Classical Cryptography Course,
Volumes I and II from Aegean Park Press

By Randy Nichols (LANAKI)
President of the American Cryptogram Association from 1994-1996.
Executive Vice President from 1992-1994

Table of Contents
  • Lesson 1
  • Lesson 2
  • Lesson 3
  • Lesson 4
  • Lesson 5
  • Lesson 6
  • Lesson 7
  • Lesson 8
  • Lesson 9
  • Lesson 10
  • Lesson 11
  • Lesson 12
  • CLASSICAL CRYPTOGRAPHY COURSE


    BY LANAKI

    December 05, 1995


    LECTURE 4
    SUBSTITUTION WITH VARIANTS
    Part III
    MULTILITERAL SUBSTITUTION

    SUMMARY

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

    In Lecture 4, we complete our look into English monoalphabeticsubstitution ciphers, by describing multiliteral substitutionwith difficult variants. The Homophonic and GrandPre Cipherswill be covered. The use of isologs is demonstrated. Asynoptic diagram of the substitution ciphers described inLectures 1-4 will be presented.

    MULTILITERAL SUBSTITUTION WITH MULTIPLE-EQUIVALENT CIPHERALPHABETS - aka "MONOALPHABETIC SUBSTITUTION WITH VARIANTS"

    Each English letter in plain text has a characteristicfrequency which affords definite clues in the solution ofsimple monoalphabetic ciphers. Associations which individualletters form in combining to make up words, and thepeculiarities which certain of them manifest in plain text,afford further direct clues by means of which ordinarymonoalphabetic substitution encipherments of such plain textmay be readily solved. [FR1]

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

    Systems involving variants are generally multiliteral. In suchsystems, there are a large number of equivalents made availableby combinations and permutations of a limited number ofelements, each letter of the plain text may be represented byseveral multiliteral cipher equivalents which may be selectedat random. For example, if 3-letter combinations are employedas multiliteral equivalents, there are 263 or 17,576available equivalents for the 26 letters of the plain text.

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

    The primary object of substitution with variants is again toprovide several values which may be employed at random in asimple substitution of cipher equivalents for the plain textletters.

    As a slight diversion, the reader may ask about uniliteralsubstitution with variants. It is but not very practical.Note the following cipher alphabet constructed in French byCaptain 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=Hcombination is not allowed.)

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

    Mixed alphabets formed by including all repeated letters of thekey word or key phrase in the cipher component were common inEdgar Allen Poe's day but are impractical because they areambiguous, 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 acipher group such as TOOET, each letter having 3 or moreequivalents, from which plain text fragments (n)inth, ftthi(s), it thi, etc. can be formed on decipherment. [FR1]

    THEORETICAL DISTINCTIONS

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

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

    SIMPLE TYPES OF CIPHER ALPHABETS WITH VARIANTS

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

    Figure 4-2
    V
    W
    X
    Y
    Z
    Q
    R
    S
    T
    U
    *
    *
    *
    *
    *
    *
    *
    *
    *
    L
    F
    A
    *
    A
    B
    C
    D
    E
    M
    G
    B
    *
    F
    G
    H
    IJ
    K
    N
    H
    C
    *
    L
    M
    N
    O
    P
    O
    I
    D
    *
    Q
    R
    S
    T
    U
    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
    K
    J
    K
    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 thesimpler means for accomplishing monoalphabetic substitutionwith variants. The matrices are extensions of the basic ideasof multiliteral substitution presented in Lecture 3.

    The variant equivalents for any plain text letter may be chosenat will; thus, in Figure 4-1, e= 10, 15, 60, or 65; in Figure4-2, 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 columnor visa versa. There is no cryptographic ambiguity. Theremaining matrices are noncommutative. The general conventionis to read row by column.

    In Figures 4-5 and 4-6, the letters in the square have beeninscribed in such a manner that, coupled with the particulararrangement of the row and column coordinates, the number ofvariants available for each plain text letter is roughlyproportional to the frequencies of the letters in theplain text. Figure 35 incorporates a keyword on top of thisidea. [FR1]

    HOMOPHONIC

    The Homophonic Cipher is a simple variant system. It is a4-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, and76. (The lowest number in each of the four sequences.)[FR1] [FR5]

    The Russians added an interesting gimmick called the DisruptionArea. Consider Figure 4-12 and note the slashes under U - Xfor the fourth level of dinomes. The famous VIC cipher usedthis feature very effectively. [NIC4]
    Figure 4-12
    A
    B
    C
    D
    E
    F
    G
    H
    I
    J
    K
    L
    M
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    N
    O
    P
    Q
    R
    S
    T
    U
    V
    W
    X
    Y
    Z
    01
    02
    03
    04
    05
    06
    07
    08
    09
    10
    11
    12
    13
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    71
    72
    73
    74
    75
    76
    77
    78
    53
    54
    55
    56
    57
    94
    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 thedinomes and the four sequences are assigned randomly. However,the easy mnemonic feature of the keyworded four sequences islost.

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

    HOMOPHONIC CRYPTANALYSIS

    Lets solve the following cryptogram.

    68321   09022   48057   65111   88648   42036   45235   0914405764   22684   00225   57003   97357   14074   82524   4076851058   93074   92188   47264   09328   04255   06186   7988285144   45886   32574   55136   56019   45722   76844   6835045219   71649   90528   65106   11886   44044   89669   7055318491   06985   48579   33684   50957   70612   09795   2914856109   08546   62062   65509   32800   32568   97216   4428234031   84989   68564   53789   12530   77401   68494   3854411368   87616   56905   20710   58864   67472   22490   0913662851   24551   35180   14230   50886   44084   06231   1287605579   58980   29503   99713   32720   36433   82689   0451652263   21175   06445   72255   68951   86957   76095   6721553049   08567   9730
    Assuming we did not know that the above cryptogram was aHOMOPHONIC, we might make a preliminary analysis to see if weare dealing with a cipher or a code. We will cover codesystems later in the course, but a few introductory remarksmight be in order. The five letter groups could indicateeither a cipher or a code.

    If the cryptogram contains an even number of digits, as forexample 494 in the previous message, this leaves open thepossibility that the message is a cipher containing 247 pairsof digits; were the number of digits an exact odd multiple offive, such as 125, 135, etc., the possibility that thecryptogram is in code of the 5-figure group type must beconsidered.

    We next study the message repetitions and what theircharacteristics are. If the cipher text is of 5-figure codetype, then such repetitions as appear should generally be inwhole groups of five digits, and they should be visible in thetext just as the message stands, unless the code message hasbeen superenciphered. If the cryptogram is a cipher, thenrepetitions should extend beyond the 5-digit groupings; if theyconform to any definite at all they should for the most partcontain even numbers of digits since each letter is probablyrepresented by a pair (dinome) of digits.

    We start with 4-part frequency distribution. We next assumea 25 character alphabet from 01-00. This is the common schemeof drawing up the alphabets. Breaking the text into dinomes(2-digit) pairs yields:
    01
    02
    03
    04
    05
    06
    07
    08
    09
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    ///
    ///
    /
    /////
    //////
    ///
    ////
    ////
    /////
    ///
    /
    /
    /
    ///
    //////
    /
    //
    /////
    //
    /
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    ///
    /
    /
    /
    //////
    /
    /
    /
    /////
    /
    /
    ///
    ////
    /
    //////
    //////
    ///
    ///
    /////
    /////
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    /////
    /////
    ///
    ////
    /////
    //////
    //
    //
    //////
    /
    //
    ///////
    //
    /
    /
    ////
    ////
    /
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    00
    //////
    /
    /
    ///
    ////
    /
    //////
    //////
    ///
    ////
    /////
    //////
    ///
    /
    /
    /
    ///
    //////
    /
    //

    What we have before us are four simple, monoalphabeticfrequency distributions similar to those involved in amonoalphabetic substitution cipher using standard cipheralphabets. The next step is to fit the distribution to thenormal. Since I=J for the 25 letter alphabet, we find thatthe 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 distributionanalysis would have been changed to be on a basis of 26, theprocess of fitting the distribution to the normal would be thesame.

    PLAIN COMPONENT COMPLETION METHOD

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

    48226   88423   52099   93604   76059   05651   36683   5226797114   54466   76
    A variation of the plain-component completion method can beused to crack the new message. We copy the message intodinomes 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
    11
    45
    44
    66
    76
    2
    1
    3
    4
    1
    3
    1
    4
    2
    1
    4
    1
    4
    3
    3
    2
    3
    2
    1
    3
    4
    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 bysetting each of the cipher sequences against the plaincomponent at an arbitrary point of coincidence, such as thefollowing:

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

    The plain-component sequence is completed on the letters of thefour levels by Caesar Rundown, as follows:
    Level 1
    Level 2
    Level 3
    Level 4
    WXIDEWLXLLKUTSBFASRQIYAPWA
    XYKEFXM YMMLVU TCGBTSRKZBQXB
    YZLFGYNZNNMWVUDHCUTSLACRYC
    ZAMGHZOAOONXWVEIDVUTMBDSZD
    ABNHIAPBPPOYXWFKEWVUNCETAE
    BCOIKBQCQQPZYXGLFXWVODFUBF
    CDPKLCRDRRQAZYHMGYXWPEGVCG
    DEQLMDSESSRBAZINHZYZQFHWDH
    EFRMNETFTTSCBAKOIAZYRGIXEI
    FGSNOFUGUUTDCBLPKBAZ SHKYFK
    GHTOPGVHVVUEDCMQLCBATILZGL
    HIUPQHWIWWVFEDNRMDCBUKMAHM
    IKVQRIXKXXWGFEOSNEDCVLNBIN
    KLWRSKYLYYXHGFPTOFEDWMOCKO
    LMXSTLZMZZYIHGQUPGFEXNPDLP
    MNYTUMANAAZKIHRVQHGFYOQEMQ
    NOZUVNBOBBALKISWRIHGZPRFNR
    OPAVWOCPCCBMLKTXSKIHAQSGOS
    PQBWXPDQDDCNMLUYTLKIBRTHPT
    QRCXYQEREEDONMVZUMLKCSUIQU
    RSDYZRFSFFEPONWAVNMLDTVKRV
    STEZASGTGGFQPOXBWONMEUWLSW
    TUFABTHUHHGRQPYCXPONFVXMTX
    UVGBCUIVIIHSRQZDYQPOGWYNUY
    VWHCDVKWKKITSRAEZRQPHXZOVZ

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

    Level 1           	 Level 2          	Level 3          	Level 4EFRMNET           REEDON           EOSNEDC          NCETAE
    Arranging the letters of these generatrices in order ofappearance of their dinome equivalents, according to levels wehave:

    482268842352099936047605905651366835226797
     E  F R  M N      E  
    R       E      E D   
      E  O       SN 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 keywordJUNE.

    In evaluating generatrices, the sum of the arithmeticfrequencies of the letters in each row may be used as anindication of the relative "goodness". A statistically betterprocedure uses the logarithm of the probabilities of the plaintext letters forming the generatrices. See [FR2]

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

    For our computer bugs, TATTERS Homophonic solver is very easyto 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 ofcipher values available for any given plain text letter closelyapproximates its relative plain text frequency.

    Figure 4-11
    ABCDEVWXYZ
    A**TGAURIECAP
    B**SLIEYFRNST
    C**CNDOMELTIH
    D**RAPTFOYSOV
    E**NTXNECERED
    V**NOATEALEZH
    W**IHROQETRTB
    X**OIETACNPES
    Y**FTLOSAMTIU
    Z**ISNDRIEDON

    ( 676 - cell matrix )

    In figure 4-11, the number of occurrences of a particularletter within the matrix is proportional to the frequency inplain text; the letters are inscribed in random manner, in orderto enhance the security of the system.

    Figure 4-12
    6891543720
    7**AAACDEEILN
    1**AACDEEHKNO
    3**ABDEEHJNOR
    8**ADEEHINORS
    9**CEEGINORST
    2**EEFIMOQSTT
    0**EFIMOPRTTU
    5**FILNPRSTUX
    6**ILNPRSTUWY
    4**LNORSTTVYZ

    In figure 4-12, the same idea as 4-11 is presented in reducedform from 26 x 26 to 10 x 10. The letters have been inscribedby a simple diagonal route, from left to right, within thesquare, and the coordinates scrambled by means of a key wordor key number.

    Figure 4-13
    "Grandpre"
    0123456789
    0**ENTRUCKING
    1**QUARANTEEN
    2**UNEXPECTED
    3**IMPOSSIBLE
    4**VICTORIOUS
    5**ADJUDICATE
    6**LABORATORY
    7**EIGHTEENTH
    8**NATURALIZE
    9**TWENTYFIVE

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

    SACCO

    General Luigi Sacco proposed a frequential-type system thatuses both enciphering and deciphering matrices. The inscribeddinomes were completely disarranged by applying a doubletransposition to suppress the relationships between letters.References [SACC] and [FR1] both give a good description of theprocess. The number of variant values in this system arereflective of the Italian language.

    BACONIAN

    The Baconian ciphers found in the Cryptogram are a variantsystem. The "a" elements may be represented by any one of 20consonants as variants, while the "b" elements may berepresented by any one of 6 vowels; or the letters A-M may beused 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 fivedigits, 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 valuefrom 1-26; this value is expressed as a trinome, the digits ofwhich sum to the designated value of the letter. The letterassigned the value of 4 may be represented by any of 15permutations and combinations. Friedman discusses further waysof complication including disarrangement, addition ofpunctuation and nulls. See [FR1] pages 109-110. Note theinverted normal distribution representation of this cipher.

    ANALYSIS OF A SIMPLE VARIANT EXAMPLE

    The following cryptogram is available for study:
    Q M D C VP L F N FD H N W JW L K D KN H B P V
    R L T V MB K L W DW V H V KS H B C LP Q K J R
    V W S M LK G C N RL R N K VM G F X WJ R G M V
    W G T J HQ K X F NZ V F D ML T B P LP V F L M
    D C N W NH B C V ZN M L W QF D H D WV Z B R V
    K L C V CV R D H LR V T L FN C D K GM X W X M
    D T S C BC L Z L RL M V T SZ N K B WV P B R N
    C L R X RD C N K VP B T N TG H J Z LF Q F V K
    B W D Z XP N H S PG H L K LF V Z L TV M L K D
    P Q R N ZL Z D T BM N T G MN Z V F XK S F D C
    L Z V T VF D F V RG C L P QP N C D WV R J T N
    H L Z L MV W N P VP D Z D WJ P N W LR J K V M
    X M D T SM G F D RD K L W JF L P J MS F Q W B
    F N C B ZD K V W GZ S H B HD H J C X

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

    We construct a digraphic distribution:
    CFHKMPRTWZ
    B*3111122121
    D*4133111342
    G*2220300101
    J*1111112111
    L*1404345334
    N*4143111233
    Q*0202111011
    S*1220210001
    V*1413444343
    X*0101211020

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

    Row L and V distributions have pronounced similarities. Theyare "heavy" in their frequency distributions in the sameplaces. So are rows D and N. They have homologous attributesin appearance.

    CFHKMPRTWZ
    L*1404345334
    V*1413444343
    D*4133111342
    N*4143111233

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

    G*2220300101
    B*3111122121
    G*B*6220300101=15

    We compare the balance of rows:
    G*B+6220300101=15
    G*J+2220300101=11
    G*Q+0400300000=7
    G*S+2440600001=17
    G*X+0200060000=8

    The results are most probably match G and S.

    The next heaviest row is B. Testing against the remainingthree rows we have:
    B*J+3111124121=17
    B*Q+0202122021=12
    B*X+0101222040=12

    The correct pairings are B with J and Q with X. Since we havenot found more than two rows for any one set of interchangeablevalues the original matrix has only five rows.

    CFHKMPRTWZ
    BJ4222234232
    DN8287222575
    GS3440510102
    LV2817789677
    QX0303322030

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

    K*T+43542-81
    K*W+449499111
    K*Z+43549-88
    T*W+63542-83
    T*Z+42524273
    W*Z+63549-90

    Combinations:
    KT, WZ+81+90=171
    KW, TZ+111+73=186
    KT, TW+88+83=171

    We would expect that the proper pairings are K with W and Twith Z.
    CFKPT
    HMWRZ
    BJ64574PHI(p)=1962
    DN16414410PHI(r)=1132
    GS79-13PHI(o)=1670
    LV315141713
    QX-66-4

    We convert the multiliteral text to uniliteral equivalentsusing an arbitrary square for reduction to plain text.
    CFKPT
    HMWRZ
    BJABCDE
    DNFGHIJK
    GSLMNOP
    LVQRSTU
    QXVWXYZ

    The converted cryptogram is solved via the principals inLecture 2 and Lecture 3.The beginning of the message reads Weatherforecast. The original keying matrix is recovered with akeyword of ATMOSPHERIC.
    CFKPT
    HMWRZ
    BJATMOS
    DNPHERI
    GSCBDFG
    LVKLNQU
    QXVWXYZ

    The method of matching rows and columns applies equally wellfor all the matrices shown previously. It is key to start withthe best rows and columns from not only heaviness standpointbut the distinctive crests and troughs. A second key is thelow frequency letters. No variant system can adequatelydisguise low frequency letters and they will have the samefrequency in the cipher text. Friedman describes a moregeneral solution to variant analysis. [FRE1, p119 ff]

    Chapter 10 of reference [FRE1] covers the disruption processassociated with monome-dinome alphabets of Irregular-Lengthcipher text units. Figures 4-14 and Figure 4-15 showenciphering matrices where the encipherment is disrupted andcommutative. The normal row conventions are used to encipherexcept when the row indicator was the same for the immediatelypreceding letter. In Figure 4-14, EIGHT could be encrypted10 29 7 8 49 and then rearranged into standard groups of 5letters (numbers). In Figure 4-15, E = 24 or 42, T = 621 or162. Figure 4-16 is an example of the Russian disruptionprocess added for security.

    ISOLOGS

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

    Take two messages A and B suspected of being isologs and writethem out under each other. We then examine the similaritiesand differences. Assume the messages both start with "Referenceyour message..." I will arrange the messages in a specialtable to facilitate the study.

                                  	    Group No.			       5                          10			    15A     82 26 56 31 03 74 83 96 98 42 32 52 97 01 15A'    30 15 08 74 97 14 51 19 73 60 49 67 65 01 06B     80 27 78 91 06 94 00 01 38 28 54 08 24 00 65B'    45 64 79 91 81 69 67 25 38 89 41 56 32 52 03C     63 62 93 39 18 43 15 88 10 48 26 45 84 50 39C'    90 62 87 75 36 20 35 11 05 70 89 27 77 50 11D     81 71 35 25 38 73 30 92 07 49 61 75 21 64 76D'    35 19 99 01 38 99 97 45 02 32 04 11 58 92 16E     38 72 89 11 47 99 92 64 14 68 13 36 53 38 81E'    38 46 31 75 47 14 64 80 06 46 85 86 45 38 98F     89 69 79 38 16 51 75 05 70 74 11 80 44 32 55F'    26 12 18 38 78 94 88 93 37 28 11 27 22 05 04G     28 12 02 77 30 31 19 97 99 62 27 86 56 06 53G'    06 48 43 21 03 98 71 54 26 62 80 76 08 98 80H     90 87 04 08 67 46 59 41 98 55 10 82 22 29 87H'    44 10 55 29 00 59 72 82 28 55 87 30 07 08 93J     46 72 93 62 45J'    59 68 24 62 53
    The dinome distributions for these two messages are as follows:
    Message AMessage B
    12345678901234567890
    1*211121-1121*41-211-121
    2*11-112221-2*11-1122211
    3*22--11-5223*12--2115-2
    4*111123111-4*1-1132111-
    5*112122--115*111121-121
    6*13121-111-6*-3-21-2111
    7*12122111117*1111211111
    8*2211-121228*11--112123
    9*1221-122219*1121--2321
    0*21111212-20*21222313-1

    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 distributionto evaluate random text. The gist of the statistics is thatthe expected number of blanks is too low. The chi testindicates extreme non randomness for both messages. The chitest applied to both distributions implies that they both havebeen enciphered by the same cryptosystem because there exists aclose correlation between the patterns of the twodistributions. [FR1, p123} discusses the potentialities of thecryptomathematics as a supporting science to cryptography.

    There are several identical values between the messages. Thisimplies that not only has the same cryptosystem been used butalso the same enciphering matrix. The values 38 and 62 mustrepresent very low frequency letters because no variants areeven 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 textpairs. Beginning with the first value in the message 82 and 30a partial chain of equivalent variants is formed; now locatingthe other occurrences of either value we note the value thatcoincides with it in the other message. We therefore extendthe chain.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 thekeys or symmetry, we find a latent diagonal pattern withoutkeyword. 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 goesfar beyond simple variant systems. Isologs produced by twodifferent code books or two different enciphered code versionsof the same plain text; or two encryptions of identical plaintext at different settings of a cipher machine, may all proveof 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. Justa plan - subject to revision.

    LECTURES 5 - 7

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

    LECTURES 8 - 12

    We will investigate and crack Polyalphabetic Substitutionsystems.

    LECTURES 13 - 18

    We will investigate and crack Cipher Exchange andTranspositions problems.

    LECTURE 19

    We will devote this lecture to International Law.

    LECTURES 20 - 23

    We will walk through the mathematical fields to solveCryptarithms.

    LECTURES 24 - 25

    We will introduce modern cryptographic systems and fieldspecial 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 notall. The Key is 01=1=a, 02=2=b,...26=z. the alphabet isstandard. Message reads: " Here's a simple alphabetic codethat I've never seen before. Maybe you can use it in youcolumn. 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 23 2 5 1 0   0 8 0 4 0   2 2 1 0 9   0 8 0 4 0   8 2 2 1 10 8 0 4 1   7 1 5 1 3   1 4 2 2 2   1 0 2 2 4   0 2 0 1 22 0 2 0 2   0 1 0 8 1   9 0 6 1 5   1 7 0 8 0   1 1 1 2 21 4 0 2 0   1 1 9 0 6   0 5 1 0 0   2 0 2 1 1   2 2 1 4 06 2 3 1 9   0 5 1 5 0   1 2 2 1 3   0 2 0 5 0   6 1 3 0 20 5 0 1 1   0 0 5 2 3   0 6 2 1 0   2 2 2 1 4   0 6 0 2 02 2 2 1 4   0 6 0 2 0   2 2 6 0 2   0 6 0 5 2   1 1 9 0 20 2 1 1 2   2 0 3 0 2   1 7 2 4 0   2 1 9 0 2   0 6 1 5 05 1 1 0 6   0 2 1 9 0   5 0 6 2 2   0 1 0 5 0   5 0 1 1 90 5 2 1 1   5 2 2 1 5   0 5 0 1 2   2 0 5 1 8   0 5 0 6 06 0 5 0 3
    Divide the original cipher into pairs, noting that each pairstarted with 0,1, or 2 and ended with 0 - 9. Construct amatrix similar to Figure 3-2. (3 x 10) Fill in the matrix withA=01, ending with Z=26. Used 00 =blank. Reduce by convertingdinomes to letters. Apply the Phi test and found mon-alphabetic. Used frequency, VOC count, and consonant line toidentify B, H, E as vowels and N,D,X,C,I,Y,R,J, as possibleconsonants. Marking the message with these assumptions, foundlast eight characters to be a pattern word in Cryptodict asTOMORROW. Working between cipher text and key alphabetmatrix, rest fell.

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

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

    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 15 4 4 4 5    4 5 3 2 5    1 4 3 4 4    1 4 1 5 2    1 4 1 1 54 3 4 5 3    5 2 1 2 3    3 5 1 2 5    1 1 4 2 1    5 3 3 3 45 3 2 4 4    2 3 1 5 4    5 4 5 2 4    4 3 2 4 1    4 4 4 3 21 2 5 3 2    4 4 3 4 4    2 4 1 5 4    4 4 5 2 4    4 3 3 5 21 5 3 3 3    1 3 1 4 4    4 1 5 4 5    4 4 5 1 4    3 2 5 1 52 3 2 4 1    5 5 2 2 4    4 3 1 5 3    1 3 3 1 3    3 1 4 5 53 2 4 1 3    4 5 2 1 2    5 3 3 5 2    2 4 3 4 1    3 1 2 4 54 4 5 2 3    3 4 4 3 3    2 2 3 3 3    5 3 3 4 5    2 1 3 5 24 4 4 4 4    4 5 3 2 1    5 1 3 1 5    5 2 2 4 4    3 1 5 3 12 4 5 1 1    3 1 4 2 4    4 4 3 3 4    3 1 5 2 2    3 5 2 4 25 3 5 2 1    3 3 1 3 3    1 2 3 1 2    1 3 1 4 3    3 4 5 3 31 2 1 3 4    4 4 1 2 4    4 3 3 3 1    2 1 4 3 2    2 4 3 3 31 3 2 4 5    1 2 2 5 3    5 1 2 5 3    2 3 3 5 1    2 5 1 1 44 4 1 5 4    5 4 1 4 3    2 4 4 4 2    4 1 3 4 5    1 5 2 2 12 5 1 4 5    1 2 1 3 2    4 4 5 3 2    1 2 5 1 4    4 1 5 1 31 4 2 5 2    4 2 4 4 5
    Noted all entries were numbered 1-5. Assumed a 5 x 5 matrixfilled with a straight alphabet, substituted letters for thedinomes. Used frequency count, contact count and phi test toconfirm mono-alphabeticity. Identified 8 consonants and 2vowels. Made the E, T assumption based on frequency. Firstword dropped as weather. Rest of message fell apart withaddition 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.

    REFERENCES / RESOURCES

    [ACA]  ACA and You, "Handbook For Members of the American       Cryptogram Association," ACA publications, 1995. [ACA1] Anonymous, "The ACA and You - Handbook For Secure       Communications", American Cryptogram Association,       1994.[ANDR] Andrew, Christopher, 'Secret Service', Heinemann,       London 1985.[ANNA] Anonymous., "The History of the International Code.",       Proceedings of the United States Naval Institute, 1934. [AFM]  AFM - 100-80, Traffic Analysis, Department of the Air       Force, 1946.[B201] Barker, Wayne G., "Cryptanalysis of The Simple       Substitution Cipher with Word Divisions," Course #201,       Aegean Park Press, Laguna Hills, CA. 1982.[BALL] Ball, W. W. R., Mathematical Recreations and Essays,       London, 1928.[BAR1] Barker, Wayne G., "Course No 201, Cryptanalysis of The       Simple Substitution Cipher with Word Divisions," Aegean       Park Press, Laguna Hills, CA. 1975. [BAR2] Barker, W., ed., History of Codes and Ciphers in the U.S.       During the Period between World Wars, Part II, 1930 -       1939., Aegean Park Press, 1990. [BARK] Barker, Wayne G., "Cryptanalysis of The Simple       Substitution Cipher with Word Divisions," Aegean Park       Press, Laguna Hills, CA. 1973.[BARR] Barron, John, '"KGB: The Secret Work Of Soviet Agents,"       Bantom Books, New York, 1981.[BAUD] Baudouin, Captain Roger, "Elements de Cryptographie,"       Paris, 1939.[BLK]  Blackstock, Paul W.  and Frank L Schaf, Jr.,       "Intelligence, Espionage, Counterespionage and Covert       Operations,"  Gale Research Co., Detroit, MI., 1978.[BLUE] Bearden, Bill, "The Bluejacket's Manual, 20th ed.,       Annapolis: U.S. Naval Institute, 1978.[BOSW] Bosworth, Bruce, "Codes, Ciphers and Computers: An       Introduction to Information Security," Hayden Books,       Rochelle Park, NJ, 1990.[BP82] Beker, H., and Piper, F., " Cipher Systems, The       Protection of Communications", John Wiley and Sons,       NY, 1982.[BRIT] Anonymous, "British Army Manual of Cryptography", HMF,       1914. [BRYA] Bryan, William G., "Practical Cryptanalysis - Periodic       Ciphers -Miscellaneous", Vol 5, American Cryptogram       Association, 1967.[CAR1] Carlisle, Sheila. Pattern Words: Three to Eight Letters       in Length, Aegean Park Press, Laguna Hills, CA 92654,       1986.[CAR2] Carlisle, Sheila. Pattern Words: Nine Letters in Length,       Aegean Park Press, Laguna Hills, CA 92654, 1986.[CASE] Casey, William, 'The Secret War Against Hitler',       Simon & Schuster, London 1989.[CAVE] Cave Brown, Anthony, 'Bodyguard of Lies', Harper &       Row, New York 1975.[CCF]  Foster, C. C., "Cryptanalysis for Microcomputers",       Hayden Books, Rochelle Park, NJ, 1990.[CI]   FM 34-60, Counterintelligence, Department of the Army,       February 1990.[COUR] Courville, Joseph B.,  "Manual For Cryptanalysis Of       The Columnar Double Transposition Cipher, by Courville       Assoc., South Gate, CA, 1986.[CLAR] Clark, Ronald W., 'The Man who broke Purple',       Weidenfeld and Nicolson, London 1977.[COVT] Anonymous, "Covert Intelligence Techniques Of the Soviet       Union, Aegean Park Press, Laguna Hills, Ca.  1980.[CULL] Cullen, Charles G., "Matrices and Linear       Transformations," 2nd Ed., Dover Advanced Mathematics       Books, NY, 1972.[DAGA] D'agapeyeff, Alexander, "Codes and Ciphers," Oxford       University Press, London, 1974.[DAN]  Daniel, Robert E., "Elementary Cryptanalysis:       Cryptography For Fun," Cryptiquotes, Seattle, WA., 1979. [DAVI] Da Vinci, "Solving Russian Cryptograms", The       Cryptogram, September-October, Vol XLII, No 5. 1976. [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)
    Text converted to HTML on May 27, 1998 by Joe Peschel.

    Any mistakes you find are quite likely mine. Please let me know about them by e-mailing:
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    Thanks.
    Joe Peschel