## Lesson 3: Substitutions With Variants Part II: Multiliteral Substitution

```                 CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI
November 13, 1995
Revision 1

LECTURE 3
SUBSTITUTION WITH VARIANTS PART II
MULTILITERAL SUBSTITUTION

SUMMARY

In Lecture 3, we continue our look into substitution ciphers,
and move into the multiliteral substitution case, we field more
tools for cryptanalysis, look at some fascinating historical
variations, we review "the unbreakable cipher" and solve
homework problems.

MULTILITERAL SUBSTITUTION WITH SINGLE-EQUIVALENT CIPHER
ALPHABETS

Monoalphabetic substitution methods are classified as
uniliteral and multiliteral systems.   Uniliteral systems
maintain a strict one-to-one correspondence between the length
of the units of the plain and those of the cipher text.  Each
letter of plain text is replaced by a single character in the
cipher text.  In multiliteral monoalphabetic substitution
systems, this correspondence is no longer one plain to one
cipher but may be one plain to two cipher, where each letter of
the plain text is replaced by two characters in the cipher
text; or one plain to three cipher, where a three-character
combination in the cipher text represents a single letter of
the plain text.  We refer to these systems as uniliteral,
biliteral, and triliteral, respectively.   Ciphers in which one
plain text letter is represented by cipher characters of two or
more elements are classed as multiliteral.   [FR1], [FR2],
[FR5]

BILITERAL CIPHERS

Friedman gives some interesting examples of biliteral
monoalphabetic substitution.  [FR1]    Many cipher systems
start with a geometric shape.  Using the square in Figure 3-1,

W   H   I   T   E
.......................
W . A   B   C   D   E
.
H . F   G   H  IJ   K
.
I . L   M   N   O   P
.
T . Q   R   S   T   U
.
E . V   W   X   Y   Z
Figure 3-1

We derive the following cipher alphabet:

Plain :  a  b  c  d  e  f  g  h  i  j  k  l  m
Cipher: WW WH WI WT WE HW HH HI HT HT HE IW IH

Plain :  n  o  p  q  r  s  t  u  v  w  x  y  z
Cipher: II IT IE TW TH TI TT TE EW EH EI ET EE

The alphabet derived from the cipher square or matrix is
referenced by row and column coordinates, respectively.

The key to this system is that when a message is enciphered by
this biliteral alphabet, the cryptogram is still monoalphabetic
in character.  A frequency distribution based upon pairs of
letters will have all the characteristics of a simple
uniliteral distribution for a monoalphabetic substitution
cipher.

Numbers can be used as effectively as letters in the biliteral
cipher.  The simplest form is A=01, B=02, C=03,...Z=26.  So,
the plain text letters have as their equivalents two-digit
numbers indicating their position in the normal alphabet.

Other dinome (two digit) cipher matrices are previewed:

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

Note that frequently-used punctuation marks can be enciphered
in the above matrix.

Another four examples are:

Figure 3-3                     Figure 3-4

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

Figure 3-5                     Figure 3-6

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

It is possible to generate false or pseudo-code or artificial
code language by using an enciphering matrix with vowels as row
indicators and consonants as column indicators.

Figure 3-7

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

Enciphering the word RAIDS  would be OCABE  FAFOD. [FR5]

Another subterfuge used to camouflage the biliteral cipher
matrix is to append a third character to the row or column
indicator.  This third character may be produced through the
use of cipher matrix shown in Figure 3-8 (wherein A=611,
B=612, etc.) or the third character can be the "sum checking"
digit which is the non-carrying sum (modulo 10) of the
preceding two digits such as trinomes 257, 831, and 662.  It
may also involve self summing groups such as 254, 830, 669 all
which sum to the constant 1, or finally the third digit can be
random, inserted solely for the pleasure of the cryptanalyst.

Figure 3-8

1  2  3  4  5
..................
61  .  A  B  C  D  E
72  .  F  G  H IJ  K
83  .  L  M  N  O  P
94  .  Q  R  S  T  U
05  .  V  W  X  Y  Z

A=611 ,  B=612    X=053

All the above matrices are bipartite.  They can be divided into
two separate parts that can be clearly and cleanly defined by
row and column indicators.  This is the primary weakness of
this type of cipher.           [FR1]

Sinkov presents a good description of the modulo arithmetic
required to solve biliteral cipher challenges.  [SINK]  A more
involved look at the statistics involved can be found in
[CULL].

BILITERAL BUT NOT BIPARTITE

Consider the following cipher matrix:

Figure 3-9

1  2  3  4  5
..................
09  .  H  Y  D  R  A
15  .  U  L  IJ C  B
21  .  E  F  G  K  M
27  .  N  O  P  Q  S
33  .  T  V  W  X  Z

We can produce a biliteral cipher alphabet in which the
equivalent for any letter in the matrix is the sum of the two
coordinates which indicate its cell in the matrix:

Plain      A   B   C   D   E   F   G   H   I   J   K   L   M
Cipher    14  20  19  12  22  23  24  10  18  18  25  17  26

Plain      N   O   P   Q   R   S   T   U   V   W   X   Y   Z
Cipher    28  29  30  31  13  32  34  16  35  36  37  11  38

A = 9+5 =14,  E = 21 + 1 =22

The cipher units are biliteral but they are not bipartite.
Cipher text equivalent of plain text letter "A" is 14 and
digits 1 and 4 have no meaning per se.  Plain text letters
whose cipher equivalents begin with 1 may be found in two
different rows of the matrix and those of whose equivalents end
in 4 appear in three different columns.  [FR1]

Another possibility lends itself to certain multiliteral
ciphers in the use of a word spacer or word separator.  The
word space might be represented by a value in the matrix;
i.e., the separator is enciphered as a value (dinome 39 in
Figure 3-4).  The word space might be an unenciphered element.

Lets break from the theory and look at four interesting
multiliteral historical ciphers before discussing the general
cryptanalytic attack on the multiliteral cipher.

TRITHEMIAN

The abbot Trithemius, born Johann von Heydenberg (1462-1516)
invented one of the first multiliteral ciphers.  It was
fashioned similar to the Baconian Cipher and was a means for
disguising secret text.  His work "Steganographia" published in
1499 describes several systems of 'covered writing.'  [TRIT]
[WATS], [FR1]   The science of steganography is named after
him.  Several Internet discussion groups currently discuss the
use of steganography to hide messages in graphics files. (.GIF
files)

His alphabet, modified to include 26 letters of present-day
English, is shown in Figure 3-10, below;  it consists of all
the permutations of three things taken three at a time or
3 ** 3 = 27 in all.

Figure 3-10

A - 111    G - 131     M - 221     S - 311    Y - 331
B - 112    H - 132     N - 222     T - 312    Z - 332
C - 113    I - 133     O - 223     U - 313    * - 333
D - 121    J - 211     P - 231     V - 321
E - 122    K - 212     Q - 232     W - 322
F - 123    L - 213     R - 233     X - 323

The cipher text does not have to be restricted to digits; any
groupings of three things taken three at a time will do.

BACON

Sir Francis Bacon (1561-1626) invented a cipher in which the
cipher equivalents are five-letter groups and the resulting
cipher is monoalphabetic in character.  Bacon uses a 24 letter
cipher with I and J, U and W used interchangeably.

A =  aaaaa      I/J  = abaaa       R  = baaaa
B =  aaaab       K   = abaab       S  = baaab
C =  aaaba       L   = ababa       T  = baaba
D =  aaabb       M   = ababb      U/V = baabb
E =  aabaa       N   = abbaa       W  = babaa
F =  aabab       O   = abbab       X  = babab
G =  aabba       P   = abbba       Y  = babba
H =  aabbb       Q   = abbbb       Z  = babbb

Bacon described the steganographic effect of message enfolding
in an innocent external message.   Suppose we let capitals be
the "a" element and lower-case letters represent the "b"
elements.   The message "All is well with me today" can be made
to convey the message "Help."   Thus,

A  L  l  i  s    W E l L   W    I t H  m E   T o d a Y
a  a  b  b  b    a a b a   a    a b a  b a   a b b b a

H              E              l            P

Bacon describes many several variations on the theme.  [FR1],
[DEAU]    Note the regularity of construction of Bacon's
biliteral alphabet, a feature which permits its reconstruction
from memory.

HAYES CIPHERS

Probably the most corrupt political election occurred on
November 7, 1876 with the election of President Rutherford B.
Hayes (Republican).  He defeated Samuel Jones Tilden
(Democrat).  Tilden had won the popular vote by 700,000 votes
but because of frauds surrounding the electoral college, he was
deprived of the high office of President.  Actual both
candidates were involved with bribery, election tampering,
voter fraud, conspiracy and a host of other goodies.  Tilden
ran on a law and order ticket that credited him with convicting
Boss Tweed and the Tweed Ring in New York City, which
controlled the city through Tammany Hall.  For two years into
Hayes Presidency, the scandals persisted.

With the help of New York Tribune, Republicans finished the
Tilden 'honesty' horse.  They published the Tilden Ciphers and
keys.  There were about 400 of them representing substitution
and transposition forms.  We will revisit the transposition
forms at a later juncture.  They represented secret and illegal
operations by Tilden's men in Florida, Louisiana, South
Carolina and Oregon.   The decipherments were done by
investigators of the Tribune.  Here are two examples and their
solution.  [TILD] , [FR1] , [TRIB]

GEO. F. RANEY, Tallahassee.

P P Y Y E M N S N Y Y Y P I M A S H N S Y Y S S I T E P A A E
N S H N S P E N N S S H N S M M P I Y Y S N P P Y E A A P I E
I S S Y E S H A I N S S S P E E I Y Y S H N Y N S S S Y E P I
A A N Y I T N S S H Y Y S P Y Y P I N S Y Y S S I T E M E I P
I M M E I S S E I Y Y E I S S I T E I E P Y Y P E E I A A S S
I M A A Y E S P N S Y Y I A N S S S E I S S M M P P N S P I N
S S N P I N S I M I M Y Y I T E M Y Y S S P E Y Y M M N S Y Y S
S I T S P Y Y P E E P P P M A A A Y Y P I I T

L' Engle goes up tomorrow.                     Daniel

Examination of the message discloses a bipartite alphabet
cipher with only ten different letters used.  Dividing the
messages by twos, assigning arbitrary letters for pairs of
letters and performing a triliteral frequency distribution will
yield a solution.

PP  YY  EM  NS  NY  YY  PI  MA  SH  NS  YY  SS  etc

A   B   C   D   E   B   F   G   H   D   B   I   etc

Have Marble and Coyle telegraph for influential men from
Delaware and Virginia.  Indications of weakening here.  Press
advantage and watch board.

Here is another Tilden cipher using numerical substitutes:

S. PASCO AND E. M. L'ENGLE

84  55  84  25  93  34  82  31  31  75  93  82  77  33  55  42

93  20  93  66  77  66  33  84  66  31  31  93  20  82  33  66

52  48  44  55  42  82  48  89  42  93  31  82  66  75  31  93

DANIEL

There were several messages of this type.  They  disclosed that
only 26 different numbers were used.

Cocke will be ignored, Eagan called in.  Authority reliable.

The Tribute experts gave the following alphabets:

AA = O   EN = Y   IT = D   NS = E   PP = H   SS = N
AI = U   EP = C   MA = B   NY = M   SH = L   YE = F
EI = I   IA = K   MM = G   PE = T   SN = P   YI = X
EM = V   IM = S   NN = J   PI = R   SP = W   YY = A
-------------------------------------------------------
20 = D   33 = N   44 = H   62 = X   77 = G   89 = Y
25 = K   34 = W   48 = T   66 = A   82 = I   93 = E
27 = S   39 = P   52 = U   68 = F   84 = C   96 = M
31 = L   42 = R   55 = O   75 = B   87 = V   99 = J

William F. Friedman correlated these alphabets with the results
being amusing:

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

The blank squares may have contained proper names and money
designations.  Key = HISPAYMENT for bribary seems to be
appropriate.   [HIS1], [TRIB], [TILD], [FR1]

BLUE AND GREY

One of the most fascinating stories of the American Civil War
(1861-65) is about communications using flag telegraphy or also
known as the wigwag signal system.

Wigwag is a system of positioning a flag (or flags) at various
angles that indicate the corresponding twenty-six letters of
the alphabet.  It was created in the mid-1800s by three men
working at separate locations: Navy Captain Phillip Colomb and,
Army Captain Francis Bolton, in England, and Surgeon-inventor
Albert J. Meyer in America.   [WRIX]    Meyer observed the
railroad electromagnetic telegraph, developed by Alexander
Bain, and invented a touch method of communication for the deaf
and later the wigwag system.  He developed companion methods
with torches and disks.   The name "wigwag" derived from the
flag movements.

Three main color combinations were used in flags measuring two,
four and six feet square. The white banners had red square
centers while the black or red flags had white centers.  Myers
method required three motions (elements) to be used for each
letter.  The first position always initiated a message
sequence.  Motion one went from head to toe and back on right
side.  Motion 2 went from head to toe and back on left side.
Motion three went from head to toe and back in front of the
man.   Each motion made quickly.  Chart 3-1 indicates the
multiliteral alphabet and directional orders required to convey
a message.

Chart 3-1

A  - 112       H  -  312        O  - 223       V  -  222
B  - 121       I  -  213        P  - 313       W  -  311
C  - 211       J  -  232        Q  - 131       X  -  321
D  - 212       K  -  323        R  - 331       Y  -  111
E  - 221       L  -  231        S  - 332       Z  -  113
F  - 122       M  -  132        T  - 133
G  - 123       N  -  322        U  - 233

Myers Signal Directions

3 - End of a word
33 - End of a sentence
333 - End of message
22.22.22.3 - Signal of assent. Message understood
22.22.22.333 - Cease signaling
121.121.121.3 - Repeat
212121.3 - Error
211.211.211.3 - Move a little to the right
221.221.221.3 - Move a little to the left

As the Civil War wore on, Myer increased the wigwag motions to
four.  This enabled more specialized words and abbreviations to
be used.  In 1864, Myer invented a similar daytime system with
disks.

For night signals, Myer applied his system with torches on the
signal poles and lanterns.  A foot torch was used as a
reference point.  Thus the direction of the flying wave could
better be seen.   Compare this to the semaphore system used by
ships at sea when radio silence is a must.

Myer continuously improved his invention through 1859 and
presented his findings gratis to the Union Army (which gave him
a luke warm yawn for his trouble).  Alexander Porter, his chief
assistant joined the Confederate Army and used the wigwag
system in actual combat.  Porter was able to warn Colonel
Nathan Evans at Manassas Junction - Stone Bridge that the Union
Army had reached Sudley Ford and was about to surprise General
Beauregard's best Division.  Porter sent from his observation
tower, the following message to Colonel Evans at the Stone
Bridge defenses: "Look out for your left, you are turned."

Colonel Evans turned his cannons and musket fire toward the
Federal troops before they could initiate their attack.  Porter
was credited later (and decorated) for his vigilance led to
changes in the tactics of the entire struggle around Manassas
Junction.  The application of the new signal system had
directly influenced the shocking Union defeat that eventful
July day.

Myers signaling system was catapulted into use at the Battle of
Gettysburg.  General Lee had invaded northern soil in June
1863.  His Potomac crossing was relayed by flag system to the
War Department.  General Joseph Hooker resigned under fire on
June 28.   General George Meade (of NSA grounds fame) took over
command of the Army of the Potomac.  His headquarters were at
Taneytown, MD.   Startling news came via signalmen on July 1.
A skirmish on the Maryland border indicated that General Buford
was facing a major force not in Maryland but in Pennsylvania.
Lee was himself in command at Gettysburg.  Signalmen of each
army unit sent out calls for help.  Reinforcements from dozens
of units several miles away were committed to the fray.  By
July 1, 73,000 gray and 88,000 blue met in one of history's
most decisive battles.  Rarely, if at all, do textbooks even
hint that the secret message system of flags affected these
history changing events.  Yet the crucial sightings by Union
observers  directly tipped the scales against Lee's best
tactics.  The most famous incident was when Captain Castle on
Cemetery Ridge, refused to submit to Confederate artillery
barrage as General George Pickett charged the "thin blue line",
used a wooden pole and a bedsheet to make a makeshift flag to
alert Union forces under General Meade who ordered counter-
measures.  Pickett's charge was stopped short of breaching the
Union lines.  General Lee's gamble failed.  Previously
disregarded flagmen enabled George Meade to enter the shrine of
heros.   [BLUE], [ANNA], [MYER], [NIBL], [TRAD], [WRIX], [KAHN]

FURTHER NOTES ON CRYPTANALYSIS OF MULTILITERAL CIPHERS

LIMITED CHARACTERS

Multiliteral ciphers are often recognized by the fact that the
cryptographic text is usually composed of but a very limited
number of different characters.  They are handled in the same
way as are uniliteral monoalphabetic substitution ciphers.  So
long as the same character or number is used to represent the
same plain text letter, and so long as a given letter of
plain text is always represented by the same character or
combination of characters, then the substitution is strictly
monoalphabetic and can be handled by methods in my Lectures 1
and 2.

BILITERAL CIPHERS

In the case of biliteral ciphers where the row and column
indicators are not identical, the direction of reading the
cipher pairs is chosen at will for each succeeding cipher pair,
and analysis of contacts of the letters comprising the cipher
pairs will disclose that there are two distinct families of
letters, and the cipher pair will never consist of two letters
of the same family.  We reduce by further substitution to
uniliteral terms and solve by known methods.

WORD SEPARATORS

If a multiliteral cipher  includes a provision for the
encipherment of a word separator, the cipher equivalent of this
word separator may be readily identified because it will have
the highest frequency of any cipher unit.

Friedman presents data on word separators:

For English, the average word length is 5.2 letters.  The word
separator will be close to 16% frequency.  [FR1]  The letters
of the alphabet take on new percentage frequencies as follows:

A - 6.2         J - 0.16         S -  5.1
B - 0.84        K - 0.25         T -  7.7
C - 2.6         L - 3.0          U -  2.2
D - 3.5         M - 2.1          V -  1.3
E - 11.0        N - 6.6          W -  1.3
F - 2.3         O - 6.3          X -  0.41
G - 1.3         P - 2.3          Y -  1.6
H - 2.9         Q - 0.25         Z -  0.08
I - 6.2         R - 6.4

On the other hand, if the word separator is a single character,
this character may be identified by its positional appearance
spaced 'wordlength-wise' in the cipher text and by the fact
that it never contacts itself.

It is advisable to reduce multiliteral cipher text to
uniliteral equivalents, especially if a triliteral frequency
distribution is made.  If not more than 36 combinations are
present in the cryptogram, the extra values over 26 may be
represented by digits for the purpose of reduction.  For more
than 36 groups, cipher text can be attacked in multiliteral
groupings.

ANAGRAMING

One of the first steps to solving a multiliteral cipher with a
cipher matrix, is to anagram the letters comprising the row and
column indicators in an attempt to disclose the key words used.
When the anagraming process does disclose any key word(s), a
skeleton reconstruction matrix which is the duplicate of the
original enciphering matrix is made to show the order of the
row and column indicators.  Partial recovery of plain text may
be possible at this point in the analysis.  Looking at the
frequency analysis (and location of the crests and troughs) may
tell us something about the enciphering alphabet as normal or
keyed.

NUMERICAL CIPHERS

Cipher alphabets whose cipher components consist of numbers are
practicable for telegraph or radio transmission.  They may take
forms corresponding to those employing letters.

Standard numerical cipher alphabets are those in which the
cipher component is a normal sequence of numbers.

Plain  -  A   B   C   D   E   F   G   H   I   J   K   L   M
Cipher - 11  12  13  14  15  16  17  18  19  20  21  22  23

Plain  -  N   O   P   Q   R   S   T   U   V   W   X   Y   Z
Cipher - 24  25  26  27  28  29  30  31  32  33  34  35  36

We could easily have started the cipher alphabet with A= 01,
B=02,..., Z=26 with the same results.

Mixed numerical cipher alphabets are those that have been keyed
by a key word turned into numerical cipher equivalents or have
a random combination of two or more digits for each letter of
plain text.

Plain  -  A   B   C   D   E   F   G   H   I - J   K   L   M
Cipher - 76  88  01  67  04  80  66  99  96  96  02  69  90

Plain  -  N   O   P   Q   R   S   T   U   V   W   X   Y   Z
Cipher - 77  05  87  60  39  79  03  78  68  98  86  70  97

The computer whizzes are now thinking that the example has
all numbers less than 100. Therefore, a brute force attack
on all combinations of two letter-equivalents of the above
ciphertext numerical values taken two at a time in combination
with the digram frequency data could be a good approach to the
cipher matrix construction problem.  The ASOLVER computer
program at the CDB does this kind analysis and adds threshold
limitations on the search.

Figure 3-3 and 3-4 could be arranged for simple numerical
equivalents like this:

Figure 3-3a                     Figure 3-4a

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

where: A = 11, R=42  Z=55

Numerical cipher values lend themselves to treatment by various
mathematical processes to further complicate the cipher system
in which they are used.  These processes, mainly addition or
subtraction, may be applied to each cipher equivalent
individually, or to the complete numerical cipher message by
considering it as one number.  [OP20]

Reference [NIC4]  on Russian Cryptography describes the VIC
Cipher and the one-time pad.  Both involve mathematical
treatment to numerical based ciphers.  The Hill cipher is
another good example of the use of mathematical transformation
processes on ciphers and is presented in David Kahn's book.
[KAHN]

In modern cryptographic systems, the DES family of ciphers use
simple S-Boxes [substitution boxes] that are reorganized by
ordered non-linear mathematical rules applied several times
over (know as rounds).   [NIC4], [OP20], [RHEE], [HILL], [IBM1]

The question of 'unbreakable' mathematical ciphers might be
poised at this juncture.   Lets look at the famous one-time pad
and see what it offers.   [NIC4]

The one-time pad is truly an unbreakable cipher system.  There
are many descriptions of this cipher.  One of the better
descriptions is by Bruce Schneier.  [SCHN]   It consists of a
nonrepetitive truly random key of letters or characters that is
used just once.  The key is written on special sheets of paper
and glued together in a pad.  The sender uses each key letter
on the pad to encrypt exactly one plain text letter or
character.  The receiver has an identical pad and uses the key
on the pad, in turn, to decrypt each letter of the ciphertext.
[SHAN]

Each key is used exactly once and for only one message.
The sender encrypts the message and destroys the pad's page.
The receiver does the same thing after decrypting the message.
New message - new page and new key letters/numbers - each time.

The one-time pad is unbreakable both in theory and in practice.
Interception of ciphertext does not help the cryptographer
break this cipher.  No matter how much ciphertext the analyst
has available, or how much time he had to work on it, he could
never solve it.  [KAHN]

The reason is that no pattern can be constructed for the key.
The perfect randomness of the one time system nullifies any
efforts to reconstruct the key or plain text via horizontal or
lengthwise analysis, via cohesion, via re-assembly (such as
Kasiski or Kerckhoff's columns) via repeats or via internal
framework erection.  [KAHN]  [KAH1], [WRIX], [NIC4], [SCHN]

Brute force (trial and error) might bring out the true
plaintext but it would also yield every other text of the same
length, and there is no way to tell which is the right one.
The worst of it is that the possible solutions increase as the
message lengthens.

Supposing the key were stolen, would this help to predict
future keys?  No, because a random key has no underling system
to exploit.  If it did, it would not be random.  [KAHN]

A random key sequence XOR 'ed with a nonrandom plain text
message produces a completely random ciphertext message and no
amount of computing will change that. [SCHN]   The  one-time
pad can be extended to encryption of binary data.  Instead of
letters, we use bits.  [SCHN]

FRESH KEY DRAWBACK

The one-time pad has a drawback - the quantities of fresh key
required.  For military messages in the field (a fluid
situation) a practical limit is reached.  It is impossible to
produce and distribute sufficient fresh key to the units.
During WWII, the US Army's  European theater HQ's transmitted,
even before the Normandy invasion, 2 million five (5) letter
code groups a day!  It would have therefore, consumed 10
million letters of key every 24 hours -the equivalent of a
shelf of 20 average books.  [KAH1] , [FRAA]

RANDOMNESS

The real issue for the one-time pad, is that the keys must be
truly random.  Attacks against the one-time pad must be against
the method used to generate the key itself. [SCHN] Pseudo-
random number generators don't count; often they have nonrandom
properties.  Reference [SCHN], Chapter 15, discusses in detail
random sequence generators and stream cipher.  I take exception
to his remarks regarding keyboard latency measurement.
People's typing patterns are anything but random (especially us
two finger types). [SCHN]  [MART]

ONE-TIME PAD SIMPLE EXAMPLE W/O SUPERENCIPHERMENT OR XOR

Begin with a cipher (A=1, B=2 ...)

PT:   T  A   X  A   T  I  O  N    I  S    T  H  E  F  T
CE:  20  1  24  1  20  9 15 14    9 19   20  8  5  6  20

>From a table of truly random numbers:

10480  15011  01536  02011  81647  91646  69719  22368
45673  25595  85393  30995  89198  27982  24130  48360
22527  97265  76393  64809  15179  42167  ....

Add the cipher equivalent to the random key:

T         A       X       A       T        I
20        1      24       1       20       9
10480    15011   01536   02011    81647   91646
-----    -----   -----   -----    -----   -----  ...
10500    15012   01560   02012    81667   91655

Transmit new cipher text:

10500  15012  01560  02012  81667  91655  69734  .....

Receiver subtract key out of message and decodes equivalents.

Many variations exist.  Note  in the cipher text  T1 .ne. T2
.ne. T(i) and A1 .ne.  A2 .ne. A(i),  etc.

[MARO]

ONE-TIME PAD HISTORICAL CONSIDERATIONS

The one-time pad  originated from the work of Gilbert Vernam in
1917.  Vernam worked for ATT.  He got his idea from the French
telegrapher Emile Baudot.  Baudot code replaced letters with
electrical impulses, called units.  Every character was given 5
units that either signified a pulse of electrical current
("marks") or its absence ("spaces") during a given time period.
[ 32 combinations in all].  In 1917, paper tape was used and
the marks and spaces were read by metallic fingers.  Vernam
essentially automated the process and devised a cipher on it.

In modern computer terms, key bits were added modulo 2 to
plaintext bits on a bit by bit basis.  If X = x1, x2, x3..
denotes the plain text, and  K = k1, k2, k3 .. the keystream,
Vernam's cipher produces a cipher text bit stream  Y = Ek(X) =
y1, y2, y3.   [VERN]

CONCURRENT DEVELOPMENTS

Other countries conducted similar research.  Between 1918-1920,
other one-time pad methods were developed.  The German Foreign
Office employed the one-time pad in 1920.  The Russians first
stole and then improved the German system.  It was fully
deployed in 1925 for diplomatic use!  OSS and SOE operatives in
WWII had special grid one-time pad's.  By 1944, OSS technicians
had developed pages made of film that were read with a hand
magnifying glass.  By 1960, Russian pads were the size of a
postage stamp or scrolls the size of a large eraser.  The
Russians were first to conceal the one-time pad in microfilm.
One-time pads were made of cellulose nitrate for rapid
destruction.  [RHEE] ,[VERN], [TERR], [KAHN]

RUSSIAN IMPLEMENTATION OF THE ONE-TIME PAD

So why classify the one-time pad with Russian Ciphers?  Because
they have been serious about using it since 1925!  Before 1917,
Russian diplomatic and military systems could be expressed by
the old axiom:

Cryptography + Loose Discipline = Chaos

After her loss of trade information to the British in 1920, and
defeats of her Army in WWI because of poor cipher handling, she
woke up.   By 1916, Russia's intercept service at Nicolaieff
was in full service against the Germans.  From 1920 through
today, Russia has targeted stealing other countries codes with
"great vigor" as Kennedy once said.  Code stealing was done
through the COMINT efforts of the former KGB and GRU.  The
Spets-Odel (Special Department) was a primary agency involved
with Ciphers and Cryptanalysis.  Section 6 grew 400% over a 10
year period prior to WWII.

The Soviet Union has employed the one-time pad to protect ALL
her diplomatic missions from 1930 on.   Consequently her
crucial Foreign Office messages were not read by foes,
neutrals, nor allies.  The GRU and the Soviet Spy rings -
"LUCY", "RED ORCHESTRA, and "Sorge's Net"  all used the one-
time pad.  They also used a straddling checkerboard variant
(not unbreakable).

The one-time pad is used in the old fashioned form in the
Soviet Mission - diplomatic , secret police, military,
commercial, political (Communist Party) - all have their own
keys.  All cables coming into a legation look alike: simple
groups of five digits.  Letters that are photographed,
codenames are applied and then enciphered in one-time pad
system.  [COVT], [BLK], [BARR]

Agents in the field use the one-time pad.  Radio links to
Moscow, are encrypted via one-time pads.  The main Soviet spy
cipher today still employs the one-time pads.

The most dramatic spy stories (Klaus Fuchs, Iger Gouzenko,
Vladimir Petrov, Colonel  Zabotin, Rudolf Abel, Gregory
Liolios, Eleftherious Voutsas, the Krogers, Guiseppe Martelli,
Ali Abbasi, Reino Hayhanen, Aldridge Ames ...) all have used

Such is cryptology in the Soviet Union -  complex, enigmatic,
focused, state-of-the-art, applying the one-time pad principles
to other ciphers.  Do you remember when the diplomatic ciphers
in use at the American embassy in Moscow were solved?  Russia
has a profound understanding of cryptography and cryptanalysis.
[VOGE], [SUVO], [KAHN]

The U.S. history was different.  Some would argue that the U.S.
became serious and superplayers in 1953.  Some would argue
1943.  But not many will argue 1925 (we still had SIGTOT then).
[SISI]

LECTURE 4

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

LECTURE 5 - 6

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

SOLUTION TO HOMEWORK PROBLEMS FROM LECTURE 2

BOZOL gets the kudo for best solution on the homework.  Both
problems were unkeyed.

Pd-1.                                            Daniel

H Z K L X   A L H X P   N C I N Z   X F L I X   G N W Q X

P N Z K T   L N K X O   L X N I Z   X G I N X   P N E Z K

X W Q X P   Z X L H X   P N C I N   Z X S N Q   N T X W Q

X P N W V   S N I K L   K H B L X   N W Q L X   H F Z I L

N X A Z K   S B W E N   I.

Problem 1 breaks down as follows:

High frequency (top 7%), count = 8 : XNLZI
Medium frequency letters:          : KPWHQS
Lo frequency  (less than 3)        : ABCEFGTOV
Zero (0) frequency                 : DJMRUY
By "N" Gram Count

6 gram         Count        CT Frequency

HXPNCI            2      5 19 6 17 2 8
LHXPNC            2      10 5 19 6 17 2
NCINZX            2      17 2 8 17 9 19
PNCINZ            2      6 17 2 8 17 9
XPNCIN            2      19 6 17 2 8 17

5  grams

CINZX             2      2 8 17 9 19
HXPNC             2      5 19 6 17 2
LHXPN             2      10 5 19 6 17
NCINZ             2      17 2 8 17 9
PNCIN             2      6 17 2 8 17
WQXPN             2      6 5 19 6 17
XPNCI             2      19 6 17 2 8
XWQXP (THATS)?    2      19 6 5 19 6

4 grams

CINX              2      2 8 17 9
HXPN              2      5 19 6 17
INZX              2      8 17 9 19
LHXP              2      10 5 19 6
NCIN              2      17 2 8 17
PNCI              2      6 17 2 8
QXPN              2      5 19 6 17
WQXP              2      6 5 19 6
YPNC              2      19 6 17 2
XWQX  (THAT)?     2      19 6 5 19

3 grams

CIN               2      2 8 17
HXP               2      5 19 6
INZ               2      8 17 9
LHX               2      10 5 19
LXN               2      10 19 17
NCI               2      17 2 8
NWQ               2      17 6 5
NZX               2      17 9 19
PNC               2      6 17 2
QXP               3      5 19 6
WQX               3      6 5 19
XPN               5      19 6 17
XWQ               2      19 6 5

2 grams          Count   CT  Frequency

CI                2      2 8
HX                2      5 19
IN                3      8 17
KL                2      7 10
KX                2      7 19
LH                2      10 5
LN                2      10 17
LX                4      10 19
NC                2      17 2
NI                2      17 8
NW                3      17 6
NX                2      17 19
NZ                3      17 9
PN                5      6 17
QX                3      5 19
SN                2      3 17
WQ                4      6 5
XA                2      19 2
XG                2      19 2
XN                2      19 17
XP                6      19 6
XW                2      19 6
ZK                4      9 7
ZX                4      9 19

Frequency  * Variety   =    Contacts
A        2           3      6      XLZ
B        2           4      8      HLSW
C        2           2      4      NI
D        0           0      0
E        2           3      6      NZW
F        2           4      8      XLHZ
G        2           3      6      XNI
H        5           6      30     ZLXKBF
I        8           7      56     CNLXZGK
J        0           0      0
K        7           8      56     ZLTNXIHS
L        10          11     110    KXAHFITNOBQ
M        0           0      0
N        17          13     221    PCIZGWLKXESQT
O        1           2      2      XL
P        6           3      18     XNZ
Q        5           4      20     WXNL
R        0           0      0
S        3           5      15     XNVKB
T        2           4      8      KLNX
U        0           0      0
V        1           2      2      WS
W        6           6      36     NQXVBE
X        19          15     285    LAHPZFIGQKONWST
Y        0           0      0
Z        9           9      81     HKNXIEPFA

>From above data we try X= t and N=e, P=h.  Then E=y, L=i,
W=o, S = D.

Message reads: Sanity is the great virtue of the ancient
literature; the want of that is the great defect of the modern,
in spite of its variety and power.      Matthew Arnold

Pd-2.   Join the army.                             Daniel

F L B B A   O I A F Q   E A O M Z   U I L O N   R Z O Q A

O P I L O   M O L S F   P F L I P   F L B B A   O E R I C

A O Q E F   O P Q B L   O W A V H   Z O W E A   P X Z Q Q

G A P Z I   V V A Z Q   E G A Q E   F H T E L   G L S A P

L R O W L   R I Q O U   F I E F P   E A Z O Q   Z I V I L

Q T F Q E   E F P G F   M P L I G   U B L G G   L T H A.

Problem 2 breaks down as follows:

High frequency (top 7%), count = 10 : LOAFQEI
Medium frequency letters:           : PZGBRVHMTUW
Lo frequency  (less than 3)         : SCNX
Zero (0) frequency                  : DJKY

By "N" Gram Count

6 gram         Count        CT Frequency

FLBBAO            2          12 15 6 6 14 15

5  grams

FLBBA             2          12 15 6  6 14
LBBAO             2          15 6 6 14 15

4 grams

BBAO              2           6 6 14 15
FLBB              2           12 15 6 6
LBBA              2           12 6 6 14

3 grams

BAO               2           6 14 15
BBA               2           6 6 14
EFP               2           11 12 10
FLB               2           12 15 6
FQE               2           12 12 11
ILO               2           11 15 15
LBB               2           15 6 6
PFL               2           10 12 15
QEF               2           12 11 12
ZIV               2           8 11 4
ZOQ               2           8 15 12

2 grams          Count   CT. Frequency

AO                5       14 15
AP                3       14 10
AZ                2       14 8
BA                2       6 14
BB                2       6 6
BL                2       6 15
EA                3       11 14
EF                4       11 12
FL                3       12 15
FP                3       12 10
FQ                2       12 12
GA                2       7 14
GL                2       7 15
IL                3       11 15
IV                2       11 4
LB                2       15 6
LG                2       15 7
LI                2       15 11
LO                3       15 15
LR                2       15 4
LS                2       15 2
OM                2       15 3
OP                2       15 10
OQ                3       15 12
OW                3       15 3
PF                2       10 12
PL                2       10 15
QE                5       12 11
RI                2       4 11
ZI                2       8 11
ZO                3       8 15
ZQ                2       8 12

Frequency  * Variety   =       Contacts
A        14         14      196       BOIFEQCWVPGZSH
B        6           5       30       LBAQU
C        1           2       2        IA
D        0           0       0
E        11         12      132       QAORFWGTLIPE
F        12         13      156       LAQSPEOHUITGM
G        7           9       63       QAELPFIUG
H        3           5       15       VZFTA
I        11         13      143       OAULPRCZVQFEG
J        0           0       0
K        0           0       0
L        15         12      180       FBIOSEGPRWQT
M        3           4       12       OZFP
N        1           2        2       OR

O        15         13      195       AIMLNZQPEFWRU
P        10         11      110       OIFQAXZLEGM
Q        12         12      144       FEOAPBZQGILT
R        4           6       24       NZEILO
S        2           3        6       LFA
T        3           5       15       HEQFL
U        3           6       18       ZIOFGB
V        4           4       16       AHIV
W        3           4       12       OAEL
X        1           2        2       PZ
Y        0           0        0
Z        8          10       80       MUROHQXPIA

BOZOL tried the crib word World from "Join the Army ..see the
world"  The crib failed but did show him some possibilities.
LANAKI's caveat - Forget the tip, it is usually a red hering.

Try the A=e, Q=t, e=h, O=r, and I=n.  Look for words offer,
battles, death, country.

Message reads: "I offer neither pay nor quarters nor
provisions.  I offer hunger, thirst, forced marches, battles
and death.  Let him who loves our country in his heart and not
with his lips only, follow me."     Made famous by Girabaldi.

HOMEWORK  LECTURE 3

Solve the following cipher problems.

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

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

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

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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.

[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.

[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,
Agean 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.

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

[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 too 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.]

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

[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.

[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.

[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 Comm-
unications,"  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/Topohraphic 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.

[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.

[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.

[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.

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