## Lesson 4: Substitutions With Variants Part III: Multiliteral Substitution

```                 CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI
December 05, 1995
Revision 0

LECTURE 4
SUBSTITUTION WITH VARIANTS PART III
MULTILITERAL SUBSTITUTION

SUMMARY

Welcome back from the Thanksgiving holiday break.   The good
news is that this lecture will come to you about Christmas,
therefore, no homework.  The not so good news is that this
concluding Lecture 4 on Substitution with Variants covers some
difficult material of wide practically in the field.

In Lecture 4, we complete our look into English monoalphabetic
substitution ciphers, by describing multiliteral substitution
with difficult variants.  The Homophonic and GrandPre Ciphers
will be covered.  The use of isologs is demonstrated.  A
synoptic diagram of the substitution ciphers described in
Lectures 1-4 will be presented.

MULTILITERAL SUBSTITUTION WITH MULTIPLE-EQUIVALENT CIPHER
ALPHABETS  - aka "MONOALPHABETIC SUBSTITUTION WITH VARIANTS"

Each English letter in plain text has a characteristic
frequency which affords definite clues in the solution of
simple monoalphabetic ciphers.  Associations which individual
letters form in combining to make up words, and the
peculiarities which certain of them manifest in plain text,
afford further direct clues by means of which ordinary
monoalphabetic substitution encipherments of such plain text
may be readily solved.                  [FR1]

Cryptographers have devised methods for disguising,
suppressing, or eliminating the foregoing characteristics in
the cryptograms produced by methods described in Lectures 1-3.
One category of methods call "variants or variant values" is
that in which the letters of the plain component of a cipher
alphabet are assigned two or more cipher equivalents.

Systems involving variants are generally multiliteral.  In such
systems, there are a large number of equivalents made available
by combinations and permutations of a limited number of
elements, each letter of the plain text may be represented by
several multiliteral cipher equivalents which may be selected
at random.  For example, if 3-letter combinations are employed
as multiliteral equivalents, there are 26**3 or 17,576
available equivalents for the 26 letters of the plain text.

They may be assigned in equal numbers of different equivalents
for the 26 letters, in which case each letter would be
representable by 676 different 3 letter equivalents or they
be assigned on some other basis, for example proportionately to
the relative frequencies of the plain text letters.  [FR1]

The primary object of substitution with variants is again to
provide several values which may be employed at random in a
simple substitution of cipher equivalents for the plain text
letters.

As a slight diversion, the reader may ask about uniliteral
substitution with variants.  It is but not very practical.
Note the following cipher alphabet constructed in French by
Captain Roger Baudouin in reference [BAUD]:

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

(Note that the Captain was not an ACA member.  The H=H
combination is not allowed.)

Baudouin proposed that the J and Y plain be replaced by I plain
and K plain by C plain or Q plain and W plain by VV plain. Four
cipher letters would be available as variants for the high-
frequency plain text letters in French.

Mixed alphabets formed by including all repeated letters of the
key word or key phrase in the cipher component were common in
Edgar Allen Poe's day but are impractical because they are
ambiguous, making decipherment difficult; for example:

Enciphering Alphabet:

Plain : 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
Cipher: N O W I S T H E T I M E F O R A L L G O O D M E N T

Inverse form for deciphering

Cipher: 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
Plain : p     v h m s g d     q k a b     o e f     c
l       j     r w y n         i
x                   t         z
u

The average cipher clerk would have difficulty in decrypting a
cipher group such as TOOET, each letter having 3 or more
equivalents, from which plain text fragments (n)inth, ft
thi(s),  it thi, etc. can be formed on decipherment.  [FR1]

THEORETICAL DISTINCTIONS

In simple or single-equivalent monoalphabetic substitution with
variants, two points are evident:

1) the same letter of the plain text is invariable represented
by but one and always the same character or cipher unit of
the cryptogram.

2) The same character or cipher unit of the cryptogram
invariably represents one and always the same letter of the
plain text.

In multiliteral - equivalent monoalphabetic substitution with
variants, two points are also evident:

1) the same letter of the plain text may be represented by one
or more different characters or cipher units of the
cryptogram.  But,

2) The same character or cipher unit of the cryptogram
nevertheless invariably represents one and always the same
letter of the plain text.

SIMPLE TYPES OF CIPHER ALPHABETS WITH VARIANTS

Figure 4-1                      Figure 4-2

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

Figure 4-3

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

Figure 4-4

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

Figure 4-5

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

Figure 4-6

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

Figure 4-7

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

Figure 4-8

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

Figure 4-9

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

Figure 4-10

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

The matrices in Figures 4 -1 to 4-10 represent some of the
simpler means for accomplishing monoalphabetic substitution
with variants.  The matrices are extensions of the basic ideas
of multiliteral substitution presented in Lecture 3.

The variant equivalents for any plain text letter may be chosen
at will; thus, in Figure 4-1, e= 10, 15, 60, or 65; in Figure
4-2, e= AU, AZ, FU, FZ, LU or LZ.

Encipherment by means of matrices shown in Figures 4-2, 4-3,
4-6 is commutative. The coordinates may be read row by column
or visa versa.  There is no cryptographic ambiguity.  The
remaining matrices are noncommutative.  The general convention
is to read row by column.

In Figures 4-5 and 4-6, the letters in the square have been
inscribed in such a manner that, coupled with the particular
arrangement of the row and column coordinates, the number of
variants available for each plain text letter is roughly
proportional to the frequencies of the letters in the
plain text.  Figure 35 incorporates a keyword on top of this
idea.  [FR1]
HOMOPHONIC

The Homophonic Cipher is a simple variant system. It is a
4-level (alphabets) dinome cipher.   Consider Figure 4-11.

Figure 4-11

A   B   C   D   E   F   G   H   IJ  K   L   M   N
08  09  10  11  12  13  14  15  16  17  18  19  20
35  36  37  38  39  40  41  42  43  44  45  46  47
68  69  70  71  72  73  74  75  51  52  53  54  55
87  88  89  90  91  92  93  94  95  96  97  98  99

O   P   Q   R   S   T   U   V   W   X   Y   Z
21  22  23  24  25  01  02  03  04  05  06  07
48  49  50  26  27  28  29  30  31  32  33  34
56  57  58  59  60  61  62  63  64  65  66  67
00  76  77  78  79  80  81  82  83  84  85  86

The keyword TRIP is found by inspecting dinomes 01, 26, 51, and
76.  (The lowest number in each of the four sequences.)
[FR1] [FR5]

The Russians added an interesting gimmick called the Disruption
Area.  Consider Figure 4-12 and note the slashes under  U - X
for the fourth level of dinomes.   The famous VIC cipher used
this feature very effectively.   [NIC4]

Figure 4-12

A   B   C   D   E   F   G   H   I   J   K   L   M   N
14  15  16  17  18  19  20  21  22  23  24  25  26  01
27  28  29  30  31  32  33  34  35  36  37  38  39  40
58  59  60  61  62  63  64  65  66  67  68  69  70  71
81  82  83  84  85  86  87  88  89  90  91  92  93  94

O   P   Q   R   S   T   U   V   W   X   Y   Z
02  03  04  05  06  07  08  09  10  11  12  13
41  42  43  44  45  46  47  48  49  50  51  52
72  73  74  75  76  77  78  53  54  55  56  57
95  96  97  98  99  00  //////////////  79  80

The keyword NAVY is represented by dinomes 01, 27, 53, and 79.

Security for Homophonic systems is greatly improved if the
dinomes and the four sequences are assigned randomly.  However,
the easy mnemonic feature of the keyworded four sequences is
lost.

The Mexican Cipher device is a Homophonic consisting of five
concentric disks, the outer disk bearing 26 letters and the
other four bearing sequences 01-26, 27-52, 53-78, 79-00.
The cipher disk enhances frequent key changes.  Figure  4-12
shows the matrix without the disruption area.  [FR5] [NIC4]
HOMOPHONIC CRYPTANALYSIS

Lets solve the following cryptogram.

68321   09022   48057   65111   88648   42036   45235   09144
05764   22684   00225   57003   97357   14074   82524   40768
51058   93074   92188   47264   09328   04255   06186   79882
85144   45886   32574   55136   56019   45722   76844   68350
45219   71649   90528   65106   11886   44044   89669   70553
18491   06985   48579   33684   50957   70612   09795   29148
56109   08546   62062   65509   32800   32568   97216   44282
34031   84989   68564   53789   12530   77401   68494   38544
11368   87616   56905   20710   58864   67472   22490   09136
62851   24551   35180   14230   50886   44084   06231   12876
05579   58980   29503   99713   32720   36433   82689   04516
52263   21175   06445   72255   68951   86957   76095   67215
53049   08567   9730

Assuming we did not know that the above cryptogram was a
HOMOPHONIC, we might may a preliminary analysis to see if we
are dealing with a cipher or a code.  We will cover code
systems later in the course, but a few introductory remarks
might be in order.  The five letter groups could indicate
either a cipher or a code.

If the cryptogram contains an even number of digits, as for
example 494 in the previous message, this leaves open the
possibility that the message is a cipher containing 247 pairs
of digits; were the number of digits an exact odd multiple of
five, such as 125, 135, etc., the possibility that the
cryptogram is in code of the 5-figure group type must be
considered.

We next study the message repetitions and what their
characteristics are.  If the cipher text is of 5-figure code
type, then such repetitions as appear should generally be in
whole groups of five digits, and they should be visible in the
text just as the message stands, unless the code message has
been superenciphered.  If the cryptogram is a cipher, then
repetitions should extend beyond the 5-digit groupings; if they
conform to any definite at all they should for the most part
contain even numbers of digits since each letter is probably
represented by a pair (dinome) of digits.

We start with 4-part frequency distribution.  We next assume
a 25 character alphabet from 01-00.  This is the common scheme
of drawing up the alphabets.  Breaking the text into dinomes
(2-digit) pairs yields:

01 ///           26 ///            51 /////         76 //////
02               27                52 /////         77 /
03 ////          28 /              53 ///           78
04 /             29 /              54               79 /
05 /////         30 ///            55 ////          80 ///
06 //////        31                56 /////         81
07 ///           32 //////         57 //////        82 ////
08               33 /              58 //            83 /
09 ////          34 /              59               84 //////
10 ////          35 //             60               85 //////
11 /////         36 /////          61               86 ///
12 ///           37 /              62 //            87
13 /             38                63               88 ////
14 /             39 /              64 //////        89 /////
15 /             40 ///            65               90 //////
16 ///           41                66 /             91 ///
17               42 ////           67 //            92 /
18 //////        43 /              68 ///////       93 /
19               44 //////         69 //            94 /
20 /             45 //////         70 /             95 ///
21 //            46 ///            71 /             96
22 /////         47                72 ////          97 //////
23 //            48 ///            73               98 /
24               49 /////          74 ////          99
25 /             50 /////          75 /             00 //

What we have before us are four simple, monoalphabetic
frequency distributions similar to those involved in a
monoalphabetic substitution cipher using standard cipher
alphabets.  The next step is to fit the distribution to the
normal.   Since I=J for the 25 letter alphabet, we find that
the Keyword is JUNE and the following alphabets result:

01  I-J    26  U     51  N      76  E
02  K      27  V     52  O      77  F
03  L      28  W     53  P      78  G
04  M      29  X     54  Q      79  H
05  N      30  Y     55  R      80  IJ
06  O      31  Z     56  S      81  K
07  P      32  A     57  T      82  L
08  Q      33  B     58  U      83  M
09  R      34  C     59  V      84  N
10  S      35  D     60  W      85  O
11  T      36  E     61  X      86  P
12  U      37  F     62  Y      87  Q
13  V      38  G     63  Z      88  R
14  W      39  H     64  A      89  S
15  X      40  IJ    65  B      90  T
16  Y      41  K     66  C      91  U
17  Z      42  L     67  D      92  V
18  A      43  M     68  E      93  W
19  B      44  N     69  F      94  X
20  C      45  O     70  G      95  Y
21  D      46  P     71  H      96  Z
22  E      47  Q     72  IJ     97  A
23  F      48  R     73  K      98  B
24  G      49  S     74  L      99  C
25  H      50  T     75  M      00  D

The first groups of the cryptogram decipher as follows:

68 32 10 90 22 48 05 76 51 11 88 64 84 20 36 45 23
e  a  s  t  e  r  n  e  n  t  r  a  n  c  e  o  f

If a 26-element alphabet were used only the distribution
analysis would have been changed to be on a basis of 26, the
process of fitting the distribution to the normal would be the
same.

PLAIN COMPONENT COMPLETION METHOD

Suppose we know that two correspondents have been using the
same variant system as in the previous Homophonic.
The message intercepted is:

48226   88423   52099   93604   76059   05651   36683   52267
97114   54466   76

A variation of the plain-component completion method can be
used to crack the new message.  We copy the message into
dinomes and separate by levels.

48 22 68 84 23 52 09 99 36 04 76 05 90 56 51 36 68 35 22 67 97
--------------------------------------------------------------
2   1  3  4  1  3  1  4  2  1  4  1  4  3  3  2  3  2  1  3  4

11 45 44 66 76
--------------
1  2  2  3  4

Levels

(1)  22 23 09 04 05 22 11
(2)  48 36 36 35 45 44
(3)  68 52 56 51 68 67 66
(4)  84 99 76 90 97 76

These dinomes are converted into terms of plain component by
setting each of the cipher sequences against the plain
component at an arbitrary point of coincidence, such as the
following:

A   B   C   D   E   F   G   H   IJ  K   L   M   N
01  02  03  04  05  06  07  08  09  10  11  12  13
26  27  28  29  30  31  32  33  34  35  36  37  38
51  52  53  54  55  56  57  58  59  60  61  62  63
76  77  78  79  80  81  82  83  84  85  86  87  88

O   P   Q   R   S   T   U   V   W   X   Y   Z
14  15  16  17  18  19  20  21  22  23  24  25
39  40  41  42  43  44  45  46  47  48  49  50
64  65  66  67  68  69  70  71  72  73  74  75
89  90  91  92  93  94  95  96  97  98  99  00

So:

Levels

(1)  22=W; 23=X; 09=I; 04=D; 05=E; 22=W; 11=L
(2)  48=X; 36=L; 36=L; 35=K; 45=U; 44=T
(3)  68=S; 52=B; 56=F; 51=A; 68=S; 67=R; 66=Q
(4)  84=I; 99=Y; 76=A; 90=P; 97=W; 76=A

This method works because both the plain component (A,B..) and
the cipher component (01, 02..) are known sequences.

The plain-component sequence is completed on the letters of the
four levels by Caesar Rundown, as follows:

Level 1           Level 2          Level 3          Level 4

WXIDEWL            XLLKUT           SBFASRQ           IYAPWA
XYKEFXM            YMMLVU           TCGBTSR           KZBQXB
YZLFGYN            ZNNMWV           UDHCUTS           LACRYC
ZAMGHZO            AOONXW           VEIDVUT           MBDSZD
ABNHIAP            BPPOYX           WFKEWVU           NCETAE
BCOIKBQ            CQQPZY           XGLFXWV           ODFUBF
CDPKLCR            DRRQAZ           YHMGYXW           PEGVCG
DEQLMDS            ESSRBA           ZINHZYZ           QFHWDH
EFRMNET            FTTSCB           AKOIAZY           RGIXEI
FGSNOFU            GUUTDC           BLPKBAZ           SHKYFK
GHTOPGV            HVVUED           CMQLCBA           TILZGL
HIUPQHW            IWWVFE           DNRMDCB           UKMAHM
IKVQRIX            KXXWGF           EOSNEDC           VLNBIN
KLWRSKY            LYYXHG           FPTOFED           WMOCKO
LMXSTLZ            MZZYIH           GQUPGFE           XNPDLP
MNYTUMA            NAAZKI           HRVQHGF           YOQEMQ
NOZUVNB            OBBALK           ISWRIHG           ZPRFNR
OPAVWOC            PCCBML           KTXSKIH           AQSGOS
PQBWXPD            QDDCNM           LUYTLKI           BRTHPT
QRCXYQE            REEDON           MVZUMLK           CSUIQU
RSDYZRF            SFFEPO           NWAVNML           DTVKRV
STEZASG            TGGFQP           OXBWONM           EUWLSW
TUFABTH            UHHGRQ           PYCXPON           FVXMTX
UVGBCUI            VIIHSR           QZDYQPO           GWYNUY
VWHCDVK            WKKITS           RAEZRQP           HXZOVZ

The generatrices with the best assortment of high frequency
letters for the four levels are:

Level 1           Level 2          Level 3          Level 4

EFRMNET           REEDON           EOSNEDC          NCETAE

Arranging the letters of these generatrices in order of
appearance of their dinome equivalents, according to levels we
have:

48 22 68 84 23 52 09 99 36 04 76 05 90 56 51 36 68 35 22 67 97
E        F     R        M     N                    E
R                      E                    E      D
E        O                       S  N      E       D
N            C        E     T                       A

The plain text reads "Reinforcements needed a[t once]".
Looking at the equivalents 01,26, 51, 76 we reveal the keyword
JUNE.

In evaluating generatrices, the sum of the arithmetic
frequencies of the letters in each row may be used as an
indication of the relative "goodness".  A statistically better
procedure uses the logarithm of the probabilities of the plain
text letters forming the generatrices.  See [FR2]

The Homophonic is a popular cipher and has been discussed in
several issues of The Cryptogram as well as LEDGES' NOVICE
NOTES.  See references [HOM1 -HOM6] and [LEDG].

For our computer bugs,  TATTERS Homophonic solver is very easy
to use and available on the Crypto Drop Box.

MORE COMPLICATED TYPES OF CIPHER ALPHABETS WITH VARIANTS

GRANDPRE

Consider the cipher matrices shown in figures 4-11 to 4-13.
These are called frequential matrices, since the number of
cipher values available for any given plain text letter closely
approximates its relative plain text frequency.

Figure 4-11

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

( 676 - cell matrix )

In figure 4-11, the number of occurrences of a particular
letter within the matrix is proportional to the frequency in
plain text; the letters are inscribe in random manner, in order
to enhance the security of the system.

Figure 4-12

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

In figure 4-12, the same idea as 4-11 is presented in reduced
form from 26 x 26 to 10 x 10.  The letters have been inscribed
by a simple diagonal route, from left to right, within the
square, and the coordinates scrambled by means of a key word
or key number.

Figure 4-13

"Grandpre"

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

Figure 4-13 illustrates the famous Grandpre Cipher; in this
square ten words are inscribed containing all the letters of
the alphabet and linked by a column keyword ("equivalent") as a
mnemonic for inscription of the row words.  ACA literature also
covers this cipher.  See references [LEDG] and [GRA1 - 3] for
solution hints for the Grandpre cipher.

SACCO

General Luigi Sacco proposed a frequential-type system that
uses both enciphering and deciphering matrices.  The inscribed
dinomes were completely disarranged by applying a double
transposition to suppress the relationships between letters.
References [SACC] and [FR1] both give a good description of the
process.   The number of variant values in this system are
reflective of the Italian language.

BACONIAN

The Baconian ciphers found in the Cryptogram are a variant
system.  The "a" elements may be represented by any one of 20
consonants as variants, while the "b" elements may be
represented by any one of 6 vowels; or the letters A-M may be
used to represent the "a" elements and the letters N-Z for the
"b" elements; digits may be used for either the "a" or "b"
elements, either on the basis of first five or last five
digits, or odd versus even digits, or the first 10 consonants
(B-M) and the last 10 consonants (N-Z)

SUMMING-TRINOME

Friedman describes a complex variant known as the summing-
trinome system.  Each plain text letter is assigned a value
from 1-26; this value is expressed as a trinome, the digits of
which sum to the designated value of the letter.  The letter
assigned the value of 4 may be represented by any of 15
permutations and combinations.  Friedman discusses further ways
of complication including disarrangement, addition of
punctuation and nulls.  See [FR1] pages 109-110.  Note the
inverted normal distribution representation of this cipher.

ANALYSIS OF A SIMPLE VARIANT EXAMPLE

The following cryptogram is available for study:

Q M D C V   P L F N F   D H N W J   W L K D K   N H B P V
R L T V M   B K L W D   W V H V K   S H B C L   P Q K J R
V W S M L   K G C N R   L R N K V   M G F X W   J R G M V
W G T J H   Q K X F N   Z V F D M   L T B P L   P V F L M
D C N W N   H B C V Z   N M L W Q   F D H D W   V Z B R V
K L C V C   V R D H L   R V T L F   N C D K G   M X W X M
D T S C B   C L Z L R   L M V T S   Z N K B W   V P B R N
C L R X R   D C N K V   P B T N T   G H J Z L   F Q F V K
B W D Z X   P N H S P   G H L K L   F V Z L T   V M L K D
P Q R N Z   L Z D T B   M N T G M   N Z V F X   K S F D C
L Z V T V   F D F V R   G C L P Q   P N C D W   V R J T N
H L Z L M   V W N P V   P D Z D W   J P N W L   R J K V M
X M D T S   M G F D R   D K L W J   F L P J M   S F Q W B
F N C B Z   D K V W G   Z S H B H   D H J C X

Note the total absence of A, E, I, O, U, and Y.  Remarkable
and definitely nonrandom event.  Since a uniliteral
substitution alphabet with 6 letters missing is highly
unlikely, the next guess is we are dealing with a multiliteral
substitution.   Closer inspection shows that ten consonants are
initials (B D G J L N Q S V X) and the remaining ten consonants
are used as terminals (C F H K M P R T W Z).  This implies both
bipartite and biliteral character.

We construct a digraphic distribution:

C  F  H  K  M  P  R  T  W  Z
...............................
B . 3  1  1  1  1  2  2  1  2  1 .
D . 4  1  3  3  1  1  1  3  4  2 .
G . 2  2  2     3        1     1 .
J . 1  1  1  1  1  1  2  1  1  1 .
L . 1  4     4  3  4  5  3  3  4 .
N . 4  1  4  3  1  1  1  2  3  3 .
Q .    2     2  1  1  1     1    .
S . 1  2  2     2  1           1 .
V . 1  4  1  3  4  4  4  3  4  3 .
X .    1     1  2  1  1     2    .
...............................

We assume the use of a small enciphering matrix with variants
for rows and columns.  We assume that the various possible
cipher variants are of approximately equal frequency; the
column indicators pair equally often with the row indicators
of the enciphering matrix.  We look for similar row profiles
and column profiles.  We match first the rows and then the
columns.

Row  L and V distributions have pronounced similarities.  They
are "heavy" in their frequency distributions in the same
places.  So are rows D and N.  They have homologous attributes
in appearance.

C  F  H  K  M  P  R  T  W  Z

L       . 1  4     4  3  4  5  3  3  4 .
V       . 1  4  1  3  4  4  4  3  4  3 .

D       . 4  1  3  3  1  1  1  3  4  2 .
N       . 4  1  4  3  1  1  1  2  3  3 .

Finding the next rows are not obvious.  We use a "goodness of
match" procedure to equate interchangeable variants.  We
calculate the cross-product sums for each trial.  The next
heavy row is G.  We test G against the remaining rows.

G       . 2  2  2     3        1     1 .
B       . 3  1  1  1  1  2  2  1  2  1 .
G*B +     6  2  2     3        1     1   = 15

We compare the balance of rows

G*B +      6  2  2     3        1     1   = 15
G*J +      2  2  2     3        1     1   = 11
G*Q +         4        3                  =  7
G*S +      2  4  4     6              1   = 17 !
G*X +         2        6                  =  8

The results are most probably match G and S.

The next heaviest row is B.  Testing against the remaining
three rows we have:

B*J +      3  1  1  1  1  2  4  1  2  1   = 17
B*Q +         2     2  1  2  2     2  1   = 12
B*X +         1     1  2  2  2     4      = 12

The correct pairings are B with J and Q with X.  Since we have
not found more than two rows for any one set of interchangeable
values the original matrix has only five rows.

C  F  H  K  M  P  R  T  W  Z
...............................
B  J . 4  2  2  2  2  3  4  2  3  2 .
D  N . 8  2  8  7  2  2  2  5  7  5 .
G  S . 3  4  4     5  1     1     2 .
L  V . 2  8  1  7  7  8  9  6  7  7 .
Q  X .    3     3  3  2  2     3    .
................................

Values represent the sums of the combined rows.
We apply the same process to matching columns.  C and H are
a matched pair.  F with M and P with R.  We use the cross
product sums for the balance of the columns.

K*T+:  4  35  - 42  - =  81
K*W+:  4  49  - 49  9 = 113
K*Z+:  4  35  - 49  - =  88
T*W+:  6  35  - 42  - =  83
T*Z+:  4  25  2 42  - =  73
W*Z+:  6  35  - 49  - =  90

Combinations:

KT, WZ:   81 +  90 = 171
KW, TZ:   113 + 73 = 186
KZ, TW:   88  + 83 = 171

We would expect that the proper pairings are K with W and T
with Z.

C  F  K  P  T
H  M  W  R  Z
..................
B  J . 6  4  5  7  4  .   PHI(p) = 1962
D  N . 16 4 14  4 10  .   PHI(r) = 1132
G  S . 7  9  -  1  3  .   PHI(o) = 1670
L  V . 3 15 14 17  13 .
Q  X . -  6  6  -  4  .
..................
We convert the multiliteral text to uniliteral equivalents
using an arbitrary square for reduction to plain text.

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

The converted cryptogram is solved via the principals in
Lectures 2 and 3.  The beginning of the message reads Weather
forecast.  The original keying matrix is recovered with a
keyword of ATMOSPHERIC.

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

The method of matching rows and columns applies equally well
for all the matrices shown previously.  It is key to start with
the best rows and columns from not only heaviness standpoint
but the distinctive crests and troughs.   A second key is the
low frequency letters.  No variant system can adequately
disguise low frequency letters and they will have the same
frequency in the cipher text.  Friedman describes a more
general solution to variant analysis. [FRE1, p119 ff]

Chapter 10 of reference [FRE1] covers the disruption process
associated with monome-dinome alphabets of Irregular-Length
cipher text units.  Figures 4-14 and Figure 4-15 show
enciphering matrices where the encipherment is disrupted and
commutative.  The normal row conventions are used to encipher
except when the row indicator was the same for the immediately
preceding letter.  In Figure 4-14, EIGHT could be encrypted
10 29 7 8 49 and then rearranged into standard groups of 5
letters (numbers).  In Figure 4-15, E = 24 or 42, T = 621 or
162.  Figure 4-16 is an example of the Russian disruption
process added for security.

ISOLOGS

Cryptograms produced using identical plain text but subjected
to different cryptographic treatment, and yielding different
cipher texts are called isologs.  (isos = equal and logos =
word in Greek).  Isologs are usually equal or nearly equal in
length.  Isologs, no matter how the cryptographic treatment
varies, are among the most powerful tools available to the
cryptanalyst to solve difficult cryptosystems.

Take two messages A and B suspected of being isologs and write
them out under each other.  We then examine the similarities
and differences.   Assume the messages both start Reference
your message...   I will arrange the messages in a special
table to facilitate the study.

Group No.

5              10             15
.............................................
A     82 26 56 31 03 74 83 96 98 42 32 52 97 01 15
A'    30 15 08 74 97 14 51 19 73 60 49 67 65 01 06

B     80 27 78 91 06 94 00 01 38 28 54 08 24 00 65
B'    45 64 79 91 81 69 67 25 38 89 41 56 32 52 03

C     63 62 93 39 18 43 15 88 10 48 26 45 84 50 39
C'    90 62 87 75 36 20 35 11 05 70 89 27 77 50 11

D     81 71 35 25 38 73 30 92 07 49 61 75 21 64 76
D'    35 19 99 01 38 99 97 45 02 32 04 11 58 92 16

E     38 72 89 11 47 99 92 64 14 68 13 36 53 38 81
E'    38 46 31 75 47 14 64 80 06 46 85 86 45 38 98

F     89 69 79 38 16 51 75 05 70 74 11 80 44 32 55
F'    26 12 18 38 78 94 88 93 37 28 11 27 22 05 04

G     28 12 02 77 30 31 19 97 99 62 27 86 56 06 53
G'    06 48 43 21 03 98 71 54 26 62 80 76 08 98 80

H     90 87 04 08 67 46 59 41 98 55 10 82 22 29 87
H'    44 10 55 29 00 59 72 82 28 55 87 30 07 08 93

J     46 72 93 62 45
J'    59 68 24 62 53

The dinome distributions for these two messages are as follows:

1 2 3 4 5 6 7 8 9 0          1 2 3 4 5 6 7 8 9 0
...................          ....................
1 . 2 1 1 1 2 1 - 1 1 2      1 . 4 1 - 2 1 1 - 1 2 1
2 . 1 1 - 1 1 2 2 2 1 -      2 . 1 1 - 1 1 2 2 2 1 1
3 . 2 2 - - 1 1 - 5 2 2      3 . 1 2 - - 2 1 1 5 - 2
4 . 1 1 1 1 2 2 1 1 1 -      4 . 1 - 1 1 3 2 1 1 1 -
5 . 1 1 2 1 2 2 - - 1 1      5 . 1 1 1 1 2 1 - 1 2 1
6 . 1 3 1 2 1 - 1 1 1 -      6 . - 3 - 2 1 - 2 1 1 1
7 . 1 2 1 2 2 1 1 1 1 1      7 . 1 1 1 1 2 1 1 1 1 1
8 . 2 2 1 1 - 1 2 1 2 2      8 . 1 1 - - 1 1 2 1 2 3
9 . 1 2 2 1 - 1 2 2 2 1      9 . 1 1 2 1 - - 2 3 2 1
0 . 2 1 1 1 1 2 1 2 - 2      0 . 2 1 2 2 2 3 1 3 - 1

Message A                       Message B

Both distributions are too flat - no crests or troughs.
We assume a variant system of a monoalphabetic cryptosystem.
[FRE3] shows us how to use a Poisson exponential distribution
to evaluate random text.  The gist of the statistics is that
the expected number of blanks is too low. The chi test
indicates extreme non randomness for both messages. The chi
test applied to both distributions implies that they both have
been enciphered by the same cryptosystem because there exists a
close correlation between the patterns of the two
distributions.  [FR1, p123} discusses the potentialities of the
cryptomathematics as a supporting science to cryptography.

There are several identical values between the messages.  This
implies that not only has the same cryptosystem been used but
also the same enciphering matrix.  The values 38 and 62 must
represent very low frequency letters because no variants are
even provided for this letter.

We now form isolog chains between the messages.

(06 14 15 26 28 31 35 73 74 81 89 98 99)
(02 07 20 22 43 44 63 90)
(12 37 48 51 69 70 83 94)
(03 30 41 54 65 82 97)
(05 10 24 32 49 87 93)
(16 18 36 76 78 79 86)
(27 45 53 64 80 92)
(11 39 75 88)
(21 58 77 84)
(46 59 68 72)
(00 52 67)
(04 55 61)
(08 29 56)
(19 71 96)
(01 25)
(13 85)          Single Dinomes:
(42 60)          (38)  (47)  (50)  (62)  (91)

These chains of cipher values represent identical plain text
pairs.  Beginning with the first value in the message 82 and 30
a partial chain of equivalent variants is formed; now locating
the other occurrences of either value we note the value that
coincides with it in the other message.  We therefore extend
the chain.

We now assign a different letter arbitrarily to each chain and
each single dinome value.  We convert the messages to
uniliteral terms and note the pattern of opening stereotype
"Reference your message" and then quickly recover text.
(This is how we attacked the German ciphers in WWII.) [NIC4]

The plain text values are arbitrarily fit into 10 x 10 square:

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

Manipulating the rows and columns with a view to uncovering the
keys or symmetry, we find a latent diagonal pattern without
keyword.   We set up the following enciphering matrix:

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

I can not over emphasize the value of isologs. The value goes
far beyond simple variant systems. Isologs produced by two
different code books or two different enciphered code versions
of the same plain text; or two encryptions of identical plain
text at different settings of a cipher machine, may all prove
of inestimable value in the attack on a difficult system.

SYNOPTIC CHART OF CRYPTOGRAPHY PRESENTED IN LECTURES 1 - 5

Cryptograms
.
.
------------------------------------------
Cipher                Code            Enciphered Code
.
.
--------------------------------------------
Substitution          Transposition       Combined
.                                     Substitution -
.                                     Transposition
.
.-------------------------------------------
Monoalphabetic        Multiple-           Polyalphabetic
.                 Alphabetic
.                 Systems
.
.
Uniliteral ......................... Multiliteral
.                                    .
.                                    .
.                                    .
Standard ... Mixed                       .
Alphabets    Alphabets                   .
.                         .
.                         .
Keyword ... Random          .
Mixed       Mixed           .
.
.
.
...............................
.                             .
Single Equivalent              Variant ........
.                                       .
.                                       .
....................                            .
.                  .                            .
Fixed Length       Mixed Length                      .
Cipher Groups      Cipher Groups                     .
.                  .                            .
.                  .......................      .
Biliteral...N-literal         .                .      .
Monome-Dinome      Others    .
.
.
.
...................................
.
.
..........................
.                        .
Matrices with            Non Bipartite
Coordinates
(Bipartite)
Here is the tentative plan for the balance of the course.  Just
a plan - subject to revision.

LECTURES 5 - 7

We will cover recognition and solution of XENOCRYPTS (language
substitution ciphers) in detail.

LECTURES 8 - 12

We will investigate and crack Polyalphabetic Substitution
systems.

LECTURES 13 - 18

We will investigate and crack Cipher Exchange and
Transpositions problems.

LECTURE 19

We will devote this lecture to International Law.

LECTURES 20 - 23

We will walk through the mathematical fields to solve
Cryptarithms.

LECTURES 24 - 25

We will introduce modern cryptographic systems and field
special topics.  We will do a primer on PGP.

SOLUTIONS TO HOMEWORK PROBLEMS FROM LECTURE 3

Thanks to JOE-O for his concise sols.

Mv-1.  From Martin Gardner.

8 5 1 8 5 1 9 1 1 9 9 1 3
1 6 1 2 5 1 1 2 1 6 8 1 2 5
2 0 9 3 3 1 5 4 5 2 0 8 1
2 0 9 2 2 5 1 4 5 2 2 5
1 8 1 9 5 5 1 4 2 5 6 1 5
1 8 5 1 3 1 2 5 2 5 2 5 1 5
2 1 3 1 1 4 2 1 1 9 5 9 2 0
9 1 4 2 5 1 5 2 1 1 8 3 1 5
1 2 2 1 1 3 1 4

1 3 1 1 8 2 0 9 1 4 7 1 1 8 4 1 4 5 1 8
8 5 1 4 4 5 1 8 1 9 1 5 1 4 2 2 9 1 2 1 2 5
1 4 1 5 1 8 2 0 8 3 1 1 8 1 5 1 2 9 1 4 1

I presented Mv-1 in a strange format.  It fooled some but not
all.  The Key is 01=1=a, 02=2=b,...26=z.  the alphabet is
standard.  Message reads: " Here's a simple alphabetic code
that I've never seen before.  Maybe you can use it in you
column.  Martin Gardner, Hendersonville, North Carolina.

Solve and reconstruct the cryptographic systems used.

Mv-2.

0 6 0 2 1   0 0 5 0 1   0 1 0 5 1   5 2 2 0 2   0 6 0 8 2
3 2 5 1 0   0 8 0 4 0   2 2 1 0 9   0 8 0 4 0   8 2 2 1 1
0 8 0 4 1   7 1 5 1 3   1 4 2 2 2   1 0 2 2 4   0 2 0 1 2
2 0 2 0 2   0 1 0 8 1   9 0 6 1 5   1 7 0 8 0   1 1 1 2 2
1 4 0 2 0   1 1 9 0 6   0 5 1 0 0   2 0 2 1 1   2 2 1 4 0
6 2 3 1 9   0 5 1 5 0   1 2 2 1 3   0 2 0 5 0   6 1 3 0 2
0 5 0 1 1   0 0 5 2 3   0 6 2 1 0   2 2 2 1 4   0 6 0 2 0
2 2 2 1 4   0 6 0 2 0   2 2 6 0 2   0 6 0 5 2   1 1 9 0 2
0 2 1 1 2   2 0 3 0 2   1 7 2 4 0   2 1 9 0 2   0 6 1 5 0
5 1 1 0 6   0 2 1 9 0   5 0 6 2 2   0 1 0 5 0   5 0 1 1 9
0 5 2 1 1   5 2 2 1 5   0 5 0 1 2   2 0 5 1 8   0 5 0 6 0
6 0 5 0 3

Divide the original cipher into pairs, noting that each pair
started with 0,1, or 2 and ended with 0 - 9.  Construct a
matrix similar to Figure 3-2. (3 x 10) Fill in the matrix with
A=01, ending with Z=26.  Used 00 =blank.  Reduce by converting
dinomes to letters.  Apply the Phi test and found mon-
alphabetic. Used frequency, VOC count, and consonant line to
identify B, H, E as vowels and N,D,X,C,I,Y,R,J, as possible
consonants.  Marking the message with these assumptions, found
last eight characters to be a pattern word in Cryptodict as
TOMORROW.   Working between cipher text and key alphabet
matrix, rest fell.

Message reads:Reconnoiter Auys Cayes Bay at daylight seventeen
April and then proceed through point George on course three
three zero speed twelve period report noon position tomorrow.

Key = NEW YORK, 3 X 10 matrix, Rows 0,1,2, columns 0-9 and 00
blank.

Mv-3.

5 3 2 4 1    5 4 5 3 2    2 4 4 3 2    5 1 2 4 3    2 4 2 3 1
5 4 4 4 5    4 5 3 2 5    1 4 3 4 4    1 4 1 5 2    1 4 1 1 5
4 3 4 5 3    5 2 1 2 3    3 5 1 2 5    1 1 4 2 1    5 3 3 3 4
5 3 2 4 4    2 3 1 5 4    5 4 5 2 4    4 3 2 4 1    4 4 4 3 2
1 2 5 3 2    4 4 3 4 4    2 4 1 5 4    4 4 5 2 4    4 3 3 5 2
1 5 3 3 3    1 3 1 4 4    4 1 5 4 5    4 4 5 1 4    3 2 5 1 5
2 3 2 4 1    5 5 2 2 4    4 3 1 5 3    1 3 3 1 3    3 1 4 5 5
3 2 4 1 3    4 5 2 1 2    5 3 3 5 2    2 4 3 4 1    3 1 2 4 5
4 4 5 2 3    3 4 4 3 3    2 2 3 3 3    5 3 3 4 5    2 1 3 5 2
4 4 4 4 4    4 5 3 2 1    5 1 3 1 5    5 2 2 4 4    3 1 5 3 1
2 4 5 1 1    3 1 4 2 4    4 4 3 3 4    3 1 5 2 2    3 5 2 4 2
5 3 5 2 1    3 3 1 3 3    1 2 3 1 2    1 3 1 4 3    3 4 5 3 3
1 2 1 3 4    4 4 1 2 4    4 3 3 3 1    2 1 4 3 2    2 4 3 3 3
1 3 2 4 5    1 2 2 5 3    5 1 2 5 3    2 3 3 5 1    2 5 1 1 4
4 4 1 5 4    5 4 1 4 3    2 4 4 4 2    4 1 3 4 5    1 5 2 2 1
2 5 1 4 5    1 2 1 3 2    4 4 5 3 2    1 2 5 1 4    4 1 5 1 3
1 4 2 5 2    4 2 4 4 5

Noted all entries were numbered 1-5.  Assumed a 5 x 5 matrix
filled with a straight alphabet,  substituted letters for the
dinomes.  Used frequency count, contact count and phi test to
confirm mono-alphabeticity.  Identified 8 consonants and 2
vowels.  Made the E, T assumption based on frequency. First
word dropped as weather.  Rest of message fell apart with
addition of W, A, R to the matrix.

Message reads: Weather forecast Thursday partly cloudy ...
at present about one thousand feet.

Key = Beginning column 1 = MONDAY, in 5 x 5 matrix.

My last two problems were taken from reference [OP20] course.

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[CI]   FM 34-60, Counterintelligence, Department of the Army,
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[COUR] Courville, Joseph B.,  "Manual For Cryptanalysis Of
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[CLAR] Clark, Ronald W., 'The Man who broke Purple',
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[COVT] Anonymous, "Covert Intelligence Techniques Of the Soviet
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[CULL] Cullen, Charles G., "Matrices and Linear
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[DAN]  Daniel, Robert E., "Elementary Cryptanalysis:
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[DAVI] Da Vinci, "Solving Russian Cryptograms", The
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[DEAU] Bacon, Sir Francis, "De Augmentis Scientiarum," tr. by
Gilbert Watts, (1640) or tr. by Ellis, Spedding, and
Heath (1857,1870).

[DOW]  Dow, Don. L., "Crypto-Mania, Version 3.0", Box 1111,
Nashua, NH. 03061-1111, (603) 880-6472, Cost \$15 for
registered version and available as shareware under
CRYPTM.zip on CIS or zipnet.

[ELCY] Gaines, Helen Fouche, Cryptanalysis, Dover, New York,
1956.

[ENIG] Tyner, Clarence E. Jr., and Randall K. Nichols,
"ENIGMA95 - A Simulation of Enhanced Enigma Cipher
Machine on A Standard Personal Computer," for
publication, November, 1995.

[EPST] Epstein, Sam and Beryl, "The First Book of Codes and
Ciphers," Ambassador Books, Toronto, Canada, 1956.

[EYRA] Eyraud, Charles, "Precis de Cryptographie Moderne'"
Paris, 1953.

[FREB] Friedman, William F., "Cryptology," The Encyclopedia
Britannica, all editions since 1929.  A classic article
by the greatest cryptanalyst.

[FR1]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part I - Volume 1, Aegean Park
Press, Laguna Hills, CA, 1985.

[FR2]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part I - Volume 2, Aegean Park
Press, Laguna Hills, CA, 1985.

[FR3]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part III, Aegean Park Press,
Laguna Hills, CA, 1995.

[FR4]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part IV,  Aegean Park Press,
Laguna Hills, CA, 1995.

[FR5]  Friedman, William F. Military Cryptanalysis - Part I,
Aegean Park Press, Laguna Hills, CA, 1980.

[FR6]  Friedman, William F. Military Cryptanalysis - Part II,
Aegean Park Press, Laguna Hills, CA, 1980.

[FRE]  Friedman, William F. , "Elements of Cryptanalysis,"
Aegean Park Press, Laguna Hills, CA, 1976.

[FREA] Friedman, William F. , "Advanced Military Cryptography,"
Aegean Park Press, Laguna Hills, CA, 1976.

[FRAA] Friedman, William F. , "American Army Field Codes in The
American Expeditionary Forces During the First World
War, USA 1939.

[FRAB] Friedman, W. F., Field Codes used by the German Army
During World War. 1919.

[FR22] Friedman, William F., The Index of Coincidence and Its
Applications In Cryptography, Publication 22, The
Riverbank Publications,  Aegean Park Press, Laguna
Hills, CA, 1979.

[FRS]  Friedman, William F. and Elizabeth S., "The
Shakespearean Ciphers Examined,"  Cambridge University
Press, London, 1957.

[GARL] Garlinski, Jozef, 'The Swiss Corridor', Dent,
London 1981.

[GAR1] Garlinski, Jozef, 'Hitler's Last Weapons',
Methuen, London 1978.

[GIVI] Givierge, General Marcel, " Course In Cryptography,"
Aegean Park Press, Laguna Hills, CA, 1978.  Also, M.
Givierge, "Cours de Cryptographie," Berger-Levrault,
Paris, 1925.

[GRA1] Grandpre: "Grandpre, A. de--Cryptologist. Part 1
'Cryptographie Pratique - The Origin of the Grandpre',
ISHCABIBEL, The Cryptogram, SO60, American Cryptogram
Association, 1960.

[GRA2] Grandpre: "Grandpre Ciphers", ROGUE, The Cryptogram,
SO63, American Cryptogram Association, 1963.

[GRA3] Grandpre: "Grandpre", Novice Notes, LEDGE, The
Cryptogram, MJ75, American Cryptogram Association,1975

[GODD] Goddard, Eldridge and Thelma, "Cryptodyct," Marion,
Iowa, 1976

[GORD] Gordon, Cyrus H., " Forgotten Scripts:  Their Ongoing
Discovery and Decipherment,"  Basic Books, New York,
1982.

[HA]   Hahn, Karl, " Frequency of Letters", English Letter
Usage Statistics using as a sample, "A Tale of Two
Cities" by Charles Dickens, Usenet SCI.Crypt, 4 Aug
1994.

[HEMP] Hempfner, Philip and Tania, "Pattern Word List For
Divided and Undivided Cryptograms," unpublished
manuscript, 1984.

[HILL] Hill, Lester, S., "Cryptography in an Algebraic
Alphabet", The American Mathematical Monthly, June-July
1929.

[HIS1] Barker, Wayne G., "History of Codes and Ciphers in the
U.S. Prior to World War I," Aegean Park Press, Laguna
Hills, CA, 1978.

[HITT] Hitt, Parker, Col. " Manual for the Solution of Military
Ciphers,"  Aegean Park Press, Laguna Hills, CA, 1976.

[HOFF] Hoffman, Lance J., editor,  "Building In Big Brother:
The Cryptographic Policy Debate," Springer-Verlag,
N.Y.C., 1995. ( A useful and well balanced book of
cryptographic resource materials. )

[HOM1] Homophonic: A Multiple Substitution Number Cipher", S-
TUCK, The Cryptogram, DJ45, American Cryptogram
Association, 1945.

[HOM2] Homophonic: Bilinear Substitution Cipher, Straddling,"
ISHCABIBEL, The Cryptogram, AS48, American Cryptogram
Association, 1948.

[HOM3] Homophonic: Computer Column:"Homophonic Solving,"
PHOENIX, The Cryptogram, MA84, American Cryptogram
Association, 1984.

[HOM4] Homophonic: Hocheck Cipher,", SI SI, The Cryptogram,
JA90, American Cryptogram Association, 1990.

[HOM5] Homophonic: "Homophonic Checkerboard," GEMINATOR, The
Cryptogram, MA90, American Cryptogram Association, 1990.

[HOM6] Homophonic: "Homophonic Number Cipher," (Novice Notes)
LEDGE, The Cryptogram, SO71, American Cryptogram
Association, 1971.

[IBM1] IBM Research Reports, Vol 7., No 4, IBM Research,
Yorktown Heights, N.Y., 1971.

[INDE] PHOENIX, Index to the Cryptogram: 1932-1993, ACA, 1994.

[JOHN] Johnson, Brian, 'The Secret War', Arrow Books,
London 1979.

[KAHN] Kahn, David, "The Codebreakers", Macmillian Publishing
Co. , 1967.

[KAH1] Kahn, David, "Kahn On Codes - Secrets of the New
Cryptology," MacMillan Co., New York, 1983.

[KOBL] Koblitz, Neal, " A Course in Number Theory and
Cryptography, 2nd Ed, Springer-Verlag, New York, 1994.

[KULL] Kullback, Solomon, Statistical Methods in Cryptanalysis,
Aegean Park Press, Laguna Hills, Ca. 1976

[LAFF] Laffin, John, "Codes and Ciphers: Secret Writing Through
The Ages," Abelard-Schuman, London, 1973.

[LANG] Langie, Andre, "Cryptography," translated from French
by J.C.H. Macbeth, Constable and Co., London, 1922.

[LEDG] LEDGE, "NOVICE NOTES," American Cryptogram Association,
1994.  [ One of the best introductory texts on ciphers
written by an expert in the field.  Not only well
written, clear to understand but as authoritative as
they come! ]

[LEWI] Lewin, Ronald, 'Ultra goes to War', Hutchinson,
London 1978.

[LEWY] Lewy, Guenter, "America In Vietnam", Oxford University
Press, New York, 1978.

[LISI] Lisicki, Tadeusz, 'Dzialania Enigmy', Orzet Biaty,
London July-August, 1975; 'Enigma i Lacida',
Przeglad lacznosci, London 1974- 4; 'Pogromcy
Enigmy we Francji', Orzet Biaty, London, Sept.
1975.'

[LYNC] Lynch, Frederick D., "Pattern Word List, Vol 1.,"
Aegean Park Press, Laguna Hills, CA, 1977.

[LYSI] Lysing, Henry, aka John Leonard Nanovic, "Secret
Writing," David Kemp Co., NY 1936.

[MANS] Mansfield, Louis C. S., "The Solution of Codes and
Ciphers", Alexander Maclehose & Co., London, 1936.

[MARO] Marotta, Michael, E.  "The Code Book - All About
Unbreakable Codes and How To Use Them," Loompanics
Unlimited, 1979.  [This is terrible book.  Badly
written, without proper authority, unprofessional, and
prejudicial to boot.  And, it has one of the better
illustrations of the Soviet one-time pad with example,
with three errors in cipher text, that I have corrected
for the author.]

[MARS] Marshall, Alan, "Intelligence and Espionage in the Reign
of Charles II," 1660-1665, Cambridge University, New
York, N.Y., 1994.

[MART] Martin, James,  "Security, Accuracy and Privacy in
Computer Systems," Prentice Hall, Englewood Cliffs,
N.J., 1973.

[MAZU] Mazur, Barry, "Questions On Decidability and
Undecidability in Number Theory," Journal of Symbolic
Logic, Volume 54, Number 9, June, 1994.

[MEND] Mendelsohn, Capt. C. J.,  Studies in German Diplomatic
Codes Employed During World War, GPO, 1937.

[MILL] Millikin, Donald, " Elementary Cryptography ", NYU
Bookstore, NY, 1943.

[MYER] Myer, Albert, "Manual of Signals," Washington, D.C.,
USGPO, 1879.

[MM]   Meyer, C. H., and Matyas, S. M., " CRYPTOGRAPHY - A New
Dimension in Computer Data Security, " Wiley
Interscience, New York, 1982.

[MODE] Modelski, Tadeusz, 'The Polish Contribution to the
Ultimate Allied Victory in the Second World War',
Worthing (Sussex) 1986.

[NIBL] Niblack, A. P., "Proposed Day, Night and Fog Signals for
the Navy with Brief Description of the Ardois Hight
System," In Proceedings of the United States Naval
Institute, Annapolis: U. S. Naval Institute, 1891.

[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
Languages," ACA-L, August 18, 1995.

[NIC2] Nichols, Randall K., "Chinese Cryptography Parts 1-3,"
ACA-L, August 24, 1995.

[NIC3] Nichols, Randall K., "German Reduction Ciphers Parts
1-4," ACA-L, September 15, 1995.

[NIC4] Nichols, Randall K., "Russian Cryptography Parts 1-3,"
ACA-L, September 05, 1995.

[NIC5] Nichols, Randall K., "A Tribute to William F. Friedman",
NCSA FORUM, August 20, 1995.

[NIC6] Nichols, Randall K., "Wallis and Rossignol,"  NCSA
FORUM, September 25, 1995.

[NIC7] Nichols, Randall K., "Arabic Contributions to
Cryptography,", in The Cryptogram, ND95, ACA, 1995.

[NIC8] Nichols, Randall K., "U.S. Coast Guard Shuts Down Morse
Code System," The Cryptogram, SO95, ACA publications,
1995.

[NIC9] Nichols, Randall K., "PCP Cipher," NCSA FORUM, March 10,
1995.

[NORM] Norman, Bruce, 'Secret Warfare', David & Charles,
Newton Abbot (Devon) 1973.

[OP20] "Course in Cryptanalysis," OP-20-G', Navy Department,
Office of Chief of Naval Operations, Washington, 1941.

[PIER] Pierce, Clayton C., "Cryptoprivacy", 325 Carol Drive,
Ventura, Ca. 93003.

[RAJ1] "Pattern and Non Pattern Words of 2 to 6 Letters," G &
C. Merriam Co., Norman, OK. 1977.

[RAJ2] "Pattern and Non Pattern Words of 7 to 8 Letters," G &
C.  Merriam Co., Norman, OK. 1980.

[RAJ3] "Pattern and Non Pattern Words of 9 to 10 Letters," G &
C.  Merriam Co., Norman, OK. 1981.

[RAJ4] "Non Pattern Words of 3 to 14 Letters," RAJA Books,
Norman, OK. 1982.

[RAJ5] "Pattern and Non Pattern Words of 10 Letters," G & C.
Merriam Co., Norman, OK. 1982.

[RHEE] Rhee, Man Young, "Cryptography and Secure
Communications,"  McGraw Hill Co, 1994

[ROBO] NYPHO, The Cryptogram, Dec 1940, Feb, 1941.

[SACC] Sacco, Generale Luigi, " Manuale di Crittografia",
3rd ed., Rome, 1947.

[SCHN] Schneier, Bruce, "Applied Cryptography: Protocols,
Algorithms, and Source Code C," John Wiley and Sons,
1994.

[SCHW] Schwab, Charles, "The Equalizer," Charles Schwab, San
Francisco, 1994.

[SHAN] Shannon, C. E., "The Communication Theory of Secrecy
Systems," Bell System Technical Journal, Vol 28 (October
1949).

[SIG1] "International Code Of Signals For Visual, Sound, and
Radio Communications,"  Defense Mapping Agency,
Hydrographic/Topographic Center, United States Ed.
Revised 1981

[SIG2] "International Code Of Signals For Visual, Sound, and
Radio Communications,"  U. S. Naval Oceanographic
Office, United States Ed., Pub. 102,  1969.

[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
Mathematical Association of America, NYU, 1966.

[SISI] Pierce, C.C., "Cryptoprivacy," Author/Publisher, Ventura
Ca., 1995. (XOR Logic and SIGTOT teleprinters)

[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret
Writing," Dover, NY, 1943.

[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I-
III, " Harper and Row, New York, N.Y., 1975.

[STEV] Stevenson, William, 'A Man Called INTREPID',
Macmillan, London 1976.

[STIN] Stinson, D. R., "Cryptography, Theory and Practice,"
CRC Press, London, 1995.

[SUVO] Suvorov, Viktor "Inside Soviet Military Intelligence,"
Berkley Press, New York, 1985.

[TERR] Terrett, D., "The Signal Corps: The Emergency (to
December 1941); G. R. Thompson, et. al, The Test(
December 1941 -  July 1943); D. Harris and G. Thompson,
The Outcome;(Mid 1943 to 1945), Department of the Army,
Office of the Chief of Military History, USGPO,
Washington,1956 -1966.

[TILD] Glover, D. Beaird, Secret Ciphers of The 1876
Presidential Election, Aegean Park Press, Laguna Hills,
Ca. 1991.

[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio
Telegraph) Department of the Army, 1948.

[TRAD] U. S. Army Military History Institute, "Traditions of
The Signal Corps., Washington, D.C., USGPO, 1959.

[TRIB] Anonymous, New York Tribune, Extra No. 44, "The Cipher
Dispatches, New York, 1879.

[TRIT] Trithemius:Paul Chacornac, "Grandeur et Adversite de
Jean Tritheme ,Paris: Editions Traditionelles, 1963.

[TUCK] Harris, Frances A., "Solving Simple Substitution
Ciphers," ACA, 1959.

[TUCM] Tuckerman, B., "A Study of The Vigenere-Vernam Single
and Multiple Loop Enciphering Systems," IBM Report
RC2879, Thomas J. Watson Research Center, Yorktown
Heights, N.Y.  1970.

[VERN] Vernam, A. S.,  "Cipher Printing Telegraph Systems For
Secret Wire and Radio Telegraphic Communications," J.
of the IEEE, Vol 45, 109-115 (1926).

[VOGE] Vogel, Donald S., "Inside a KGB Cipher," Cryptologia,
Vol XIV, Number 1, January 1990.

[WAL1] Wallace, Robert W. Pattern Words: Ten Letters and Eleven
Letters in Length, Aegean Park Press, Laguna Hills, CA
92654, 1993.

[WAL2] Wallace, Robert W. Pattern Words: Twelve Letters and
Greater in Length, Aegean Park Press, Laguna Hills, CA
92654, 1993.

[WATS] Watson, R. W. Seton-, ed, "The Abbot Trithemius," in
Tudor Studies, Longmans and Green, London, 1924.

[WEL]  Welsh, Dominic, "Codes and Cryptography," Oxford Science
Publications, New York, 1993.

[WELC] Welchman, Gordon, 'The Hut Six Story', McGraw-Hill,
New York 1982.

[WINT] Winterbotham, F.W., 'The Ultra Secret', Weidenfeld
and Nicolson, London 1974.

[WOLE] Wolfe, Ramond W., "Secret Writing," McGraw Hill Books,
NY, 1970.

[WOLF] Wolfe, Jack M., " A First Course in Cryptanalysis,"
Brooklin College Press, NY, 1943.

[WRIX] Wrixon, Fred B. "Codes, Ciphers and Secret Languages,"
Crown Publishers, New York, 1990.

[YARD] Yardley, Herbert, O., "The American Black Chamber,"
Bobbs-Merrill, NY, 1931.

[ZIM]  Zim, Herbert S., "Codes and Secret Writing." William
Morrow Co., New York, 1948.

[ZEND] Callimahos, L. D.,  Traffic Analysis and the Zendian
Problem, Agean Park Press, 1984.  (also available through
NSA Center for Cryptologic History)

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