -.-- ..- becoming -.- -..-

Line 3, Y should be I. The corresponding cipher letter should be L
instead of V. Another error in copying by the encipherer.

Line 4, JX should be OS. The corresponding cipher letters should be
FK instead of KF; an error on the part of the encipherer in copying.

Line 7, V should be Y. A mistake in copying.

Line 8, SKZRX. If we take X as a period, then this line might be OVER,
the R being correct and SKZ being in question. The corresponding
cipher letters are AEO and if we encipher OVE we get ETJ. Here again
we have a telegrapher's error, . - .--- becoming .- . ---

Line 9, L should be I. The corresponding cipher letter should be K
instead of H; an error in copying by the encipherer.

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's hand writing or printing. Other errors, besides
those noted, are the confusion of C, G, and Q; I, and J; B and R, etc.

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.

Telegraphers' 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.

The deciphered and corrected message is:

    "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 your
    district. Will you take necessary steps to prevent this shipment
    going over? Leader of smugglers said to be Juan Hernandez of Naco."

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


                           GA GTXIEIT EIDISXQ


This, deciphered as far as possible by the alphabet determined by
analysis of the rest of the cipher, read


                           SU SME_Y_M Y_O_GES


It was finally decided that the context required a single word like
SUSPENDIO or SUSPENDIOLES for this cipher group. An examination along
this line showed that the cipher words should have been


received            G   A   G   L   X   C    U    R    D   P    X   G
and were received   G   A   G   T   X   IE   IT   EI   D   IS   X   Q


and that there were five errors in transmission in these three cipher
groups alone.








NOTES

[1] Occurrence rare, usually in proper names.

[2] 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.