## Lesson 12: Polyalphabetic Substitution Systems III Cryptanalysis Of Viggy's Extended Family Decimation In Detail

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CLASSICAL CRYPTOGRAPHY COURSE
BY
LANAKI

May 30, 1996
Revision 0

LECTURE 12

POLYALPHABETIC SUBSTITUTION SYSTEMS III
CRYPTANALYSIS OF VIGGY'S EXTENDED FAMILY
DECIMATION IN DETAIL

SUMMARY

In Lectures 12 - 13, we continue our study of the "Viggy"
cipher family or Polyalphabetic Substitution systems.  We
will cover decimation processes in detail and investigate
special solutions for periodic ciphers. The important
principle of Superimposition will be introduced.

The Resources Section has been updated with more than 50 ACA
published references on these and similar systems - focusing
on the cryptanalytic attack and areas of historical interest.
Thanks to PHOENIX for his help in compiling these sources.
[INDE]

"INCOMING"

In Lecture 13, we will tackle the difficult aperiodic
polyalphabetic case and introduce auto/running key systems.
We will diagram the topics covered in Lectures 10 - 13.

Lecture 14 will be presented by LEDGE.  He will cover further
Cryptarithm topics.

Lectures 15-18 will discuss the various geometric,
transposition and fractionation ciphers.

PORTAX CIPHER

Lecture 11.   The PORTAX uses pairs of letters as a unit for
encipherment and decipherment as apart from single letters.

A special slide is required for its operation, and a keyword
is needed.

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

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

(The above slide-setting is for G-H (key) directly under the
A-indicator of the stationary alphabet.)

To encipher the digraph RE, we take the R in the upper row of
letters (stationary slide) and the E from the lower pair of
letters (sliding), and use the opposite corners of the
rectangle formed to obtain the ciphertext, or PI.  However,
if the digram ER is to be enciphered, we take the E from the
stationary alphabet at the top, and the R from the sliding
alphabet at the bottom to obtain FP.

Note that if the first letter of a digraph is in the range of
A-M, the equivalent ciphertext is dependent on where the
slide is used for the key-letter; but, if the first letter of
the digraph is in the range of N-Z, then it slides along with
the paired rows of lower letters, and therefore all such
digraphs having the first letter in the N-Z are constant,
without dependent of the key.  There is an exception when
both letters in the plaintext digraph are in the same column,
in which case the key letter has to be known, for letters
appearing above the needed letters are used for the
ciphertext. [BRYA]

To encipher with keyword, the plaintext is written in two
rows under it; continuing to the end of the message.  When
the final group is reached, if there are not enough letters
to make it complete (an even number), add a single null.

For example, encipher the word INNOVATION using the key
OFTEN :

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

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

O F T E N   (keyword)
---------
I N N O V
A T I O N
g w
e b
---------
S A R E F
O U N D x
u i
k e

Setting the O of the sliding pairs under the 'A' indicator
of the stationary alphabet, we enciphering IA as GE (opposite
corners); then SO, continuing down the column we encipher the
whole column.  We then slide the strip until E-F (key) is
under the A indicator and encipher that column.

To find the period in the PORTAX is dependent on possible
fragments of the plaintext which are known (through the N-Z
combinations produced from the unchanged relationship of
letters).   Lets partially decipher the following PORTAX:

SNPOW  LBAMP  ISCWU  OOBXC  WKMAT  ZKTOW  JCBLN   CBJGB
TAAJD  IWUKW  HHVZN  MNUFM  APBJW  PCBSX  JCJQX   TMVUB
MDCBJ  CGUGR.   (90)

Assuming a period of 6:

S N P O W L
B A M P I S
n   t u r                   natural ?
l   e d s        good
-----------
C W U O O B
X C W K M A
o y s
s o c          ok
-----------
T Z K T O W
J C B L N C
r o   s t o
n y   n d s      better
-----------
B J G B T A
A J D I W U
y
m
-----------
K W H H V Z
N M N U F M
t     p t
s     r y
-----------
A P B J W P
C B S X J C
n     r o
f     t e
-----------
J Q X T M V
U B M D C B
n   t o n
h u n   r
-----------
J C R  - -
U G R
-----------

Note the NY-NDS which could be NYaNDS or NYeNDS.  Look at the
final group, we find -NTON -HUN-R (hundred?) We next test the
keyword by putting T in the final position and testing the
precursor letter; A C E F H I L N O P R S and U, At the E
setting, OM = TC, making -OYST/-SOCCU with R in the next
group confirming OCCUR.  The E substitution also gives us the
HUNDRED.  The rest of the analysis is left for the student
for credit.

THE NIHILIST SUBSTITUTION CIPHER

One of my favorite ciphers is the Nihilist Substitution
Cipher.  Classified as a periodic, it employs numbers to
represent letters.  Numbers are derived from a 5 x 5 Polybius
Square.

We set up a block of 25 letters and combine I/J in one cell.

Figure 12-1a

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

So A = 11, L = 31, T = 44.  (Row by Column)

The Polybius Square can be keyed.  For example, using
UNITED STATES OF AMERICA and eliminating the duplicate
letters, we have:

Figure 12-1b

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

We can also mix it up further with a little transposition.

Use BLACKSMITH, transpose and remove the ciphertext by
columns starting at 1:

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

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

Figure 12-1c

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

Figure 12-1c shows the effect of the transposition applied
first.

Now the message COME AT ONCE enciphered with a keyword of
TENT (period = 4) is:

T-44  E-15  N-35  T-44
----------------------
C-13  O-34  M-32  E-16
A-11  T-44  O-34  N-33
C-13  E-15   -     -

We add the key and the plaintext equivalents together to
produce the ciphertext: COME: 57 49 65 59;  ATON: 55 59 67
77; CE: 57 30.   Each column represents a monoalphabetic
substitution in itself, and the reading or value of these
letters is dependent on the letters on either side of them.

WEAKNESSES

The lowest number of any key-letter which may be added to the
lowest plaintext letter is 11, with a total of 22; the
highest combination is two 55's or 10 (110).  The numbers
6,7,8, or 9, are not involved in either the tens or the one's
additions - but they may result in a sum.  Cipher 22 must
equal 11 plus 11; and 10 can only mean the sum of two 55's.
Zero in the one's column means that two 5's have been added.
This is also true in the ten's column. If at any time we find
that a 6-7-8-9 is involved we can discard the period assumed
as wrong.  What we are looking for is a number in the 1-2-3-
4-5 range that may be added to produce first the ten's sum
and then the one's sum.

FINDING THE PERIOD

There are two ways to find the period - the short and the
long way.

SHORT METHOD

The short way of finding the period is to look for two or
more 30's.  We treat them like a repeated digraph and factor
the interval between them looking for a common factor. We may
also try the same procedure with the lowest number versus the
highest number, for example the distance between two 94's or
two 26's.

LONG METHOD

The long way is to assume a 3 period and test the 1'st and
4'th, 2'nd and 5'th, 3'rd and 6'th in the same manner as the
short method.  When conflicts arise, discard the choice.
We continue with an assumption of periods 4, 5, 6, etc. and
increase the differentials between ciphertext numbers. [BRYA]

CRYPTANALYSIS OF THE NIHILIST SUBSTITUTION

Gaines [ELCY] suggests that cracking this cipher parallels
the Viggy. The period is found through repeated sequences, or
in their absence, through repeated single letters, yielding
individual frequency counts on the several alphabets of the
period.  If the arrangement of the ciphertext follows the
normal Polybius (aka Checkerboard) Square, the frequency
counts will follow the graph of the normal alphabet less one
letter.  Even with the keyword mixed ciphertext alphabet,
no matter how badly mixed, the frequency counts are parallel,
the several alphabets combined follow one graph, and can be
"lined up."

Notice that the primary alphabet contains only the digits 1-
2-3-4-5. The maximum difference is 4 and addition of any
number to all of them does not change this fact.  the maximum
difference between any to sums is still 4.  Now the number
added during encipherment is also a number containing no
digit other than 1-2-3-4-5; thus any number found in the
cryptogram can be considered as carrying two separate
additions, one for tens and one for ones.  The two 5's added
give us the revealing 0; the carried digit 1 can be mentally
borrowed back, by decreasing the size of the digit preceding
the zero.  If we find a 40 , we look at it as 3 tens with ten
units or finding 110, we may regard this as ten tens and ten
units.  If we find the numbers 29 and 87 in the cryptogram,
we know they were not enciphered by the same key.  This is
because a difference greater than 4 in the respective tens
units exists and no digit whatever added to any two digits of
the original square can produce a difference greater than 4.
Say we have 30 and 77, with no difference greater than 4, the
presence of the zero needs to be accounted for.  The number
30 has 2 tens and ten units;   7 - 2 >4,  hence, we reject
the same key hypothesis.

Four giveaways are 22, 30, 102, and 110.  The presence of any
one of these numbers gives away the key to the whole cipher
alphabet.

[BRYA] presents a useful aid for the standard Polybius
Square in Table 12-1.  At the top is the key-number, at the
left is the plaintext letter, and at ciphertext is found at
the intersection.   Any two of the three variables yields the
unknown letter/number.

Table 12-1

11  12  13  14  15  21  22  23  24  25  31  32
A   B   C   D   E   F   G   H I/J  K   L   M
A 11  22  23  24  25  26  32  33  34  35  36  42  43
B 12  23  24  25  26  27  33  34  35  36  37  43  44
C 13  24  25  26  27  28  34  35  36  37  38  44  45
D 14  25  26  27  28  29  35  36  37  38  39  45  46
E 15  26  27  28  29  30  36  37  38  39  40  46  47

F 21  32  33  34  35  36  42  43  44  45  46  52  53
G 22  33  34  35  36  37  43  44  45  46  47  53  54
H 23  34  35  36  37  38  44  45  46  47  48  54  55
I 24  35  36  37  38  39  45  46  47  48  49  55  56
K 25  36  37  38  39  40  46  47  48  49  50  56  57

L 31  42  43  44  45  46  52  53  54  55  56  62  63
M 32  43  44  45  46  47  53  54  55  56  57  63  64
N 33  44  45  46  47  48  54  55  56  57  58  64  65
O 34  45  46  47  48  49  55  56  57  58  59  65  66
P 35  46  47  48  49  50  56  57  58  59  60  66  67

Q 41  52  53  54  55  56  62  63  64  65  66  72  73
R 42  53  54  55  56  57  63  64  65  66  67  73  74
S 43  54  55  56  57  58  64  65  66  67  68  74  75
T 44  55  56  57  58  59  65  66  67  68  69  75  76
U 45  56  57  58  59  60  66  67  68  69  70  76  77

V 51  62  63  64  65  66  72  73  74  75  76  82  83
W 52  63  64  65  66  67  73  74  75  76  77  83  84
X 53  64  65  66  67  68  74  75  76  77  78  84  85
Y 54  65  66  67  68  69  75  76  77  78  79  85  86
Z 55  66  67  68  69  70  76  77  78  79  80  86  87

Table 12-1
continued

33  34  35  41  42  43  44  45  51  52  53  54  55
N   O   P   Q   R   S   T   U   V   W   X   Y   Z
A 11  44  45  46  52  53  54  55  56  62  63  64  65  66
B 12  45  46  47  53  54  55  56  57  63  64  65  66  67
C 13  46  47  48  54  55  56  57  58  64  65  66  67  68
D 14  47  48  49  55  56  57  58  59  65  66  67  68  69
E 15  48  49  50  56  57  58  59  60  66  67  68  69  70

F 21  54  55  56  62  63  64  65  66  72  73  74  75  76
G 22  55  56  57  63  64  65  66  67  73  74  75  76  77
H 23  56  57  58  64  65  66  67  68  74  75  76  77  78
I 24  57  58  59  65  66  67  68  69  75  76  77  78  79
K 25  58  59  60  66  67  68  69  70  76  77  78  79  80

L 31  64  65  66  72  73  74  75  76  82  83  84  85  86
M 32  65  66  67  73  74  75  76  77  83  84  85  86  87
N 33  66  67  68  74  75  76  77  78  84  85  86  87  88
O 34  67  68  69  75  76  77  78  79  85  86  87  88  89
P 35  68  69  70  76  77  78  79  80  86  87  88  89  90

Q 41  74  75  76  82  83  84  85  86  92  93  94  95  96
R 42  75  76  77  83  84  85  86  87  93  94  95  96  97
S 43  76  77  78  84  85  86  87  88  94  95  96  97  98
T 44  77  78  79  85  86  87  88  89  95  96  97  98  99
U 45  78  79  80  86  87  88  89  90  96  97  98  99  00

V 51  84  85  86  92  93  94  95  96  02  03  04  05  06
W 52  85  86  87  93  94  95  96  97  03  04  05  06  07
X 53  86  87  88  94  95  96  97  98  04  05  06  07  08
Y 54  87  88  89  95  96  97  98  99  05  06  07  08  09
Z 55  88  89  90  96  97  98  99  00  06  07  08  09  10

Consider Edwin Linquist's challenge:

24 66 35 77 37 77 55 59 55 45 55 88 28 66 46

88 37 67 33 59 58 65 45 66 67 58 44 55 34 79

44 59 55 45 42 87 28 76 43 78 46 86 26 67 24

85 26 67 28 76 26 78 46 65 65 88 36 49 54 67

28 65 42 88 36 49 44 89 57 58 54 66 47 67 26

Try period = 2.  Starting at the first number 24 constant we
scan the line looking for differences greater than 4 using a
constant difference of 2.  We come to 33 and 38 and stop.

Try period = 3.  The first comparison fails at 24 and 77.

Try period = 4.  We are able to go through the entire
cryptogram, comparing numbers at an interval of 4, without
find any difference in either tens or units greater than 4.
We now must look at the numbers collectively in columns to
verify the period is 4.  We recopy the cryptogram into a
block.
Key = 4?

24  66  35  77
37  77  55  59
55  45  55  88
28  66  46  88
37  67  33  59
58  65  45  66
67  58  44  55
34  79  44  59
55  45  42  87
28  76  43  78
46  86  26  67
28  76  26  78
46  65  65  88
36  49  54  67
28  65  42  88
36  49  44  89
57  58  54  65
47  67  26  -

Alphabet 1: The tens-half of the first column contains the
digit 2 and since this can only come from the addition of 1
plus 1, the only possible key digit is 1.  The units-half has
a range of 4-5-6-7-8, maximum range possible.  The smallest
digit to result in 8 is 3, the largest digit to result in 4
is also 3, that is the only digit which can result in all of
the digits 4-5-6-7-8 is 3, so that the cipher key for this
column is 13.  It cannot be anything else.

Alphabet 2: The tens-half of the second column ranges over
the full five digits 4-5-6-7-8 (key 3), and the units-half
ranges over 5-6-7-8-9 (key 4). This suggests the key digit
is 34.

Alphabet 3: The tens-half of the third column contains the
'giveaway' digit of 2 and the units-half also contains the
digit 2.  The key digit to produce this situation is 11.

Alphabet 4: The tens-half of the fourth column ranges only
over the digits 5-6-7-8, with nothing to indicate whether the
missing digit is 4 or 9.  The key might be either 3 or 4.
The units has the full range of digits 5-6-7-8-9, hence key =
4.  So we have either 34 o 44 for our key digit.  The normal
square suggests COAO or COAT as the key word.  We use Table
12-1 to good advantage and decipher this cryptogram.

We decipher the whole cryptogram a column at a time:

'C'    'O'   'A'   'T'
--     --    --    --
A      M     I     N
I      S     T     E
R      A     T     T
E      M     P     T
I      N     G     E
U      L     O     G
Y      I     N     A
F      U     N     E
R      A     L     S
E      R     M     O
M      W     E     H
A      V     E     H
E      R     E     O
N      L     Y     T
H      E     S     H
E      L     L     T
H      E     N     U
T      I     S     G
O      N     E

Reads: A minister attempting eulogy in a funeral sermon: We
have here only the shell, the nut has gone.

For the  most difficult case presenting multiple key
possibilities, we line up the alphabets graphically against
their frequency counts to eliminate the extra key digits.

GROMARK

MASTERTON describes a cipher called the GROMARK.  The Gromark
is akin to the GRONSFELD in that the components never change
their position relative to each other and every plain text
values has 10 possible cipher representatives.  The GROMARK
uses a different keying method; encipherment is effected by
means of a normal alphabet plain set against a mixed cipher
text alphabet.  However, instead of cycles or predictable
slides of the cipher component, one finds the plain value on
the top (normal) component and counts a specified number of
positions to the right, then takes the letter in the cipher
alphabet immediately below.  The choice of how far to count
along the sequence is determined by the digital key. One
essentially is adding 0 to 9 to the plain value, as in the
Gronsfeld, but it is on the mixed sequence, set underneath a
plain sequence.  The key is derived from a Fibonacci series.
On some cycle (frequently 5 wide) the key is derived from a
starting group, by adding the first position to the second
and placing the result in the sixth position.  Similarly,
positions 2 and 3 are added to make position number 7, 3, and
4 to make 8, and so forth.  All additions are non carrying -a
very common cryptographic practice.  [MAST]

Example:

Use the starter or "seed" of 48671, the key is:

48671  24383  67119  382021 ...

Solution follows the normal Viggy methods.   The crib
placement can be interesting.

Example:

7 7 2 6 6 4 9 8 2 0 3 7 0 2 3 0 7 2 5 3 7 9 7
J C N W Z Y C A C J N A Y N L Q P W W S T W P

without knowing the cipher sequence, we are given the crib
SUBSTITUTES and runs somewhere from the J to the final P
above.

Since the plain sequence is normal, a repeated cipher letter,
with different key letters on it, must stand for plain values
removed from each other exactly by the difference of the two
numbers.  Thus C A C with keys 9 8 2 above it implies that
the first cipher C is M for example, the second C is seven
positions to the right on the plain sequence, or T.

Or:

J K L M N O P Q R S T U V W X
C
*

We prepare a difference table.  We are looking for a
favorable case where the differences in the cipher repeats
matches the plain differences, at the correct interval.
To match these differences, we measure them in one direction
for the plain and the reverse for the cipher. Table 12-1
shows subtraction of the left hand letter from the right, and
we must look at the cipher in the other direction.
Differences may be calculated modulo 26.

Table 12-1

adjacent         19 21  2 19 20  9 20 21 20  5 19
diff's            S  U  B  S  T  I  T  U  T  E  S
xx                2  7 17  1 15 11  1  25 11 14
x-x                9 24 18 16  0  12  0  10
x--x                  0  25  7 ...

There is a difference of 7 with the C-C hit, but it doesn't
appear on the second row of the table.   The keyword must
first between A (between C's) and W.

7 7 2 6 6 4 9 8 2 0 3 7 0 2 3 0 7 2 5 3 7 9 7
J C N W Z Y C A C J N A Y N L Q P W W S T W P
S U B S T I T U T E S
This is a good tip placement and confirmed by the N-N hit.
The A---A in the cipher matches the S---T plain.  We build
the cipher component by writing the cipher component, and a
normal alphabet, count along it from any given plain the
number of steps given by the key, then write the cipher
value.  Find S on the top strip, count 8 to right, place an
A.  C is two spaces to the right of the position held by the
U, and so on. Decipher other letters by counting backwards
the number of steps given by the key. Cipher C ahead of thew
crib translates to N.

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

Without a tip the system will fall to statistics. The numbers
associated with any given cipher letter represent a stretch
of 10 consecutive values along a normal alphabet such as C to
L or X to G, we could prepare a table with A to Z as the rows
and 9 to 0 as the columns.  Frequencies can be combined
and a stretch such as PQRST area will show as the normal.
The backwards normal sequence yields a bar graph of the
segment of the normal alphabetic frequencies.

DECIMATION PROCESSES - FURTHER REMARKS

In Lecture 11, we presented QUAGMIRES I-IV and solved them by
a variety of methods.  Inherent in their solution was
Friedman's principle of indirect symmetry.  [FRE7]  Prima
facie to this symmetry principle is a process of alphabet
dissociation called Decimation.  This same process effects
all Viggy class ciphers and is important from a theoretical
point of view.  Decimation is especially effective in solving
mixed alphabet systems like the Quagmire III & IV.
Decimation is a process of selection and derivation of a
sequence of equivalent components according to some fixed
interval.  For example, the sequence A E I M is derived by
decimation of extracting every fourth letter from a normal
alphabet.

Consider the two mixed alphabets in a QUAGMIRE III:

O1
*       *
Plain:           QUESTIONABLYCDFGHJKMPRVWXZ
Cipher:  QUESTIONABLYCDFGHJKMPRVWXZQUESTIONABLYCDFGHJKMPRVWXZ
*       *
Ok

By setting the two sliding components against each other in
the two positions shown: A in the first set and B in the
second set we can derive two, we can derive two different
sets of secondary alphabets based on the key letters.

O1 *       *
Plain:            QUESTIONABLYCDFGHJKMPRVWXZ
Cipher:  QUESTIONABLYCDFGHJKMPRVWXZQUESTIONABLYCDFGHJKMPRVWXZ
*       *
Ok

Secondary Alphabet (1)

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

Secondary Alphabet (2)

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

Sliding strips will yield the same results as a Viggy type
table based on the Keyword QUESTIONABLY (see a partial table
in Table 11-2.

Table 12-2
Partial Reconstruction

QUESTIONABLYCDFGHJKMPRVWXZ
UESTIONABLYCDFGHJKMPRVWXZQ
ESTIONABLYCDFGHJKMPRVWXZQU
STIONABLYCDFGHJKMPRVWXZQUE
TIONABLYCDFGHJKMPRVWXZQUES
IONABLYCDFGHJKMPRVWXZQUEST
ONABLYCDFGHJKMPRVWXZQUESTI
NABLYCDFGHJKMPRVWXZQUESTIO
ABLYCDFGHJKMPRVWXZQUESTION
BLYCDFGHJKMPRVWXZQUESTIONA
LYCDFGHJKMPRVWXZQUESTIONAB
YCDFGHJKMPRVWXZQUESTIONABL
CDFGHJKMPRVWXZQUESTIONABLY
.                        .

Superficially secondary alphabets (1) and (2) show no
resemblance of symmetry despite the fact that they were both
created from the same primary alphabet.  We do find a Latent
Symmetry Of Position (aka Indirect Symmetry of Position).
This phenomenon has widespread use in the Viggy family.
Consider alphabet (2):

Secondary Alphabet (2)

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

We construct a chain of alternating plaintext and ciphertext
equivalents, beginning at any point and continuing until the
chain is completed.  We start Aplain = Jcipher, Jplain =
Qcipher, Qplain = Bcipher...., dropping the common letters
we have A J Q B.  The complete sequence of letters is:

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

When slid against itself it will produce exactly the same
secondary alphabets as do the primary components based upon
the word QUESTIONABLY.  For example, compare the secondary
alphabets given by the two settings of the externally
different components below:

*        *
Plain:            QUESTIONABLYCDFGHJKMPRVWXZ
Cipher:  QUESTIONABLYCDFGHJKMPRVWXZQUESTIONABLYCDFGHJKMPRVWXZ
*        *

Secondary Alphabet (1)

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

*  *
Plain:   AJQBKULMEYPSCRTDVIFWOGXNHZ
Cipher: AJQBKULMEYPSCRTDVIFWOGXNHZAJQBKULMEYPSCRTDVIFWOGXNHZ
*  *

Secondary Alphabet (2)

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

Since the sequence A J Q B K ... gives exactly the same
equivalents in the secondary alphabets as does the sequence
QUEST......XZ, the former is cryptographically equivalent to
the latter sequence.  For this reason the A J Q B K ..
sequence is termed an equivalent primary component.  If the
real or original primary component is a keyword mixed
sequence, it is hidden or latent  within the equivalent
primary sequence; it can also be made patent by the process
of decimation of the equivalent primary component.

Friedman in [FRE7] describes the process as follows: find
three letters in the equivalent primary component that are a
likely unbroken sequence in the original primary component,
and see if the interval between the first and second is the
same as that of the second and third.  Try X, Y, Z in the
equivalent primary component above.  Note the sequence ..W O
G X N H Z...; the distance or interval between W X Z is three
letters.  Continuing the chain by adding letters three
intervals removed, the latent original primary component is

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 W
X Z Q U E S T I  O  N  A  B  L  Y  C  D  F  G  H  J  K  M

24 25 26
P  R  V

KEYWORD - MIXED SEQUENCE

We can combine the previous steps into one operation.
Starting with any pair of letters in the cipher component of
the secondary alphabets, likely to be sequent in the keyword-
mixed sequence, such as JK, the following chains of digraphs
may be produced.  Thus JK plain stand over QU cipher
respectively, QU in the plain stand over BL in the cipher,
respectively, etc. Connecting the pairs:

JK>QU>BL>KM>UE>LY>MP>ES>YC>PR>ST>CD>RV>TI>DF>VW>IO>FG>WX>
ON>GH>XZ>NA>HJ>ZQ>AB>JK.....

We then unite by common letters:

JK>KM>MP>PR>RV>VW>WX>XZ>ZQ>QU>UE>ES>ST>TI>IO>ON>NA>
AB>BL>LY>YC>CD>DF>FG>GH>HJ>JK.....

or:

JKMPRVWXZ-QUESTIONABLY-CDFGH

HALF CHAINS

Only 12 /26 alphabets will yield a complete equivalent
primary component, as shown above.  Even number of intervals
for sliding the alphabets will yield half chains or 13 letter
chains.  Friedman [FRE7] describes several methods to combine
the half chains into fully equivalent primary components.

FRIEDMAN'S OBSERVATIONS

Friedman observed that in the case of a 26-element component
sliding against itself (both components proceeding in the
same direction), it is only the secondary alphabets resulting
from odd-interval displacements of the primary components
which permit reconstructing a single 26-letter chain of
equivalents.  This is true except for the 13th interval
displacement, which acts like an even number displacement, in
that no complete chain of equivalents can be established from
the secondary alphabet.  Friedman states the general rule as:
any displacement interval which has a factor in common with
the number of letters in the primary sequence will yield a
secondary alphabet from which no complete chain of 26
equivalents can be derived for the construction of a complete
equivalent primary component.  Components sliding in opposite
directions act as a 13 interval displacement because of their
reciprocal nature.

Friedman concluded that whether or not a complete equivalent
primary component is derivable by decimation from an original
primary component (and if not, the lengths and numbers of
chains of letters, or incomplete components, that can be
constructed in attempts to derive such equivalent components)
will depend upon the number of letters in the original
primary component and the specific decimation interval
selected.  [FRE7]  Friedman constructed a table relating the
number of characters in the original primary component,
decimation interval and total number of complete sequences
that can be formed.  See Table 12-3.

TABLE 12-3

Number of Characters in Original Primary Component
Decimation Interval    32  30  28  27  26  25  24  22  21  20
18  16
----------------------------------------------
2       16  15  14  27  13  25  12  11  21  10   9   8
3       32  10  28   9  26  25   8  22   7  20   6  16
4        8  15   7  27  13  25   6  11  21   5   9   4
5       32   6  28  27  26   5  24  22  21   4  18  16
6       16   5  14   9  13  25   4  11   7  10   3   8
7       32  30   4  27  26  25  24  22   3  20  18  16
8        4  15   7  27  13  25   3  11  21   5   9   2
9       32  10  28   3  26  25   8  22   7  20   2  16
10      16   3  14  27  13   5  12  11  21   2   9   8
11      32  30  28  27  26  25  24   2  21  20  18  16
12       8   5   7   9  13  25   2  11   7   5   3   4
13      32  30  28  27   2  25  24  22  21  20  18  16
14      16  15   2  27  13  25  12  11   3  10   9   8
15      32   2  28   9  26   5   8  22   7   4   6
16       2  15   7  27  13  25   3  11  21   5   9
17      32  30  28  27  26  25  24  22  21  20
18      16   5  14   3  13  25   4  11   7  10
19      32  30  28  27  26  25  24  22  21
20       8   3   7  27  13   5   6  11
21      32  10   4   9  26  25   8
22      16  15  14  27  13  25  12
23      32  30  28  27  26  25
24       4   5   7   9  13
25      32   6  28  27
26      16  15  14
27      32  10
28       8  15
29      32
30      16

Total Number
Of
Sequences   14   6  10  16  10  18   6   8  10   6   4   6

>From Table 12-3, we see that in a 26-letter original primary
component, decimation interval 5 will yield a complete
equivalent primary component of 26 letters, whereas
decimation intervals of 4 or 8 will yield 2 chains of 13
each.  In a 24-letter component, decimation interval 5 will
also yield a complete equivalent primary component of 24
letters, but decimation interval 4 will yield 6 chains of 4
letters each, and decimation interval 8 will yield 3 chains
of 8 letters each.

It follows that in the case of an original primary component
in which the total number of characters is a prime number,
all decimation intervals will yield complete equivalent
primary components.  Table 12-3 omits the prime number
sequences from 16-32.  [FRE7]

SPECIAL SOLUTIONS FOR PERIODIC CIPHERS

Special circumstances give rise atypical solutions of
periodic ciphers.  We shall look at four special cases:
1) isologs, 2) 'stagger',  3) long latent repetition and 4)
superimposition.

ISOLOGS

Recall that an Isolog is defined as the exact same plain text
message enciphered by two different keys in the same
cryptosystem.  Lets use two monoalphabetic substitution
systems to illustrate the point. Assume two messages are
intercepted going from station A to B.  B had called for a
retransmit because of some error in transmission. We suspect
the messages are the same plaintext content and they both
have the same length. We superimpose one message over the
other:

1. NXGRV MPUOF ZQVCP VWERX QDZVX WXZQE TBDSP VVXJK RFZWH 2.
EMLHJ FGVUB PRJNG JKWHM RAPJM KMPRW ZTAXG JJMCD HBPKY

chaining from 1 to 2:  NE>EW>WK>KD>DA ......

1. ZUWLU IYVZQ FXOAR
2. PVKIV QOJPR BMUSH

Next we initiate a chain of ciphertext equivalents (reducing
the common letter) from message 1 to message 2, yielding:
*
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 N
E W K D A S X M  F  B  T  Z  P  G  L  I  Q  R  H  Y  O  U
*         *            *                 *              *

24 25 26
V  J  C

With some experimentation, we find the Key word QUESTIONABLY
and the decimation interval of +5 Modulo 26.  The complete 26
letter chain was available for reconstruction, but this is
not a requirement.

Why is it possible to reconstruct the primary component and
solve the above two messages without having any plain text at
all?  Since the plain text of both messages is the same, the
relative displacement of the same primary components in the
case of message 1 differs from the relative displacement of
the same primary components in message 2 by a FIXED interval.
Therefore, the distance between N and E (1st two cipher
letters of the two messages) on the primary component,
regardless of what plaintext letter these two cipher letters
represent, is the same distance between E and W (18th
letters), W and K (17th letters), and so forth. Thus this
fixed interval permits the establishing of a complete chain
of letters separated by constant intervals and this chain
becomes an equivalent primary component.

To solve, we take the frequency distributions of message 1
and 2:
E       S T I   O
1 1 1 2 2 3 1 1 1 1 1 1 1 1 2 3 4 4 1 1 3 7 4 6 1 6
1:   A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

E   S T   I     O
2 3 1 1 1 1 3 4 1 7 4 1 6 1 1 7 1 4 1 1 2 3 2 1 1 1
2:   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

We set up two key word mixed alphabets and slide against each
other.  With some trial and error we find:

NABLYCDFGHJKMPRVWXZQUESTIO
QUESTIONABLYCDFGHJKMPRVWXZ

The plain text reads: Five squadrons must be in position by H
plus six zero two at Jackson Ridge.

The same procedure is applied on two repeating key ciphers
suspected of being Isologs:

Message 1

YHYEX  UBUKA  PVLLT  ABUVV  DYSAB  PCQTU
NGKFA  ZEFIZ  BDJEZ  ALVID  TROQS  UHAFK

Message 2

CGSLZ  QUBMN  CTYBV  HLQFT  FLRHL  MTAIQ
ZWMDQ  NSDWN  LCBLQ  NETOC  VSNZR  BJNOQ

The first step is to find the length of the period.  The
usual method fails for lack of long repetitions and the
digraphs are not promising.  We use the Principle of
Superimposition to get a hold on the period for both
cryptograms.

1 2 3 4 5 6 7 8 9101112131415161718192021222324252627282930
Y H Y E X U B U K A P V L L T A B U V V D Y S A B P C Q T U
C G S L Z Q U B M N C T Y B V H L Q F T F L R H L M T A I Q

313233343536373839404142434445464748495051525354555657585960
N G K F A Z E F I Z B D J E Z A L V I D T R O Q S U H A F K
Z W M D Q N S D W N L C B L Q N E T O C V S N Z R B J N O Q

We employ a subterfuge will be employed based upon the theory
of factoring. We search for cases of identical
superimposition.  We have:

4      44                               6  18    30
E  and E   are separated by 40 letters, U, U and U  which
L      L                                Q  Q     Q

are separated by 12 letters. We factor these intervals as if
they were ordinary repetitions.  The most frequent factor
should correspond to the period.  We are dealing with
Isologs. The plain text is the same in both messages, so the
principle of identity of superimposition can only be the
result of identity of encipherments by identical cipher
alphabets.  The same relative position in the keying cycle
has been reached in both cases of the identity.  The distance
between identical superimpositions must be equal to or a
multiple of the length of the period.  The following is the
complete set of superimposed pairs:

Repetition         Interval          Factors
--------------------------------------------
EL - EL             40           2,4,5,8,10,20
UQ - UQ -UQ         12           2,3,4,6
UB - UB             48           2,3,4,6,,8,12,24
KM - KM             24           2,3,4,6,12
AN -AN -AN          36/12        2,3,4,6;9,12,18
VT -VT -VT          8/28         2,4; 2,4,7,14
TV - TV             36           2,3,4,6,9,12,18
AH - AH             8            2,4
BL -BL -BL          8/16         2,4,;8
SR - SR             32           2,4,8,16
FD - FD             4            2
ZN - ZN             4            2
DC - DC             8            2, 4
------------------------------------------------

Only the factors 2 and 4 are common.  We discard 2 as
improbable.  We break up the message into groups of four.

1234 1234 1234 1234 1234 1234 1234 1234
1.   YHYE XUBU KAPV LLTA BUVV DYSA BPCQ TUNG 2.   CGSL ZQUB
MNCT YBVH LQFT FLRH LMTA IQZW
*    *    *    *

1234 1234 1234 1234 1234 1234 1234
1.   KFAZ EFIZ BDJE ZALV IDTR OQSU HAFK
2.   MDQN SDWN LCBL QNET OCVS NZRB JNOQ

We develop a decipherment Tableaux:

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

Using the meyhods previously described, we build up the
equivalent primary component and combine our digrams.

BL, DF, ES, HJ, IO, KM, LY, ON,TI, XZ, YC, ZQ.

BLYC .DF    TION    XZQ(U) [ES]TION(A)BLY CDF (G) H

JKM(P) (R) (V) XZ

It is not a long jump to a key word QUESTIONABLY and the
equivalent primary component:

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

The fact that the original primary component was exposed was
pure chance, it could have been an equivalent primary
sequence alphabet.

>From here we apply the completion of the plain-component
sequence using the high frequency letter assortments.
For the first message:

Gen Alphabet 1    Alphabet 2    Alphabet 3    Alphabet 4

1   YXKLBDBTKE   1HUALUYPUFF   5YBPTVSCNAI    EUVAVAQGZZ
2  2CZMYLFLIMS   4JEBYECREGG   5CLRIWTDABO    SEWBWBUHQQ
3  2DQPCYGYOPT   3KSLCSDVSHH   3DYVOXIFBLN    TSXLXLEJUU
4  4FURDCHCNRI    MTYDTFWTJJ   3FCWNZOGLYA    ITZYZYSKEE
5  3GEVFDJDAVO    PICFIGXIKK    GDXAQNHYCB    OIQCQCTMSS
6  2HSWGFKFBWN   4RODGOHZOMM    HFZBUAJCDL   5NOUDUDIPTT
7   JTXHGMGLXA    VNFHNJQNPP    JGQLEBKDFY   8ANEFEFORII*
8   KIZJHPHYZB    WAGJAKUARR   1KHUYSLMFGC   6BASGSGNVOO
9   MOQKJRJCQL    XBHKBMEBVV   2MJECTYPGHD   5LBTHTHAWNN
10  PNUMKVKDUY    ZLJMLPSLWW    PKSDICRHJF    YLIJIJBXAA
11 4RAEPMWMFEC    QYKPYRTYXX    RMTFODVJKG    CYOKOKLZBB
12 3VBSRPXPGSD    UCMRCVICZZ   2VPIGNFWKMH   2DCNMNMYQLL
13 4WLTVRZRHTF    EDPVDWODQQ    WROHAGXMPJ   2FDAPAPCUYY
14  XYIWVQVJIG   3SFRWFXNFUU    XVNJBHZPRK   3GFBRBRDECC
15  ZCOXWUWKOH    TGVXGZAGEE    ZWAKLJQRVM   1HGLVLVFSDD
16  QDNZXEXMNJ    IHWZHQBHSS    QXBMYKUVWP   1JHYWYWGTFF
17  UFAQZSZPAK    OJXQJULJTT    UZLPCMEWXR    KJCXCXHIGG
18  EGBUQTQRBM    NKZUKEYKII    EQYRDPSXZV    MKDZDZJOHH
19 3SHLEUIUVLP   5AMQEMSCMOO    SUCVFRTZQW    PMFQFQKNJJ
20 6TJYSEOEWYR?  4BPUSPTDPNN    TEDWGVIQUX    RPGUGUMAKK
21  IKCTSNSXCV   8LRETRIFRAA*   ISFXHWOUEZ   3VRHEHEPBMM
22 5OMDITATZDW?  3YVSIVOGVBB    OTGZJXNESQ    WVJSJSRLPP
23  NPFOIBIQFX   3CWTOWNHWLL    NIHQKZASTU    XWKTKTVYRR
24 5ARGNOLOUGZ?   DXINXAJXYY    AOJUMQBTIE    ZXMIMIWCVV
25 4BVHANYNEHQ    FZOAZBKZCC   5BNKEPULIOS    QZPOPOXDWW
26  LWJBACASJU    GQNBQLMQDD   7LAMSREYONT*   UQRNRNZFXX

We choose generatrices 20/22/24; 21; 26; 7 because of the
highest two category scores.  it is not much of a jump to
find Alphabet 1 generatrix as alphabet 24:

1 2 3 4
A L L A
R R A N
G E M E
N T S F
O R R E
L I E F
O F Y O
U R O R
G A N I
Z A T I

>From a Vigenere Square (Figure 12-1) based on the keyword
QUESTIONABLY, we find the key words SOUP for message 1 and
TIME for message 2.

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

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

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

T I M E  T I M E  T I M E  T I M E  T I M E  T I M E
____________________________________________________

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

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

O C V S   N Z R B  J N O Q
E N S U   S P E N   D E D X

Figure 12-1

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

SOLUTION OF ISOLOGS INVOLVING THE SAME SET OF PRIMARY
COMPONENTS BUT WITH KEY WORDS OF DIFFERENT LENGTHS

The example previous had two keywords the same lengths.
The Method of Superimposition works with Keywords of
different lengths. Friedman works an interesting example:

Message 1

VMYZG  EAUNT  PKFAY  JIZMB  UMYKB  VFIVV
SEOAF  SKXKR  YWCAC  ZORDO  ZRDEF  BLKFE
SMKSF  AFEKV  QURCM  YZVOX  VABTA  YYUOA
YTDKF  ENWNT  DBQKU  LAJLZ  IOUMA  BOAFS
KXQPU  YMJPW  QTDBT  OSIYS  MIYKU  ROGMW
CTMZZ  VMVAJ

Message 2

ZGANW  IOMOA  CODHA  CLRLP  MOQOJ  EMOQU
DHXBY  UQMGA  UVGLQ  DBSPU  OABIR  PWXYM
OGGFT  MRHVF  GWKNI  VAUPF  ABRVI  LAQEM
ZDJXY  MEDDY  BOSVM  PNLGX  XDYDO  PXBYU
QMNKY  FLUYY  GVPVR  DNCZE  KJQOR  WJXRV
GDKDS  XCEEC.

Both messages permit factoring at periods of 4 and 6 letters,
respectively.  Superimposing the two messages and marking the
position of each letter in the corresponding period, we have:

12341  23412  34123  41234  12341  23412
No. 1     VMYZG  EAUNT  PKFAY  JIZMB  UMYKB  VFIVV
No. 2     ZGANW  IOMOA  CODHA  CLRLP  MOQOJ  EMOQU
12345  61234  56123  45612  34561  23456

34123  41234  12341  23412  34123  41234
No. 1     SEOAF  SKXKR  YWCAC  ZORDO  ZRDEF  BLKFE
No. 2     DHXBY  UQMGA  UVGLQ  DBSPU  OABIR  PWXYM
12345  61234  56123  45612  34561  23456

12341  23412  34123  41234  12341  23412
No. 1     SMKSF  AFEKV  QURCM  YZVOX  VABTA  YYUOA
No. 2     OGGFT  MRHVF  GWKNI  VAUPF  ABRVI  LAQEM
12345  61234  56123  45612  34561  23456

34123  41234  12341  23412  34123  41234
No. 1     YTDKF  ENWNT  DBQKU  LAJLZ  IOUMA  BOAFS
No. 2     ZDJXY  MEDDY  BOSVM  PNLGX  XDYDO  PXBYU
12345  61234  56123  45612  34561  23456

12341  23412  34123  41234  12341  23412
No. 1     KXQPU  YMJPW  QTDBT  OSIYS  MIYKU  ROGMW
No. 2     QMNKY  FLUYY  GVPVR  DNCZE  KJQOR  WJXRV
12345  61234  56123  45612  34561  23456

34123  41234
No. 1     CTMZZ  VMVAJ.
No. 2     GDKDS  XCEEC.
12345  61234

establish secondary alphabets by distributing the letters
from the 12 different superimposed pairs of numbers.
The 1 - 1 superimposition is placed in the tableau at the
0 - 1 row, column in the tableaux.

0     1 2 3 4 5 6 7 8 91011121314151617181920212223242526
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
---------------------------------------------------
1-1   I J   P   D         Q G C E       K O   R Z
2-2   H V N                   G   U     W       E D M L X
3-3   E         M     X   G   I D J   N     R         A O
4-4               X   O C         D K   A F Y Q       V N
1-5         B   T W   L       R   E     M N   Y       U A
2-6   M O     I       C       D               U V     F R
3-1   O   G     R             L   P   S   D           Z
4-2   L P     H         U V               E D M      F
1-3       Q J             V W K O X Y         M A
2-4   B               J   X P O             A   F Y     D
3-5   N R       Y                 B C G               Q S
4-6           M         L O             S U V W X
---------------------------------------------------
We construct the complete equivalent primary component:

1 2 3 4 5 6 7 8 91011121314151617181920212223242526
I T K N P Z H M W B Q E U L F C S J A X R G D V O Y

Ok. We have the cipher component. Is it normal? reversed?
Mixed?  Same questions for the plain component sequence.
We assume that the primary plain component is normal direct
sequence.  We attempt to solve and fail.  Normal reverse will
also fail. We assume a K3 situation, i.e. the plain and
cipher components are identical.  Again the test fails.  We
assume that the plain is in reverse mode. Nope. So we have a
K4 situation, both primary components are different mixed
sequences.

Message 1 transcribed into periods of four letters.

Message 1

VMYZ GEAU NTPK FAYJ IZMB UMYK BVFI VVSE
OAFS KXKR YWCA CZOR DOZR DEFB LKFE SMKS
FAFE KVQU RCMY ZVOX VABT AYYU OAYT DKFE
NWNT DBQK ULAJ LZIO UMAB OAFS KXQP UYMJ
PWQT DBTO SIYS MIYK UROG MWCT MZZV MVAJ

The Uniliteral frequency distributions for the four secondary
alphabets are shown in 1A -4A.  We have the reconstructed
cipher alphabet, 1B-4b shows the sequences rearranged.

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

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

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

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

We now shift 1B-4B for superimposition and combine the
distributions.  The latter distributions may be combined so
as to yield a single monoalphabetic distribution for the
entire message.  In other words, the polyalphabetic message
can be converted into monoalphabetic terms, and thereby
simplifying the situation considerably.

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

6 2 5 4 2 7  15 9 2    21 9 6 410 3 1 1 7 2 918 9 1
1B-4B   I T K N P Z H M W B Q E U L F C S J A X R G D V O Y
combinedH M       L   R S       O       A       I Y N E T
Plain
Equiv's

I have converted 2B-4B into terms of 1B.  The 2 E's of 2B add
to 1B I. The two K's of alphabet 3 becomes I's and the N
becomes a T, and so forth.  We solve the monoalphabetic
cipher.

12341  23412  34123  41234  12341  23412

ENEMY  HASCA  PTURE  DHILL  ONETW  OONEO
VDVTG  ISWNZ  KOFMV  LIRZZ  UDVOB  UUDVU

URTRO  OPSHA  VEDUG  INAND  CANHO  LDFOR
FMOMU  UKWIS  YVLFC  RDSDL  NSDIU  ZLJUM

ANHOU  RORPO  SSIBL  YLONG  ERREQ  UESTR
SDIUF  MUMKU  WWRPZ  GZUDC  VMMVA  FVWOM

EINFO  RCEME  NTSTO  PADDI  TIONA  LTROO
VVDJU  MNVTV  DOWOU  KSLLR  ORDUS  ZOMUU

PSSHO  ULDBE  SENTV  IAGEO  RGETO  WNFRE
KWWIU  FZLPV  WVDOY  RSCVU  MCVOU  BDJMV
LVMRN  XMUSL.

Having the plain text, the derivation of the plain or
equivalent plain component is straightforward. We may base
the reconstruction upon any of the secondary alphabets, since
the plaintext - ciphertext relationship is known directly,
and the primary cipher component is at hand. So:

1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526
H M P C B L . R S  W . . O D U G A F Q K I Y N E T V

with Key words of STAR and OCEANS for messages 1 and 2.

NECESSARY AND SUFFICIENT CONDITIONS FOR SUPERIMPOSITION AND
CONVERSION TO MONOALPHABETIC TERMS

This example shows the power of the method of superimposition
and conversion of a polyalphabetic cipher to monoalphabetic
terms.  This conversion is possible because the sequence of
letters forming the cipher component has been reconstructed
and was known, and the uniliteral distributions for the
respective secondary cipher alphabets could theoretically be
shifted to correct superimpositions for monoalphabeticity.
The data was sufficient to give proper indications for
alignment of the alphabets and relative displacements. The
chi test could also have been brought to bear to match
columns.  The above constitutes the necessary and sufficient
conditions to convert theory to actuality.

SOLUTION OF ISOLOGS INVOLVING DIFFERENT PAIRS OF UNKNOWN
PRIMARY COMPONENTS

The principle of superimposition continues to work for us
even when the primary components are different, and the
repeating keys are of different lengths.

There are two general attacks.  The first is a slight
modification of the procedures previously discussed. We first
factor the messages, then superimpose the messages on a width
of the least common multiple, then create a reconstruction
matrix based on the cipher values.  We must limit our
observations to within the matrix, because the given messages
are different and therefore the indirect symmetry does not
extend to the 0 or assumed plain line. The wrinkle in the
fabric is we must restrict our observations to a homogeneous
set of lines, like 1-1,1-2,1-3,1-4 etc.  From this data, we
reduce the reconstruction matrix to a smaller set and solve
for the equivalent primary component.  It is possible to
invert the matrix so that values for the second message will
yield its equivalent primary component.

ARBITRARY REDUCTION METHOD

It is not necessary to recognize the plain text to solve a
problem involving Isologs.  The next cryptanalytic attack is
applicable for many types of ciphers.  The procedure exposes
latent letter relationships and reduces the imposed chaos of
the cryptogram.  Given:
Message 1

BWXPS  OBYII  UYHLF  KFSOP  VGEYW  PBVXO
UGJPB  WDXUG  HSWDH  KHKHC  UAYKP  NFSPD
OBBYB  INKFL  WABOX  PJXUV  WKFXR  WXYWS
SDYZQ  ZHETA  JXXZW  XJROS  PDEEW  OJONK
GIRXR  WUYDK  NTJWR  EVBUR  DLISJ  BLCKK
FODEV  DYZQZ  SHCTW  DIEXZ

Factoring gives us periods of 4 and 5 for messages 1 and 2,
respectively.  We write out the messages on a width of the
least common multiple of 20.

Message 2

JNLEJ  HWUAH  JHUIV  YNCHC  HLPKD  EWZJJ
JNAHB  HZBIM  TUBQE  FJAKM  JVBEF  XNCTL
FAAKV  KIABG  CVFNY  FWBIQ  GERSA  TZUSD
SXBUD  SHAWA  YXLJD  CQLED  HXGZL  ZWHNB
VTJSA  TSUUC  MIAKK  JEMIY  DSKGB  VTJYC
XYLZE  CXLSU  MVMND  ONFJY

12341  23412  34123  41234        20
BWXPS  OBYII  UYHLF  KFSOP
JNLEJ  HWUAH  JHUIV  YNCHC
12345  12345  12345  12345
A             A  A
12341  23412  34123  41234        40
VGEYW  PBVXO  UGJPB  WDXUG
HLPKD  EWZJJ  JNAHB  HZBIM
12345  12345  12345  12345
A         A
12341  23412  34123  41234        60
HSWDH  KHKHC  UAYKP  NFSPD
TUBQE  FJAKM  JVBEF  XNCTL
12345  12345  12345  12345
A
12341  23412  34123  41234        80
OBBYB  INKFL  WABOX  PJXUV
FAAKG  KIABG  CVFNY  FWBIQ
12345  12345  12345  12345
A      A    A       A
12341  23412  34123  41234       100
WQFXR  WXYWS  SDYZQ  ZHETA
GERSA  TZUSD  SXBUD  SHAWA
12345  12345  12345  12345

12341  23412  34123  41234       120
JXXZW  XJROS  PDEEW  OJONK
YXLJD  CQLED  HXGZL  ZWHNB
12345  12345  12345  12345

12341  23412  34123  41234       140
GIRXR  WUYDK  NTJWR  EVBUR
VTJSA  TSUUC  MIAKK  JEMIY
12345  12345  12345  12345
A            A  A
12341  23412  34123  41234       160
DLISJ  BLCKK  FODEV  DYZQZ
DSKGB  VTJYC  XYLZE  CXLSU
12345  12345  12345  12345
A
12341  23412                     170
SHCTW  DIEXZ
MVMND  ONFJY
12345  12345
A

We arbitrarily assign the value of A(plain) as the first
letter of the plain text. Since in message 1, B(cipher)=
A(plain), then every B(cipher) in alphabet 1 must equal
A(plain); these values are entered in the table above.  Also
the 65th and 73rd letter of message 1 are A(plain), this
establishes that in message 2, G(cipher) in alphabet 5 and
F(cipher) in alphabet 3 are also A(plain); we enter these
values.  Similarly, every J(cipher) in alphabet 1 of message
2 equals A(plain).  We continue the process and recover all
the A(plains) of the pseudo-plain text with the resulting
worksheet shown above.

We arbitrarily assign the value of B(plain) to the V(cipher)
at the 21st position of message 1. The other V(cipher) of
message number 1 establishes the E(cipher) of message 2 also
as a B(plain).  This procedure of arbitrary assignments is
continued until all the cipher letters of alphabet 1 of
message 1, are placed.  we are able to reduce most of the
text to monoalphabetic terms.  The worksheet is as follows:

12341  23412  34123  41234        20
BWXPS  OBYII  UYHLF  KFSOP
JNLEJ  HWUAH  JHUIV  YNCHC
12345  12345  12345  12345
ACHDIIFCK     ACCA   FME D

12341  23412  34123  41234        40
VGEYW  PBVXO  UGJPB  WDXUG
HLPKD  EWZJJ  JNAHB  HZBIM
12345  12345  12345  12345
B  CE   F LI  AMF F  BHOAM

12341  23412  34123  41234        60
HSWDH  KHKHC  UAYKP  NFSPD
TUBQE  FJAKM  JVBEF  XNCTL
12345  12345  12345  12345
CEOOC  D FCM  AJODB   MEBO

12341  23412  34123  41234        80
OBBYB  INKFL  WABOX  PJXUV
FAAKG  KIABG  CVFNY  FWBIQ
12345  12345  12345  12345
DGFCA   IFMA  OJAIH  DFOA

12341  23412  34123  41234       100
WQFXR  WXYWS  SDYZQ  ZHETA
GERSA  TZUSD  SXBUD  SHAWA
12345  12345  12345  12345
EB EJ  CHCEE  LOOHE  LCF J

12341  23412  34123  41234       120
JXXZW  XJROS  PDEEW  OJONK
YXLJD  CQLED  HXGZL  ZWHNB
12345  12345  12345  12345
FOHLE  O HDE  BOPFO   FIIF

12341  23412  34123  41234       140
GIRXR  WUYDK  NTJWR  EVBUR
VTJSA  TSUUC  MIAKK  JEMIY
12345  12345  12345  12345
G  EJ  CACHD  IIFC   ABGAH

12341  23412  34123  41234       160
DLISJ  BLCKK  FODEV  DYZQZ
DSKGB  VTJYC  XYLZE  CXLSU
12345  12345  12345  12345
HAM F  G  ND    HFC  OOHEL

12341  23412                     170
SHCTW  DIEXZ
MVMND  ONFJY
12345  12345
IJGIE   MALH

The above table is about 85% reduced and note the idiomorphic
repetition ACHDIIFC representing Artillery becomes patent in
the reduction process.  This is rather exciting. From no
patent clues to reduction and latent clues exposed. Clever.

The solution is continued by setting up sequence recon-
struction matrices for both messages.   The 0 line represents
the pseudo-plain text and the values inside the matrix being
cipher text.

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

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

>From the above we chain out the equivalent primary components
used for each message. Having reconstructed the cipher
component for each message, the alphabets are aligned,
combined and reduced to monoalphabetic terms.  After solution
of these messages, we find message 1 is a case of direct
symmetry with the cipher component based on the keyword
HYDRAULIC, and message 2 is a case of indirect symmetry with
both components being keyword-mixed sequences based on our
favorite keyword QUESTIONABLY. Friedman points out that the
keywords are prime to each other (9 vs 11). Primality is not
a necessary condition for solution based on this procedure.
[FRE7]

The method of Arbitrary Reduction is very powerful and works
in other ares besides solving periodic polyalphabetic
ciphers.  It represents a workable approach where the
cryptosystem involves nonrelated, random-mixed secondary
alphabets among which no symmetry of any sort exists!

SOLUTION BASED ON INDIRECT SYMMETRY OF A "STAGGER'

Given two messages with group counts nearly identical and two
isologous initial fragments which are identical except by one
letter (called a 'stagger') we can solve the isologous
portions of the messages and recover the primary cipher
component by the process of indirect symmetry. Transmission
garble usually creates stagger messages. Machine cipher
systems sometimes produce these when a word separator is
added.  Staggers may be progressively larger as further word

Given:

Message A

*                *
ZFWAY  ITBVX  XWZQV  PEBGS  GGFIZ  TUAMF
RFEQX  PEPPO  PCNBP  QPOTX  VNAIH  HVRXC
NHVGM  FRFSI  ESQMV
*
Message B
*                 *
ZFWAY  ITBVX  XWZQV  PDRKF  USVAG  XLJKC
NDVPR  OWBRH  YFJMS  HRFVS  BAHWG  ZFAJO
JMFAV  CNDVD  ORZPH  A
*

We note that both messages have the same 16 letter beginnings
and that message B is 1 letter longer than message A. Note
that the tetragraphs MFRF (29) and (65) are spaced 1 less
letter than CNDV at (30) and (66).  The D in position 17 of
message 2 is the extra letter.

Starting from the E in position 17 of message 1, we
superimpose message one over message 2 starting at the R in
position 18. [We use a period of 6 because the tetragraph
delta equals 36 which factors into 3,4,6 and 9; 6 is
confirmed via the message.]

56123456123456123456123456123456123456123456123456123456123
EBGSGGFIZTUAMFRFEQXPEPPOPCNBPQPOTXVNAIHHVRXCNHVGMFRFSIESQMV
RKFUSVAGXLJKCNDVPROWBRHYFJMSHRFVSBAHWGZFAJOJMFAVCNDVDORZPHA

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

It is fairly easy to align properly the cipher components
after the primary cipher component or its equivalent have
been recovered, thereby expediting the reduction of the
cipher into monoalphabetic terms. Note that B(cipher) of
alphabet 2 is under E(cipher) of alphabet 1; V(cipher) of
alphabet 3 is under F(cipher) alphabet 2;P(cipher) of
alphabet 4 is under E(cipher) of alphabet 1. From this point
on solution follows the normal path of reconstruction,
keyword recovery and combination of alphabets, reduction to
monoalphabetic terms and solution by frequency analysis.

LONG LATENT REPETITIONS

The stagger procedure applies to a periodic cryptogram which
contains a long passage repeated in its plain text, the
second occurrence occurring at a point in the keying cycle
different from the first occurrence.  If the passage is long
enough, the equivalencies from the two corresponding
sequences may be chained together to yield an equivalent
primary component. In effect, we by-pass the solution by
frequency analysis or making assumptions in the plain text of
a polygraphic cipher.

FINAL REMARKS REGARDING SOLUTION BY SUPERIMPOSITION

In solving an ordinary repeating-key cipher the first step,
ascertaining the length of the period, is a relatively minor
consideration. It paves the way for the second step, which
consists of allocating the letters of the cryptogram into
individual monoalphabetic distributions. The third step is to
solve these distributions.  The text is transcribed into its
periods and written out in successive lines corresponding to
the length of the period.  The columns of letters as a series
belong to the same monoalphabet.

We also can see the letters as transcribed into superimposed
periods; in such a case the letters in each column have
undergone the same kind of treatment by the same elements
(plain and cipher components of the cipher alphabet.)

If we have a case of a very long repeating key and a short
message ( few cycles in the text) we have a difficult
problem.  But supposing there were several short cryptograms
enciphered by the same key, each message beginning at
identical starting points in the key. We can superimpose
these messages "in flush depth" or "head on" and know that 1)
the letters in the columns belong to the same individual
alphabets, 2) and that if there are enough messages (about
25-30 in English), then the frequency distributions
applicable to the successive columns of text can be solved -
without knowing the length of the key.  Any difficulties that
may have arisen because we were not able to factor the
problem correctly are circumvented. The second step of the
normal solution to the problem is by-passed.  The assumption
of probable initial words of messages and stereotyped
beginnings is a powerful method of attack in such situations.
Since the superimposed texts in these cases comprise only the
beginnings of messages, assumptions of probable words are
more easily made than when words are sought in the interior
of the messages. Some common introductory words are REQUEST,
REFER, ENEMY, WHAT, WHEN, and SEND.  High frequency initial
digraphs will manifest themselves in the first two columns of
the superimposed diagram.  The high frequency RE diagram
manifests itself in such words as REQUEST, REQUIRE,
REFERENCE, REFERRING, REQUISITIONS, REPEAT, RECOMMEND,
REPORT, RECONNAISSANCE, REINFORCEMENTS and perhaps REGIMENT.
(I assume the military text here.)

This same superimposition principle applies even if the
messages start at different initial points, providing the
messages can be correctly superimposed, so that the letters
which fall in one column really belong to one cipher
alphabet. The superimposed messages are said to be "in
depth."  The chi test may be used to advantage in finding and
combining columns of the superimposed diagram which were
enciphered by identical keys, thus assisting in the analysis
of frequencies of larger samples than were available before
the amalgamation. [FRE7]

CONCLUSION

In summary, we have seen that the chaining process between
cipher texts applies to the latent characteristics of the
cipher components, regardless of the identity of the plain
components and regardless whether direct or indirect symmetry
is involved in the cryptosystems.  The principle of super-
imposition ranks as one of the most important principles of
cryptanalysis.  A pretty impressive tool.

LECTURE 11 SOLUTIONS

Thanks to BOZOL for the quick response and correct too!

11.1 Vigenere.  Key= SLEEP. "Any reputable physician will
agree..

11.2 Beaufort.  Key = SILENCE. "Although every one may not
subscribe to ..

11.3 Variant.  Key = IMPSHGXW (HINSNOTI).  Because of the
many pressures...   [the correct key is SOLITUDE]

11.4 GRONSFELD. 6-3-8-4-0. "Too much discussion, especially..

11.5 BEAUFORT.  Key = OCCUPATION.  "Almost every man has a
job, many find..

BOZOL reports that the tip did not help him and that the
first pass at the key was ORCUPATMON which he mystically
came up with organization.

LECTURE 12 PROBLEMS

12.1 Nihilist Substitution

74 46 66 44 79 47 45 37 58 66 37 60 25 54 33 69 78 35 68 27
47 36 28 88 36 60 33 48 43 29 87 35 49 57 76 37 37 88 36 60
33 77 74 50 86 55 47 27 76 45 40 55 56 58 66 78 57 30 94 58
38 26 55 57 59 88 56 79 46 46 66 60 58 55 48 56.  (DGGLWLRQ,
ends WXEOIW)

12.2 Nihilist Substitution

38 76 54 76 64 76 76 54 74 55 35 76 77 76 47 58 76 85 74 44
65 88 63 74 47 36 95 74 63 44 37 58 57 96 65 36 66 85 74 63
55 79 53 67 57 56 58 64 67 67 56 67 57 74 55 55 57 86 03 43
46 67 73 96 67 39. (ETARVQITCO, ends HSMX)

12.3 PORTA

QLAMU  CHQGO  FTESV  XKEWC  GMXPH
UCLUS  WSGXT  EVURH  TMTSU  TKVSQ  GCQCW
LHMDX  NUFUE  EFXRF  XPHUN  RGPKC  OXULB
BBCUS  IBBHW.  (HAVE)

12.4 PORTA

XFXYW  ZJICZ  IBUZN  HJXEA  ACWBE
JOOCZ  UPXFQ  BXHFI  CGMAZ  KVQEG  BBCAF
KLLXF  BVOUN  TSAYZ  KKXLR  CWAJC  LVVVI
XNBFQ  JVWBW  BSWEY  VUNGX  ODFRZ  PTEWO
PJQNH  WZPNA  YRCLV  YYWCQ  ULOJB  VK.  (GSRWXERX)

12.5 PORTAX

UXCUD  ZMVBA  FWWPV  DIKDO  JISMA
WRBBA  YLOYX  AKUXR  JGDCJ  MYAPV  RJWJA
DMUKL  KLUAM  KAOEN  YBFCC  IQGFK  QZAA. (PQXKEG)

12.6 PORTAX

WWQPE  JBDTM  TMNWH  CTJSW  WKIAC
BJKWL  YHBYN  OAKRZ  PDYZM  DIVGB  QKNJP
RNSRU  FXWMU  TKMJS  KDNLW  WFHKR  JSCVF
HTJIS  JD.  (UHDOLCH)

12.7 GROMARK

HPMZU  IBQHI  SDHHH  JKUNC  OYJSC
24106
RBLOF  REXTG  EXAZA  ILAXX  XHFNH  CDUYQ

YUOMQ  NVOIN  XYMBR  WAHNT  FGPFB  DOOMA

CWHDH  JXTTX  CJIUR  PVMZR  EILDZ  QJJTT

ILNNP  TREVL  BQLL. ( tip: UCAUKYKUJK; ends tivpw.)
REFERENCES / RESOURCES    [updated 30 May 1996]

[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.

[ACM]  Association For Computing Machinery, "Codes, Keys and
Conflicts: Issues in U.S. Crypto Policy," Report of a
Special Panel of ACM U. S. Public Policy Committee
(USACM), June 1994.

1918," AS53, The Cryptogram, American Cryptogram
Association, 1953.

[AFM]  - 100-80, Traffic Analysis, Department of the Air
Force, 1946.

[ALAN] Turing, Alan,  "The Enigma", by A. Hodges. Simon and
Schuster, 1983.

[ALBA] Alberti, "Treatise De Cifris," Meister Papstlichen,
Princeton University Press, Princeton, N.J., 1963.

[ALEX] Alexander, D. A., "Secret codes and Decoding," Padell
Book Co., New York, 1945.

[ALGE] MINIMAX, "Introduction To Algebraic Cryptography,"
FM51, The Cryptogram, American Cryptogram Association,
1951.

[ALKA] al-Kadi, Ibrahim A., Origins of Cryptology: The Arab
Contributions, Cryptologia, Vol XVI, No.  2, April
1992, pp. 97-127.

[ALP1] PICCOLA, "Lining Up the Alphabets," AM37, The
Cryptogram, American Cryptogram Association, 1937.

[ALP2] PICCOLA, "Recovering a Primary Number Alphabet," JJ37,
The Cryptogram, American Cryptogram Association, 1937.

[ALP3] CLEAR SKIES, "Method For Recovering Alphabets," AM46,
The Cryptogram, American Cryptogram Association, 1946.

[ALP4] PICCOLA, "Lining Up the Alphabets," AM37, The
Cryptogram, American Cryptogram Association, 1937.

[ALP5] MACHIAVELLI,"Recovery of Incomplete Cipher Alphabets,"
SO78, The Cryptogram, American Cryptogram Association,
1978.

[ALP6] BOZO,"Recovery of Primary Alphabets I," JJ35, The
Cryptogram, American Cryptogram Association, 1935.

[ALP7] BOZO,"Recovery of Primary Alphabets II," AS35, The
Cryptogram, American Cryptogram Association, 1935.

[ALP8] ZYZZ,"Sinkov - Frequency-Matching," JA93, The
Cryptogram, American Cryptogram Association, 1993.

[AMS1] RED E RASER,"AMSCO," ON51, The Cryptogram, American
Cryptogram Association, 1951.

[AMS2] PHOENIX,"Computer Column: Amsco Encipherment," SO84,
The Cryptogram, American Cryptogram Association, 1984.

[AMS3] PHOENIX,"Computer Column: Amsco Decipherment," MA85,
The Cryptogram, American Cryptogram Association, 1985.

[AMS4] PHOENIX,"Computer Column: Amsco Decipherment," MJ85,
The Cryptogram, American Cryptogram Association, 1985.

[AMS5] PHOENIX,"Computer Column: Amsco Decipherment," JA85,
The Cryptogram, American Cryptogram Association, 1985.

[AND1] Andree, Josephine, "Chips from the Math Log," Mu Alpha
Theta, 1966.

[AND2] Andree, Josephine, "More Chips from the Math Log," Mu
Alpha Theta, 1970.

[AND3] Andree, Josephine, "Lines from the O.U. Mathematics
Letter,"  Vols. I,II,III, Mu Alpha Theta, 1971, 1971,
1971.

[AND4] Andree, Josephine and Richard V., "RAJA Books: a
Puzzle Potpourri," RAJA, 1976.

[AND5] Andree, Josephine and Richard V., "Preliminary
Instructors Manual for Solving Ciphers," Project
CRYPTO, Univ of Oklahoma, Norman, OK, 1977.

[AND6] Andree, Josephine and Richard V., "Teachers Handbook
For Problem Solving and Logical Thinking," Project
CRYPTO, Univ of Oklahoma, Norman, OK, 1979.

[AND7] Andree, Josephine and Richard V., "Preliminary
Instructors Manual for Cryptarithms," Project CRYPTO,
Univ of Oklahoma, Norman, OK, 1976.

[AND8] Andree, Josephine and Richard V., "Sophisticated
Ciphers: Problem Solving and Logical Thinking,"
Project CRYPTO, Univ of Oklahoma, Norman, OK, 1978.

[AND9] Andree, Josephine and Richard V., "Logic Unlocs
Puzzles," Project CRYPTO, Univ of Oklahoma, Norman,
OK, 1979.
[ANDR] Andrew, Christopher, 'Secret Service', Heinemann,
London 1985.

[ANK1] Andreassen, Karl, "Cryptology and the Personal
Computer, with Programming in Basic," Aegean Park
Press, 1986.

[ANK2] Andreassen, Karl, "Computer Cryptology, Beyond Decoder
Rings," Prentice-Hall 1988.

[ANNA] Anonymous., "The History of the International Code.",
Proceedings of the United States Naval Institute,
1934.

[ANN1] Anonymous., " Speech and Facsimile Scrambling and
Decoding," Aegean Park Press, Laguna Hills, CA, 1981.

[ARI1] OZ,"The Construction of Medium - Difficulty
Aristocrats," MA92, The Cryptogram, American
Cryptogram Association, 1992.

[ARI2] HELCRYPT,"Use of Consonant Sequences for Aristocrats,"
ON51, The Cryptogram, American Cryptogram Association,
1951.

[ARI3] HELCRYPT,"Use of Tri-Vowel Sequences for Aristocrats,"
JJ52, The Cryptogram, American Cryptogram Association,
1952.

[ARI4] AB STRUSE, "Equifrequency Crypts," JF74, The
Cryptogram, American Cryptogram Association, 1974.

[ARI5] HOMO SAPIENS,"End-letter Count for Aristocrats," FM45,
The Cryptogram, American Cryptogram Association, 1945.

[ARI6] S-Tuck, "Aristocrat Affixes," ON45, The Cryptogram,
American Cryptogram Association, 1945.

[ASA ] "The Origin and Development of the Army Security
Agency  1917 -1947," Aegean Park Press, 1978.

[ASHT] Ashton, Christina, "Codes and Ciphers: Hundreds of
Unusual and Secret Ways to Send Messages," Betterway
Books, 1988.

[ASIR] Anonymous, Enigma and Other Machines, Air Scientific
Institute Report, 1976.

[AUG1] D. A. August, "Cryptography and Exploitation of
Chinese Manual Cryptosystems - Part I:The Encoding
Problem", Cryptologia, Vol XIII, No. 4, October 1989.

[AUG2] D. A. August, "Cryptography and Exploitation of
Chinese Manual Cryptosystems - Part II:The Encrypting
Problem", Cryptologia, Vol XIV, No. 1, August 1990.

[AUT1] PICCOLA,"Autokey Encipherment,"DJ36, The Cryptogram,
American Cryptogram Association, 1936.

[AUT2] PICCOLA,"More about Autokeys,"FM37, The Cryptogram,
American Cryptogram Association, 1937.

[AUT3] ISKANDER,"Converting an Autokey to a Periodic," "JJ50,
The Cryptogram, American Cryptogram Association, 1950.

[BAC1] SHMOO,"Quicker Baconian Solutions," ND80, The
Cryptogram, American Cryptogram Association, 1980.

[BAC2] XERXES,"Sir Francis Bacon Cipher," AS36, The
Cryptogram, American Cryptogram Association, 1936.

[BAC3] AB STRUSE,"Solving a Baconian," JJ48, The Cryptogram,
American Cryptogram Association, 1948.

[BAC4] B.NATURAL,"Tri-Bac Cipher," JA69, The Cryptogram,
American Cryptogram Association, 1969.

[BAC5] annonomous,"Numerical Baconian," JF62, The Cryptogram,
American Cryptogram Association, 1962.

[BAC6] FIDDLE,"Extended Baconian," SO69, The Cryptogram,
American Cryptogram Association, 1969.

Civilization: Source of Renaissance.  Second Edition.
Cambridge: MIT Press. 1983.

[BAMF] Bamford, James, "The Puzzle Palace: A Report on
America's Most Secret Agency," Boston, Houghton
Mifflin, 1982.

[BARB] Barber, F. J. W., "Archaeological Decipherment: A
Handbook," Princeton University Press, 1974.

[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.

[BAR3] Barker, Wayne G., "Cryptanalysis of the Hagelin
Cryptograph, Aegean Park Press, 1977.

[BAR4] Barker, Wayne G., "Cryptanalysis of the Enciphered
Code Problem - Where Additive Method of Encipherment
Has Been Used," Aegean Park Press, 1979.

[BAR5] Barker, W., ed., History of Codes and Ciphers in the
U.S.  Prior To World War I," Aegean Park Press, 1978.

[BAR6] Barker, W., " Cryptanalysis of Shift-Register
Generated Stream Cipher Systems,"  Aegean Park Press,
1984.

[BAR7] Barker, W., ed., History of Codes and Ciphers in the
U.S.  During the Period between World Wars, Part I,
1919-1929, Aegean Park Press, 1979.

[BAR8] Barker, W., ed., History of Codes and Ciphers in the
U.S.  During World War I, Aegean Park Press, 1979.

[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.

[BAZE] Bazeries, M. le Capitaine, " Cryptograph a 20
rondelles-alphabets,"  Compte rendu de la 20e session
de l' Association Francaise pour l'Advancement des
Scienses, Paris: Au secretariat de l' Association,
1892.

[BEA1] S-TUCK, "Beaufort Auto-key," JJ46, The Cryptogram,
American Cryptogram Association, 1946.

[BEA2] PICCOLA, "Beaufort Ciphers," JJ36, The Cryptogram,
American Cryptogram Association, 1936.

[BEA3] LEDGE, "Beaufort Fundamentals (Novice Notes)," ND71,
The Cryptogram, American Cryptogram Association, 1971.

[BEA4] SI SI, "Comparative Analysis of the Vigenere, Beaufort
and Variant Ciphers," JA80, The Cryptogram, American
Cryptogram Association, 1980.

[BEA5] O'PSHAW, "Porta, A special Case of Beaufort," MA91,
The Cryptogram, American Cryptogram Association, 1991.

[BECK] Becket, Henry, S. A., "The Dictionary of Espionage:
Spookspeak into English,"  Stein and Day, 1986.

[BEES] Beesley, P., "Very Special Intelligence", Doubleday,
New York, 1977.

[BENN] Bennett, William, R. Jr., "Introduction to Computer
Applications for Non-Science Students," Prentice-Hall,
1976.  (Interesting section on monkeys and historical
cryptography)

[BIGR] PICCOLA, "Use of Bigram Tests" AS38, The Cryptogram,
American Cryptogram Association, 1938.

[BLK]  Blackstock, Paul W.  and Frank L Schaf, Jr.,
"Intelligence, Espionage, Counterespionage and Covert
Operations,"  Gale Research Co., Detroit, MI., 1978.

[BLOC] Bloch, Gilbert and Ralph Erskine, "Exploit the Double
Encipherment Flaw in Enigma", Cryptologia, vol 10, #3,
July 1986, p134 ff.  (29)

[BLUE] Bearden, Bill, "The Bluejacket's Manual, 20th ed.,
Annapolis: U.S. Naval Institute, 1978.

[BODY] Brown, Anthony - Cave, "Bodyguard of Lies", Harper and
Row, New York, 1975.

[BOLI] Bolinger, D. and Sears, D., "Aspects of Language,"
3rd ed., Harcourt Brace Jovanovich,Inc., New York,
1981.

[BOSW] Bosworth, Bruce, "Codes, Ciphers and Computers: An
Introduction to Information Security," Hayden Books,
Rochelle Park, NJ, 1990.

[BOWE] Bowers, William Maxwell, "The Bifid Cipher, Practical
Cryptanalysis, II, ACA, 1960.

[BOW1] Bowers, William Maxwell, "The Trifid Cipher,"
Practical Cryptanalysis, III, ACA, 1961.

[BOW2] Bowers, William Maxwell, "The Digraphic Substitution,"
Practical Cryptanalysis, I, ACA, 1960.

[BOW3] Bowers, William Maxwell, "Cryptographic ABC'S:
Substitution and Transposition Ciphers," Practical
Cryptanalysis, IV, ACA, 1967.

[BOWN] Bowen, Russell J., "Scholar's Guide to Intelligence
Literature: Bibliography of the Russell J. Bowen
Collection," National Intelligence Study Center,
Frederick, MD, 1983.

[BP82] Beker, H., and Piper, F., " Cipher Systems, The
Protection of Communications", John Wiley and Sons,
NY, 1982.

[BRAS] Brasspounder, "Language Data - German," MA89, The
Cryptogram, American Cryptogram Association, 1989.

[BREN] Brennecke, J., "Die Wennde im U-Boote-Krieg:Ursachen
und Folgren 1939 - 1943," Herford, Koehler, 1984.

[BROO] Brook, Maxey, "150 Puzzles in Cryptarithmetic,"
Dover, 1963.

[BROW] Brownell, George, A. "The Origin and Development of
the National Security Agency, Aegean Park Press, 1981.

[BRIG] Brigman,Clarence S., "Edgar Allan Poe's Contribution
to Alexander's Weekly Messenger," Davis Press, 1943.

[BRIT] Anonymous, "British Army Manual of Cryptography",
HMF, 1914.

[BROG] Broglie, Duc de, Le Secret du roi: Correspondance
secrete de Louis XV avec ses agents diplomatiques
1752-1774, 3rd ed.  Paris, Calmann Levy, 1879.

[BRYA] Bryan, William G., "Practical Cryptanalysis - Periodic
Ciphers -Miscellaneous", Vol 5, American Cryptogram
Association, 1967.

[BUGS] Anonymous, "Bugs and Electronic Surveillance," Desert
Publications, 1976.

[BUON] Buonafalce, Augusto, "Giovan Battista Bellaso E Le Sue
Cifre Polialfabetiche," Milano, 1990

[BURL] Burling, R., "Man's Many Voices: Language in Its
Cultural Context," Holt, Rinehart & Winston, New York,
1970.

[BWO]  "Manual of Cryptography," British War Office, Aegean
Park Press, Laguna Hills, Ca. 1989. reproduction 1914.

[CAND] Candela, Rosario, "Isomorphism and its Application in
Cryptanalytics, Cardanus Press, NYC 1946.

[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.

[CCF]  Foster, C. C., "Cryptanalysis for Microcomputers",
Hayden Books, Rochelle Park, NJ, 1990.

[CHEC] CHECHEM,"On the Need for a Frequency Counter," AM48,
The Cryptogram, American Cryptogram Association, 1948.

[CHOI] Interview with Grand Master Sin Il Choi.,9th DAN, June
25, 1995.

[CHOM] Chomsky, Norm, "Syntactic Structures," The Hague:
Mouton, 1957.

[CHUN] Chungkuo Ti-erh Lishih Tangankuan, ed "K'ang-Jih
chengmien chanch'ang," Chiangsu Kuchi Ch'upansheh,
1987., pp. 993-1026.

[CI]   FM 34-60, Counterintelligence, Department of the Army,
February 1990.

[CONS] S-TUCK and BAROKO, "Consonant-Line and Vowel-Line
Methods," MA92, The Cryptogram, American Cryptogram
Association, 1992.

[CONT] F.R.CARTER,"Chart Showing Normal Contact Percentages,"
AM53, The Cryptogram, American Cryptogram Association,
1953.

[CON1] S-TUCK."Table of Initial and Second-Letter Contacts,"
DJ43, The Cryptogram, American Cryptogram Association,
1943.

[COUR] Courville, Joseph B., "Manual For Cryptanalysis Of The
Columnar Double Transposition Cipher, by Courville
Associates., South Gate, CA, 1986.

[CLAR] Clark, Ronald W., 'The Man who broke Purple',
Weidenfeld and Nicolson, London 1977.

[COLF] Collins Gem Dictionary, "French," Collins Clear Type
Press, 1979.

[COLG] Collins Gem Dictionary, "German," Collins Clear Type
Press, 1984.

[COLI] Collins Gem Dictionary, "Italian," Collins Clear Type
Press, 1954.

[COLL] Collins Gem Dictionary, "Latin," Collins Clear Type
Press, 1980.

[COLP] Collins Gem Dictionary, "Portuguese," Collins Clear
Type Press, 1981.

[COLR] Collins Gem Dictionary, "Russian," Collins Clear Type
Press, 1958.

[COLS] Collins Gem Dictionary, "Spanish," Collins Clear Type
Press, 1980.

[COPP] Coppersmith, Don.,"IBM Journal of Research and
Development 38, 1994.

[COVT] Anonymous, "Covert Intelligence Techniques Of the
Soviet Union, Aegean Park Press, Laguna Hills, Ca.
1980.

[CREM] Cremer, Peter E.," U-Boat Commander: A Periscope View
of The Battle of The Atlantic," New York, Berkley,
1986.

[CRYP] "Selected Cryptograms From PennyPress," Penny Press,
Inc., Norwalk, CO., 1985.

[CRY1] NYPHO'S ROBOT, "Cryptometry Simplified," DJ40, FM41,
Cryptogram Association, 1940, 1941, 1941.

[CRY2] AB STRUSE, "Non-Ideomorphic Solutions," AM51, The
Association, 1951.

[CRY3] MINIMAX, "Problems in Cryptanalysis - A Transposition
that cannot be Anagrammed," MA60, The Cryptogram,
1960.

[CRY4] FAUSTUS, "Science of Cryptanalysis," AS32, The
Association, 1932.

[CRY5] FAUSTUS, "Science of Cryptanalysis,The " JA91, The
Association, 1991.

[CRY6] BEAU NED, "Semi-Systems in Crypt-Cracking," FM36, The
Association, 1936.

[CRY7] Y.NOTT, "Systems Of Systems," ON35, The Cryptogram,
1935.

[CULL] Cullen, Charles G., "Matrices and Linear
Transformations," 2nd Ed., Dover Advanced Mathematics
Books, NY, 1972.

[CUNE] CHECHACO, "The Decipherment of Cuneiform," JJ33, The
Association, 1933.

[DAGA] D'agapeyeff, Alexander, "Codes and Ciphers," Oxford
University Press, London, 1974.

[DALT] Dalton, Leroy, "Topics for Math Clubs," National
Council of Teachers and Mu Alpha Theta, 1973.

[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.

[DEAC] Deacon, R., "The Chinese Secret Service," Taplinger,
New York, 1974.

[DEAU] Bacon, Sir Francis, "De Augmentis Scientiarum," tr. by
Gilbert Watts, (1640) or tr. by Ellis, Spedding, and
Heath (1857,1870).

[DELA] Delastelle, F., Cryptographie nouvelle, Maire of
Saint-Malo, P. Dubreuil, Paris, 1893.

[DENN] Denning, Dorothy E. R.," Cryptography and Data

[DEVO] Deavours, Cipher A. and Louis Kruh, Machine
Cryptography and Modern Cryptanalysis, Artech, New
York, 1985.

[DEV1] Deavours, C. A., "Breakthrough '32: The Polish
Solution of the ENIGMA,"  Aegean Park Press, Laguna
Hills, CA, 1988.

[DEV2] Deavours, C. A. and Reeds, J.,"The ENIGMA,"
CRYPTOLOGIA, Vol I No 4, Oct. 1977.

[DEV3] Deavours, C. A.,"Analysis of the Herbern Cryptograph
using Isomorphs," CRYPTOLOGIA, Vol I No 2, April,
1977.

[DEV4] Deavours, C. A., "Cryptographic Programs for the IBM
PC," Aegean Park Press, Laguna Hills, CA, 1989.

[DIFF] Diffie, Whitfield," The First Ten Years of Public Key
Cryptography," Proceedings of the IEEE 76 (1988): 560-
76.

[DIFE] Diffie, Whitfield and M.E. Hellman,"New Directions in
Cryptography, IEEE Transactions on Information Theory
IT-22, 1976.

[DONI] Donitz, Karl, Memoirs: Ten Years and Twenty Days,
London: Weidenfeld and Nicolson, 1959.

[DOUB] TIBEX, " A Short Study in doubles ( Word beginning or
ending in double letters)," FM43, The Cryptogram,
1943.

[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.

[EIIC] Ei'ichi Hirose, ",Finland ni okeru tsushin joho," in
Showa gunji hiwa: Dodai kurabu koenshu, Vol 1,  Dodai
kurabu koenshu henshu iinkai, ed., (Toyko: Dodai
keizai konwakai, 1987), pp 59-60.

[ELCY] Gaines, Helen Fouche, Cryptanalysis, Dover, New York,
1956. [ A text that every serious player should have!]

[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

[ERSK] Erskine, Ralph, "Naval Enigma: The Breaking of
Heimisch and Triton," Intelligence and National
Security 3, Jan.  1988.

[EVES] , Howard, "An Introduction to the History of
Mathematics, " New York, Holt Rinehart winston, 1964.

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

[FIBO] LOGONE BASETEN, "Use of Fibonacci Numbers in
American Cryptogram Association, 1969.

[FING] HELCRYPT, "Cryptography in Fingerprinting," FM51, The
Association, 1951.

[FL]   Anonymous, The Friedman Legacy: A Tribute to William
and Elizabeth Friedman, National Security Agency,
Central Security Service, Center for Cryptological
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[FLI1] Flicke, W. F., "War Secrets in the Ether - Volume I,"
Aegean Park Press, Laguna Hills, CA, 1977.

[FLIC] Flicke, W. F., "War Secrets in the Ether - Volume II,"
Aegean Park Press, Laguna Hills, CA, 1977.

[FLIC] Flicke, W. F., "War Secrets in the Ether," Aegean Park
Press, Laguna Hills, CA, 1994.

[FORE] DELAC, "Solving a Foreign Periodic by Lining Up the
American Cryptogram Association, 1946.

[FOWL] Fowler, Mark and Radhi Parekh, " Codes and Ciphers,
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(clever and work)

[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.

[FRAN] Franks, Peter, "Calculator Ciphers," Information
Associates, Champaign, Il. 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.

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

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

[FRSG] Friedman, William F., "Solving German Codes in World
War I, " Aegean Park Press, Laguna Hills, CA, 1977.

[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.

[FR7]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part II - Volume 1, Aegean
Park Press, Laguna Hills, CA, 1985.

[FR8]  Friedman, William F. and Callimahos, Lambros D.,
Military Cryptanalytics Part II - Volume 2, Aegean
Park Press, Laguna Hills, CA, 1985.

[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.

[FRS6] Friedman, W. F., "Six Lectures On Cryptology,"
National Archives, SRH-004.

[FR8]  Friedman, W. F., "Cryptography and Cryptanalysis
Articles," Aegean Park Press, Laguna Hills, CA, 1976.

[FR9]  Friedman, W. F., "History of the Use of Codes," Aegean
Park Press, Laguna Hills, CA, 1977.

[FRZM] Friedman, William F.,and Charles J. Mendelsohn, "The
Zimmerman Telegram of January 16, 1917 and its
Cryptographic Background," Aegean Park Press, Laguna
Hills, CA, 1976.

[FROM] Fromkin, V and Rodman, R., "Introduction to Language,"
4th ed.,Holt Reinhart & Winston, New York, 1988.

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

[FUMI] Fumio Nakamura, Rikugun ni okeru COMINT no hoga to
hatten," The Journal of National Defense, 16-1 (June
1988) pp85 - 87.

[GAJ]  Gaj, Krzysztof, "Szyfr Enigmy: Metody zlamania,"
Warsaw Wydawnictwa Komunikacji i Lacznosci, 1989.

[GAR1] Gardner, Martin, "536 Puzzles and Curious Problems,"
Scribners, 1967.

[GAR2] Gardner, Martin, "Mathematics, Magic, and Mystery ,"
Dover, 1956.

[GAR3] Gardner, Martin, "New Mathematical Diversions from
Scientific American," Simon and Schuster, 1966.

[GAR4] Gardner, Martin, "Sixth Book of Mathematical Games
from Scientific American," Simon and Schuster, 1971.

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

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

[GAR2] Garlinski, Jozef, 'The Enigma War', New York,
Scribner, 1979.

[GE]   "Security," General Electric, Reference manual Rev.
B., 3503.01, Mark III Service,  1977.

[GERH] Gerhard, William D., "Attack on the U.S., Liberty,"
SRH-256, Aegean Park Press, 1981.

[GERM] "German Dictionary," Hippocrene Books, Inc., New York,
1983.

[GILE] Giles, Herbert A., "Chinese Self-Taught," Padell Book
Co., New York, 1936?

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

[GLEN] Gleason, Norma, "Fun With Codes and Ciphers Workbook,"
Dover, New York, 1988.

[GLE1] Gleason, Norma, "Cryptograms and Spygrams," Dover, New
York, 1981.

[GLEA] Gleason, A. M., "Elementary Course in Probability for
the Cryptanalyst," Aegean Park Press, Laguna Hills,
CA, 1985.

[GLOV] Glover, D. Beaird, "Secret Ciphers of the 1876
Presidential Election," Aegean Park Press, Laguna
Hills, CA, 1991.

[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.

[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

[GRAH] Graham, L. A., "Ingenious Mathematical Problems and
Methods,"  Dover, 1959.

[GRAN] Grant, E. A., "Kids Book of Secret Codes, Signals and
Ciphers, Running Press, 1989.

[GRAP] DR. CRYPTOGRAM,"The Graphic Position Chart (On
Aristocrats)," JF59, The Cryptogram, American
Cryptogram Association, 1959.

[GREU] Greulich, Helmut, "Spion in der Streichholzschachtel:
Raffinierte Methoden der Abhortechnik, Gutersloh:
Bertelsmann, 1969.

[GRI1] ASAP,"An Aid For Grille Ciphers," SO93, The
Cryptogram, American Cryptogram Association, 1993.

[GRI2] DUN SCOTUS,"Binary Number Grille," JA60, The
Cryptogram, American Cryptogram Association, 1960.

[GRI3] S-TUCK,"Grille Solved By the Tableaux Method," DJ42,
The Cryptogram, American Cryptogram Association, 1942.

[GRI4] The SQUIRE,"More About Grilles," ON40,DJ40, The
Cryptogram, American Cryptogram Association, 1940,
1940.

[GRI5] OMAR,"Rotating Grille Cipher," FM41, The Cryptogram,
American Cryptogram Association, 1941.

[GRI6] S-TUCK,"Solving The Grille. A New Tableaux Method,"
FM44, The Cryptogram, American Cryptogram Association,
1944.

[GRI7] LABRONICUS,"Solving The Turning Grille," JF88, The
Cryptogram, American Cryptogram Association, 1988.

[GRI8] BERYL,"The Turning Grille," ND92, The Cryptogram,
American Cryptogram Association, 1992.

[GRI9] SHERLAC and S-TUCKP,"Triangular Grilles," ON45, The
Cryptogram, American Cryptogram Association, 1945.

[GRIA] SHERLAC,"Turning Grille," ON49, The Cryptogram,
American Cryptogram Association, 1949.

[GRIB] DUN SCOTUS,"Turning (by the numbers)," SO61, The
Cryptogram, American Cryptogram Association, 1961.

[GRIC] LEDGE,"Turning Grille (Novice Notes)," JA77, The
Cryptogram, American Cryptogram Association, 1977.

[GRO1] DENDAI, DICK," Analysis of Gromark Special,"ND74, The
Cryptogram, American Cryptogram Association, 1974.

[GRO2] BERYL," BERYL'S Pearls: Gromark Primers by hand
calculator," ND91, The Cryptogram, American Cryptogram
Association, 1991.

[GRO3] MARSHEN," Checking the Numerical Key,"JF70, The
Cryptogram, American Cryptogram Association, 1970.

[GRO4] PHOENIX," Computer Column: Gronsfeld -> Gromark,"
"MJ90, The Cryptogram, American Cryptogram
Association, 1990.

[GRO5] PHOENIX," Computer Column: Perodic Gromark," MJ90
The Cryptogram, American Cryptogram Association, 1990.

[GRO6] ROGUE," Cycles for Gromark Running Key," JF75, The
Cryptogram, American Cryptogram Association, 1975.

[GRO7] DUMBO," Gromark Cipher," MA69, JA69, The Cryptogram,
American Cryptogram Association, 1969.

[GRO8] DAN SURR," Gromark Club Solution," MA75, The
Cryptogram, American Cryptogram Association, 1975.

[GRO9] B.NATURAL," Keyword Recovery in Periodic Gromark,"
SO73, The Cryptogram, American Cryptogram Association,
1973.

[GROA] D.STRASSE," Method For Determining Term of Key," MA75,
The Cryptogram, American Cryptogram Association, 1975.

[GROB] CRUX," More On Gromark Keys," ND87, The Cryptogram,
American Cryptogram Association, 1987.

[GROC] DUMBO," Periodic Gromark ," MA73, The Cryptogram,
American Cryptogram Association, 1973.

[GROD] ROGUE," Periodic Gromark ," SO73, The Cryptogram,
American Cryptogram Association, 1973.

[GROE] ROGUE," Theoretical Frequencies in the Gromark," MA74,
The Cryptogram, American Cryptogram Association, 1974.

[GRON] R.L.H., "Condensed Analysis of a Gronsfeld," AM38,
ON38,The Cryptogram, American Cryptogram Association,
1938,1938.

[GRN1] CHARMER, "Gronsfeld," AS44, The Cryptogram, American
Cryptogram Association, 1944.

[GRN2] PICCOLA, "Gronsfeld Cipher," ON35, The Cryptogram,
American Cryptogram Association, 1935.

[GRN3] S-TUCK, "Gronsfeld Cipher," AS44, The Cryptogram,
American Cryptogram Association, 1944.

[GROU] Groueff, Stephane, "Manhattan Project: The Untold
Story of the Making of the Atom Bomb," Little, Brown
and Company,1967.

[GUST] Gustave, B., "Enigma:ou, la plus grande 'enigme de la
guerre 1939-1945." Paris:Plon, 1973.

[GYLD] Gylden, Yves, "The Contribution of the Cryptographic
Bureaus in the World War," Aegean Park Press, 1978.

[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.

[HAFT] Haftner, Katie and John Markoff, "Cyberpunk,"
Touchstine, 1991.

[HAGA] Hagamen,W. D. et. al., "Encoding Verbal Information as
Unique Numbers," IBM Systems Journal, Vol 11, No. 4,
1972.

[HAWA] Hitchcock, H. R., "Hawaiian," Charles E. Tuttle, Co.,
Toyko, 1968.

[HAWC] Hawcock, David and MacAllister, Patrick, "Puzzle
Power!  Multidimensional Codes, Illusions, Numbers,
and Brainteasers," Little, Brown and Co., New York,
1994.

[HEBR] COMET, "First Hebrew Book (of Cryptology)," JF72, The
Association, 1972.

[HELD] , Gilbert, "Top Secret Data Encryption Techniques,"
Prentice Hall, 1993.  (great title..limited use)

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

[HEPP] Hepp, Leo, "Die Chiffriermaschine 'ENIGMA'", F-Flagge,
1978.

[HIDE] Hideo Kubota, " Zai-shi dai-go kokugun tokushu joho
senshi."  unpublished manuscript, NIDS.

[HIER] ISHCABIBEL, "Hieroglyphics: Cryptology Started Here,
MA71, The Cryptogram, American Cryptogram Association,
1971.

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

[HIL1] Hill, L. S. 1929. Cryptography in an Algebraic
Alphabet.  American Mathematical Monthly. 36:306-312.

[HIL2] Hill, L. S.  1931.  Concerning the Linear
Transformation Apparatus in Cryptography.  American
Mathematical Monthly. 38:135-154.

[HINS] Hinsley, F. H.,  "History of British Intelligence in
the Second World War", Cambridge University Press,
Cambridge, 1979-1988.

[HIN2] Hinsley, F. H.  and Alan Strip in "Codebreakers -Story
of Bletchley Park", Oxford University Press, 1994.

[HIN3] Hinsley, F. H., et. al., "British Intelligence in The
Second World War: Its Influence on Strategy and
Operations," London, HMSO vol I, 1979, vol II 1981,
vol III, 1984 and 1988.

[HISA] Hisashi Takahashi, "Military Friction, Diplomatic
Suasion in China, 1937 - 1938," The Journal of
International Studies, Sophia Univ, Vol 19, July,
1987.

[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.

[HODG] Hodges, Andrew, "Alan Turing: The Enigma," New York,
Simon and Schuster, 1983.

[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. )

[HOF1] Hoffman, Lance. J., et. al.," Cryptography Policy,"
Communications of the ACM 37, 1994, pp. 109-17.

[HOLM  Holmes, W. J., "Double-Edged Secrets: U.S. Naval
Intelligence Operations in the Pacific During WWII",
Annapolis, MD: Naval Institute Press, 1979.

[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.

[HYDE] H. Montgomery Hyde, "Room 3603, The Story of British
Intelligence Center in New York During World War II",
New York, Farrar, Straus, 1963.

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

[IC1 ] GIZMO, "Bifid Period Determination Using a Digraphic
Index of Coincidence, JF79, The Cryptogram, American
Cryptogram Association, 1979.

[IC2 ] PHOENIX, "Computer Column: Applications of the Index
of Coincidence, JA90, The Cryptogram, American
Cryptogram Association, 1990.

[IC3 ] PHOENIX, "Computer Column: Digraphic Index of
Coincidence, ND90, The Cryptogram, American Cryptogram
Association, 1990.

[IC4 ] PHOENIX, "Computer Column: Index of Coincidence (IC),
JA82, The Cryptogram, American Cryptogram Association,
1982.

[IC5 ] PHOENIX, "Computer Column: Index of Coincidence,
(correction) MA83, The Cryptogram, American Cryptogram
Association, 1983.

[IMPE] D'Imperio, M. E, " The Voynich Manuscript - An Elegant
Enigma," Aegean Park Press, Laguna Hills, CA, 1976.

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

[ITAL] Italian - English Dictionary, compiled by Vittore E.
Bocchetta, Fawcett Premier, New York, 1965.

[JAPA] Martin, S.E., "Basic Japanese Conversation
Dictionary," Charles E. Tuttle Co., Toyko, 1981.

[JAPH] "Operational History of Japanese Naval Communications,
December 1941- August 1945, Monograph by Japanese
General Staff and War Ministry, Aegean Park Press,
1985.

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

Cryptographic Properties of Arabic, Proceedings of the
Third Saudi Engineering Conference. Riyadh, Saudi
Arabia: Nov 24-27, Vol 2:910-921., 1991.

[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.

[KAH2] Kahn, David, "An Enigma Chronology", Cryptologia Vol
XVII,Number 3, July 1993.

[KAH3] Kahn, David, "Seizing The Enigma: The Race to Break
the German U-Boat Codes 1939-1943 ", Houghton Mifflin,
New York, 1991.

[KARA] Karalekas, Anne, "History of the Central Intelligence
Agency,"  Aegean Park Press, Laguna Hills, CA, 1977.

[KASI] Kasiski, Major F. W. , "Die Geheimschriften und die
Dechiffrir-kunst," Schriften der Naturforschenden
Gesellschaft in Danzig, 1872.

[KAS1] Bowers, M. W., {ZEMBIE} "Major F. W. Kasiski -
Cryptologist," The Cryptogram, XXXI, JF, 1964.

[KAS2] ----, "Kasiski Method," JF64,MA64, The Cryptogram,
American Cryptogram Association, 1964.

[KAS3] PICCOLA, "Kasiski Method for Periodics," JJ35,AS35,
The Cryptogram, American Cryptogram Association, 1935,
1935.

[KAS4] AB STRUSE, "Who was Kasiski?" SO76, The Cryptogram,
American Cryptogram Association, 1976.

[KATZ] Katzen, Harry, Jr., "Computer Data Security,"Van
Nostrand Reinhold, 1973.

[KERC] Kerckhoffs, "la Cryptographie Militaire, " Journel des
Sciences militaires, 9th series, IX, (January and
February, 1883, Libraire Militaire de L. Baudoin &Co.,
Paris.  English trans. by Warren T, McCready of the
University of Toronto, 1964

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

[KONH] Konheim, Alan G., "Cryptography -A Primer" , John
Wiley, 1981, pp 212 ff.

[KORD] Kordemsky, B., "The Moscow Puzzles," Schribners, 1972.

[KOTT] Kottack, Phillip Conrad, "Anthropology: The
Exploration Of Human Diversity," 6th ed., McGraw-Hill,
Inc., New York, N.Y.  1994.

[KOZA] Kozaczuk, Dr. Wladyslaw,  "Enigma: How the German
Machine Cipher was Broken and How it Was Read by the
Allies in WWI", University Pub, 1984.

[KRAI] Kraitchek, "Mathematical Recreations," Norton, 1942,
and Dover, 1963.

[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.

[LAI]  Lai, Xuejia, "On the Design and Security of Block
Ciphers," ETH Series in Information Processing 1,
1992.  (Article defines the IDEA Cipher)

[LAIM] Lai, Xuejia, and James L. Massey, "A Proposal for a
New Block Encryption Standard," Advances in Cryptology
-Eurocrypt 90 Proceedings, 1992, pp. 55-70.

[LAKE] Lakoff, R., "Language and the Women's Place," Harper &
Row, New York, 1975.

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

[LAN1] Langie, Andre, "Cryptography - A Study on Secret
Writings", Aegean Park Press, Laguna Hills, CA. 1989.

[LAN2] Langie, Andre, and E. A. Soudart, "Treatise on
Cryptography, " Aegean Park Press, Laguna Hills, CA.
1991.

[LATI] BRASSPOUNDER, "Latin Language Data, "The Cryptogram,"
July-August 1993.

[LAUE] Lauer, Rudolph F.,  "Computer Simulation of Classical
Substitution Cryptographic Systems" Aegean Park Press,
1981, p72 ff.

[LEAR] Leary, Penn, " The Second Cryptographic Shakespeare,"
Omaha, NE [from author]  1994.

[LEA1] Leary, Penn, " Supplement to The Second Cryptographic
Shakespeare," Omaha, NE [from author]  1994.

[LEAU] Leaute, H., "Sur les Mecanismes Cryptographiques de M.
de Viaris,"  Le Genie Civil, XIII, Sept 1, 1888.

[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! ]

[LENS] Lenstra, A.K. et. al. "The Number Field Sieve,"
Proceedings of the 22 ACM Symposium on the Theory of
Computing," Baltimore, ACM Press, 1990, pp 564-72.

[LEN1] Lenstra, A.K. et. al. "The Factorization of the Ninth
Fermat Number," Mathematics of Computation 61 1993,
pp.  319-50.

[LEWF] Lewis, Frank, "Problem Solving with Particular
Reference to the Cryptic (or British) Crossword and
other 'American Puzzles', Part One," by Frank Lewis,
Montserrat, January 1989.

[LEW1] Lewis, Frank, "The Nations Best Puzzles, Book Six," by
Frank Lewis, Montserrat, January 1990.

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

[LEW1] Lewin, Ronald, 'The American Magic - Codes, ciphers
and The Defeat of Japan', Farrar Straus Giroux, 1982.

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

[LEVI] Levine, J.,  U.S. Cryptographic Patents 1861-1981,
Cryptologia, Terre Haute, In 1983.

[LEV1] Levine, J.  1961.  Some Elementary Cryptanalysis
of Algebraic Cryptography.  American Mathematical
Monthly.  68:411-418

[LEV2] Levine, J.  1961.  Some Applications of High-
Speed Computers to the Case n =2 of Algebraic
Cryptography.  Mathematics of Computation.  15:254-260

[LEV3] Levine, J. 1963.  Analysis of the Case n =3 in
Algebraic Cryptography With Involuntary Key Matrix
With Known Alphabet.  Journal fuer die Reine und
Angewante Mathematik.  213:1-30.

[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.

[LYN1] Lynch, Frederick D., "An Approach To Cryptarithms,"
ACA, 1976.

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

[MACI] Macintyre, D., "The Battle of the Atlantic," New York,
Macmillan, 1961.

1972.

[MAGN] Magne, Emile, Le plaisant Abbe de Boisrobert, Paris,
Mecure de France, 1909.

[MANN] Mann, B.,"Cryptography with Matrices," The Pentagon,
Vol 21, Fall 1961.

[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 a 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.

[MAST] Lewis, Frank W., "Solving Cipher Problems -
Cryptanalysis, Probabilities and Diagnostics," Aegean
Park Press, Laguna Hills, CA, 1992.

[MAU]  Mau, Ernest E., "Word Puzzles With Your
Microcomputer," Hayden Books, 1990.

[MAVE] Mavenel, Denis L.,  Lettres, Instructions
Diplomatiques et Papiers d' Etat du Cardinal
Richelieu, Historie Politique, Paris 1853-1877
Collection.

[MAYA] Coe, M. D., "Breaking The Maya Code," Thames and
Hudson, New York, 1992.

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

[MELL] Mellen G.  1981. Graphic Solution of a Linear
Transformation Cipher. Cryptologia. 5:1-19.

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

[MERK] Merkle, Ralph, "Secrecy, Authentication and Public Key
Systems," Ann Arbor, UMI Research Press, 1982.

[MER1] Merkle, Ralph, "Secure Communications Over Insecure
Channels," Communications of the ACM 21, 1978, pp.
294-99.

[MER2] Merkle, Ralph and Martin E. Hellman, "On the Security
of Multiple Encryption ," Communications of the ACM
24, 1981, pp. 465-67.

[MER3] Merkle, Ralph and Martin E. Hellman, "Hiding
Information and Signatures in Trap Door Knapsacks,"
IEEE Transactions on Information Theory 24, 1978, pp.
525-30.

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

[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.

[MRAY] Mrayati, Mohammad, Yahya Meer Alam and Hassan al-
Tayyan., Ilm at-Ta'miyah wa Istikhraj al-Mu,amma Ind
al-Arab. Vol 1. Damascus: The Arab Academy of
Damascus.,
1987.

[MULL] Mulligan, Timothy," The German Navy Examines its
Cryptographic Security, Oct. 1941, Military affairs,
vol 49, no 2, April 1985.

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

[NBS]  National Bureau of Standards, "Data Encryption
Standard," FIPS PUB 46-1, 1987.

[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.

[NICX] Nichols, R. K., Keynote Speech to A.C.A. Convention,
"Breaking Ciphers in Other Languages.," New Orleans,
La., 1993.

[NICK] Nickels, Hamilton, "Codemaster: Secrets of Making and
Breaking Codes," Paladin Press, Boulder, CO., 1990.

[NIHL] PHOENIX," Computer Column: Nihilist Substitution,"
MA88,  The Cryptogram, American Cryptogram
Association, 1988.

[NIH1] PHOENIX," Computer Column: Nihilist Substitution,"
MJ88,  The Cryptogram, American Cryptogram
Association, 1988.

[NIH2] PHOENIX," Computer Column: Nihilist Substitution,"
JA88,  The Cryptogram, American Cryptogram
Association, 1988.

[NIH3] PHOENIX," Computer Column: Nihilist Substitution,"
JA89,  The Cryptogram, American Cryptogram
Association, 1989.

[NIH4] FIDDLE and CLEAR SKYS," FIDDLE'S slide for Nihilist
Number Substitution," ON48,  The Cryptogram, American
Cryptogram Association, 1948.

[NIH5] RIG R. MORTIS," Mixed Square Nihilist," JA60, The
Cryptogram, American Cryptogram Association, 1960.

[NIH6] PICCOLA," Nihilist Number Cipher," AS37, The
Cryptogram, American Cryptogram Association, 1937.

[NIH7] PICCOLA," Nihilist Transposition," DJ38, The
Cryptogram, American Cryptogram Association, 1938.

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

[NORW] Marm, Ingvald and Sommerfelt, Alf, "Norwegian," Teach
Yourself Books, Hodder and Stoughton, London, 1967.

[NSA]  NSA's Friedman Legacy - A Tribute to William and
Elizabeth Friedman, NSA Center for Cryptological

[NSA1] NMasked Dispatches: Cryptograms and Cryptology in
American History, 1775 -1900. Series 1, Pre World War
I Volume I, National Security Agency, Central Security
Service, NSA Center for Cryptological History, 1993.

[OHAV] OHAVER, M. E., "Solving Cipher Secrets," Aegean Park
Press, 1989.

[OHA1] OHAVER, M. E., "Cryptogram Solving," Etcetera Press,
1973.

[OKLA] Andre, Josephine and Richard V. Andree,
"Cryptarithms," Unit One, Problem Solving and Logical
Thinking, University of Oklahoma, Norman, Ok.  Copy
No: 486, 1976.

[OKLI] Andre, Josephine and Richard V. Andree, " Instructors
Manual For Cryptarithms," Unit One, Problem Solving
and Logical Thinking, University of Oklahoma, Norman,
Ok.  Copy No: 486, 1976.

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

[OTA]  "Defending Secrets, Sharing Data: New Locks and Keys
for Electronic Information," Office of Technology
Assessment, 1988.

[OZK ] OZ,"Variation in Letter Frequency with Cipher Length
or Where Did All Those K's Come From? ," SO59, The
Cryptogram, American Cryptogram Association, 1959.

[PEAR] "Pearl Harbor Revisited," U.S. Navy Communications
Intelligence, 1924-1941, U.S. Cryptological History
Series, Series IV, World War II, Volume 6, NSA CSS ,
CH-E32-94-01, 1994.

[PECK] Peck, Lyman C., "Secret Codes, Remainder Arithmetic,
and Matrices," National Counsil of Teachers of
Mathematics, Washington, D.C. 1971.

[PERR] Perrault, Charles, Tallement des Reaux, Les
Historiettes, Bibliotheque del La Pleiade, Paris 1960,
pp 256-258.

[PGP]  Garfinkel, Simson, "PGP: Pretty Good Privacy,"
O'reilly and Associates, Inc. Sebastopol, CA. 1995.

[PHL ] PHIL,"System Identification by General Frequencies,"
AM48, The Cryptogram, American Cryptogram Association,
1948.

[PHIL] Phillips, H., "My Best Puzzles in Logic and
Reasoning," Dover, 1961.

[PIER] Pierce, Clayton C., "Cryptoprivacy", 325 Carol Drive,
Ventura, Ca. 93003, 1994.

[PIE1] Pierce, Clayton C., "Privacy, Cryptography, and Secure
Communication ", 325 Carol Drive, Ventura, Ca. 93003,
1977.

[POLY] Polya, G., "Mathematics and Plausible Reasoning,"
Princeton Press, 1954.

[POL1] Polya, G., "How To Solve It.," Princeton Press, 1948.

[POPE] Pope, Maurice, "The Story of Decipherment: From
Egyptian Hieroglyphic to Linear B., Thames and Hudson
Ltd., 1975.

[PORT] Barker, Wayne G. "Cryptograms in Portuguese," Aegean
Park Press, Laguna Hills, CA., 1986.

[POR1] Aliandro, Hygino, "The Portuguese-English Dictionary,"
Pocket Books, New York, N.Y., 1960.

[POUN] Poundstone, William, "Biggest Secrets," Quill
Publishing, New York, 1993. ( Explodes the Beale
Cipher Hoax.)

[PRIC] Price, A.,"Instruments of Darkness: the History of
Electronic Warfare, London, Macdonalds and Janes,
1977.

[PROT] "Protecting Your Privacy - A Comprehensive Report On
Eavesdropping Techniques and Devices and Their
Corresponding Countermeasures," Telecommunications
Publishing Inc., 1979.

[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.

[RAND] Randolph, Boris, "Cryptofun," Aegean Park Press, 1981.

[RB1]  Friedman, William F., The Riverbank Publications,
Volume 1,"   Aegean Park Press, 1979.

[RB2]  Friedman, William F., The Riverbank Publications,
Volume 2,"   Aegean Park Press, 1979.

[RB3]  Friedman, William F., The Riverbank Publications,
Volume 3,"   Aegean Park Press, 1979.

[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma
Cipher" published in vol 6, #1, Jan 1982 Cryptologia
pp 1-37.

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[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'",
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[RIVE] Rivest, Ron, "Ciphertext: The RSA Newsletter 1, 1993.

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[ROAC] Roach, T., "Hobbyist's Guide To COMINT Collection and
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[ROBO] NYPHO, The Cryptogram, Dec 1940, Feb, 1941.

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[RYP1] A B C, "Adventures in Cryptarithms (digital maze),"
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[RYP2] CROTALUS "Analysis of the Classic Cryptarithm,"MA73,
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[RYP3] CLEAR SKIES "Another Way To Solve Cryptarithms,"DJ44,
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[RYP4] CROTALUS "Arithemetic in Other Bases (Duodecimal
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[RYP5] LEDGE, "Basic Patterns in Base Eleven and Twelve
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[RYP6] COMPUTER USER, "Computer Solution of Cryptarithms,"
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[RYPA] APEX DX, "Cryptarithm Line of Attack," ND91, The
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[RYPB] HUBBUBBER and CROTALUS, "Cryptarithm Observations,"
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[RYPC] CROTALUS, "Cryptarithms and Notation," JF73, The
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[RYPD] JUNKERL, "Cryptarithms: The digital root method,"
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[RYPE] CROTALUS, "Divisibility by Eleven," ND89, The
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[RYPF] S-TUCK, "Double Key Division," JJ43, The Cryptogram,
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[RYPG] NEOTERIC, "Duo-Decimal Cryptarithms," AM40, The
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[RYPH] QUINTUPLEX, "Duo-Decimal Cryptarithms," JJ40, The
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[RYPI] FIDDLE, "Exhausitive for Three," JF59, The Cryptogram,
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[RYPJ] ---, "Finding the Zero In Cryptarithms," DJ42, The
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[RYPK] FILM-D, "Greater than Less than Diagram for
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[WILL] Williams, Eugenia, "An Invitation to Cryptograms,"
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[YARD] Yardley, Herbert, O., "The American Black Chamber,"
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[YOUS] Youshkevitch, A. P., Geschichte der Mathematik im
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[YUKI] Yukio Nishihara, "Kantogan tai-So Sakusenshi," Vol
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[ZIM]  Zim, Herbert S., "Codes and Secret Writing." William
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[ZEND] Callimahos, L. D.,  Traffic Analysis and the Zendian
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[ZYZZ] ZYZZ,"Sinkov's Frequency Matching," JA93, The
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