## Lesson 15: Statistical Attacks

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CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI

July 01, 1996

LECTURE 15

STATISTICAL ATTACKS

SUMMARY

Lecture 15 considers the role and influence that statistics
and probability theory exert on the cryptanalysis of unknown
ciphers.  We develop our subject by the following references:
[FRE3], [SINK], [MAST], [ELCY], [GLEA], [KULL].

DISCUSSION

As you may know, William F. Friedman and Dr. Solomon Kullback
were the first Americans to apply Probability Theory and
Applied Statistics to the Science of Cryptanalysis. Their
achievements were so dynamic that American Crypee's  were
able to read the secret messages of many of the Foreign
Governments that it dealt with. [YARD]

SCOPE

We shall look at three tests: Kappa test for coincidences,
Chi test or cross product test for superimposition, and Phi
test for monoalphabeticity.  We will briefly touch on
Gleason's logarithmic weighting scheme for determination of
number of letters to differentiate a transposition.  The
References and Resource section is substantially broadened
with nearly 150 more choice plums.

BASIC THEORY OF COINCIDENCES

We have already looked at a table of Phi Values For
Monoalphabetic and Digraphic Text By Kullback in Lecture 1.
We have also studied various Phi values for Xenocrypts
in Lecture 5. We found that the probability is related to
coincidences and that it is of significance when we
investigate repetitions of letters in a cipher.

We know that the probability of monographic coincidence (1)
of random text employing a 26 letter alphabet is 0.0385 , (2)
in English telegraphic plain text is 0.0667.  We have defined
these values as Kr and Kp respectively.

One of the most important techniques in cryptanalysis is that
of applying the Kappa Test or Test of Coincidences.  The most
important purpose for this test is to ascertain whether two
or more sequences are correctly superimposed.  Correct means
the sequences are so arranged to facilitate or make possible
a solution.  The Kappa test has the following theoretical
basis the following circumstances:

(1) If any two rather lengthy sequences of characters are
superimposed, it will be found that as successive pairs
of letters are brought into vertical juxtaposition, that
in a certain number of cases the two superimposed letters
will coincide,

(2) If we are dealing with random text (26 alphabet) there
will be 38 or 39 cases of coincidence per 1000 pairs of
letters examined because Kr = 0.0385.

(3) If we are dealing with plain text (English) there will be
66 or 67 cases of coincidence per 1000 pairs of letters
examined because Kp = 0.0667.

(4) If the superimposed sequences are wholly monoalphabetic
encipherments of plain text by the same cipher alphabet,
there will be 66 or 67 cases of coincidence per 1000
pairs of letters examined because in monoalphabetic
substitution there is a fixed or unvarying relation
between plain text and cipher text, so that for
statistical purposes the cipher text behaves just as if
it were normal plain text.

(5) Even if the two superimposed sequences are polyalphabetic
in character, there still will be 66 or 67 cases of
coincidence or identity per 1000 pairs of letters
examined provided the two sequences really belong to the
same cryptographic system and are superimposed at the
proper point with respect to the keying sequence.

(6) This last point may be seen in the two polyalphabetic
messages below:  They have been enciphered poly-
alphabetically by the same two primary components sliding
against each other.  The two messages begin at the same
point in the keying sequence.  Consequently, they are
identically enciphered, letter for letter, the only
differences between them is due to differences in plain
text.

No. 1

Alpha   16 21 13 5 6 4 17 19 21 21 2 6 3 6 13 13 1 7 12 6
Plain   W  H  E  N I N T  H  E  C  O U R S E  L  O N G M
Cipher  E  Q  N  B T F Y  R  C  X  X L Q J N  Z  O Y A W

No. 2

Alpha   16 21 13 5 6 4 17 19 21 21 2 6 3 6 13 13 1 7 12 6
Plain   T  H  E  G E N E  R  A  L  A B S O L  U  T E L Y
Cipher  P  Q  N  T U F B  W  D  J  L Q H Y Z  P  T M Q I

Note, that (a) in every case in which two superimposed cipher
letters are the same, the plain text letters are identical
and (b)  in every case in which two superimposed cipher
letters are the different, the plain text letters are
different.  In such a system, even though the cipher alphabet
changes from letter to letter, the number cases of identity
or coincidence in the two members of a pair of superimposed
cipher letters will still be about 66 or 67 per thousand
cases examined, because the two members of each pair of
superimposed letters are in the same alphabet and it has been
seen in (4) that in monoalphabetic cipher text K is the same
as for plain text, viz, 0.667.  The fact that in this case
each monoalphabet contains just two letters does not affect
the theoretical value of K (Kappa) and whether the actual
number of coincidences agrees closely with the expected
number based upon Kp = 0.0667 depends upon the lengths of the
two superimposed sequences.  Messages No's 1 and 2 are said
to be superimposed correctly , that is brought into proper
juxtaposition with respect to the keying sequences.

(7) Now change the situation by changing the juxtaposition to
an incorrect superimposition with respect to the keying
sequence.

No. 1

Alpha   16 21 13 5 6 4 17 19 21 21 2 6 3 6 13 13 1 7 12 6
Plain   W  H  E  N I N T  H  E  C  O U R S E  L  O N G M
Cipher  E  Q  N  B T F Y  R  C  X  X L Q J N  Z  O Y A W

No. 2

Alpha     16 21 13 5 6 4 17 19 21 21 2 6 3 6  13 13 1 7
Plain      T  H  E G E N E  R  A  L  A B S O   L  U  T E
Cipher     P  Q  N T U F B  W  D  J  L Q H Y   Z  P  T M

It is evident that the two members of every pair are not in
the same cipher alphabets and any identical letters after
superimposition is strictly accidental. Actually the number
of repetitions will approximate Kr = 0.0385.

Note again, that in every case in which two superimposed
cipher letters are the same, the plain text letters are
not identical and in every case in which two superimposed
cipher letters are the different, the plain text letters are
no always different.  Look at the superimposed T(cipher)'s
representing two different plain text letters and that the S
in "COURSE" gives the value J (cipher) and in the word
ABSOLUTELY gives H (cipher).   It should be clear that an
incorrect superimposition by two different plain-text letters
enciphered by two different alphabets may "by chance" produce
identical cipher letters, which on superimposition yield
coincidence but have no external indications as to
dissimilarity in plain text equivalents.  This incorrect
superimposition will coincide by a value of Kr = 0.0385.

(8) Note the two Z's and they represent the plain text L.
This occurred because the same cipher alphabet came into
play by chance twice to encipher the same plain text
letter both times.  This may distort the Kr value for
some systems.

(9) In general, in the case of correct superimposition the
probability of identity or coincidence is Kp = 0.0667; in
the case of incorrect superimposition, the probability is
greater than or equal to Kr = 0.0385.  The Kappa test,
aka coincidence test is defined by these values.

APPLYING THE KAPPA TEST

When we say Kp = 0.0667, this means that in a 1000 cases
where two letters are drawn at random from a large volume of
plain text, we should expect 66 or 67 cases of two letters to
coincide or be identical.  Nothing is specified what these
letters shall be; they can be two Z's or two E's.  Another
way is to consider that at random 6.67% of the comparisons
made will yield coincidences. So for 2000 examinations, we
expect 2000 x 6.67% = 133.4 coincidences [ use integers and
round down to 133].  Or 20,000 comparisons means 1,334
coincidences.

A more practical approach is to find the ratio of observed
number of coincidences to the total number of cases in
question that may occur, i.e. the total number of comparisons
of superimposed letters.  When the ratio is closer to 0.0667
than 0.0385 the correct superimposition has been found.  This
is true because both members of each pair of superimposed
letters belong to the same monoalphabet and therefore the
probability of their coinciding is 0.067; whereas, in the
case of incorrect superimposition, each pair belongs to
different monoalphabets and the probability of their
coinciding approaches 0.0385 rather than 0.0667.

To use the Kappa test requires calculating the total number
of comparisons in a given case and the actual number of
coincidences in the case under consideration. When two
messages are superimposed, the total number of comparisons
made equals the number of superimposed letters. When more
than two messages are superimposed in a superimposition
diagram (Lecture 13) it is necessary to calculate the number
of comparisons based on the number of letters in the column.

n letters  =  n(n-1)/2  pairs or comparisons,
in column

For a column of 3 letters , there are 3(2)/2 = 3 comparisons.
We compare the 1st with the 2nd, 2nd with 3rd and 1st with
3rd columns.  The more general probability formula is

nCr = n!/r!(n-r)!

where we determine the number of combinations of n different
things taken r at a time.  For two letters, r is always 2,
so n!/r!(n-r)! is the same as

n(n-1)(n-2)!/2(n-2)!

becomes   n(n-1)/2

with the cancellation of terms using (n-2)!.

RULE

The number of comparisons per column times the number of
columns in the superimposition diagram of letters gives the
total number of comparisons.  The extension to this reasoning
is where the superimposition diagram involves columns of
various lengths, then we add together  the number of
comparisons for columns of different lengths to obtain a
grand total.  Table 15-1 shows the number of letters in a
column versus the number of comparisons calculated.  [FRE3]

Table 15 -1

Number of    Number of      Number of    Number of
letters in   comparisons    letters in   comparisons
column                      column

2             1             16            120
3             3             17            136
4             6             18            153
5             10            19            171
6             15            20            190
7             21            21            210
8             28            22            231
9             36            23            253
10            45            24            276
11            55            25            300
12            66            26            325
13            78            27            351
14            91            28            378
15            105           29            406
30            435

In ascertaining the number of coincidences in the case of a
column containing several letters, we still use the n(n-1)/2
formula, only in this case,  n is the number of identical
letters in the column. The reasoning is essentially the same
as above.  The total number of coincidences is the sum of the
number of coincidences for each case of identity.

Given the column:

C
K
B
K
Z
K
C
B
B
K

There are 10 letters with 3B's, 2C's 4K's and 1 Z. The 3B's
yield 3 coincidences, the 2 C's yield 1 coincidence, the 4
K's yield 6 coincidences. The sum is 3 + 1 + 6 = 10
coincidences in 45 comparisons = 0.2222

ENCIPHERMENT WITH SAME KEY BUT DIFFERENT INITIATION POINTS

In Lecture 13, I ended with the note that several messages
enciphered by the same keying sequence but each beginning at
a different point presented a challenge.  The best attack is
that by superimposition and the Kappa test is used to
correctly line up the messages with respect to each other.

It is understood that the messages may be shifted relative to
each other at many points of superimposition but their is
only one point of superimposition for each message which
corresponds to monoalphabetic columnar superimposition of the
cipher text.

The method:

(1) Number the message according to their lengths.

(2) Fix message 1, message 2 is placed under it so that the
first pair of letters coincide.

(3) Examine, calculate total number of cases in which
superimposed letters are identical, thus the observed
number of coincidences. The total number of superimposed
pairs is calculated and multiplied by 0.0667 to find the
expected number of coincidences.

(4) If the observed number is considerably below the expected
number, or if the ratio of the observed number of
coincidences to the total is closer to 0.0385 than
0.0667, then the superimposition is wrong and we shift
message 2 one letter to the left.

(5) Repeat steps (3) - (4) until the correct superimposition
is found.

(6) Test message 3 against message 1 and then against message
2.

(7) Continue the process until all the messages are lined up
correctly.

Computers are a big help in this process.

EXAMINE OF KAPPA TEST

Given 4 messages of 30 intercepted using a long enciphered
keying sequence:

Message 1

PGLPN  HUFRK  SAUQQ  AQYUO  ZAKGA  EOQCN
PRKOV  HYEIU  YNBON  NFDMW  ZLUKQ  AQAHZ
MGCDS  LEAGC  JPIVJ  WVAUD  BAHMI  HKORM
LTFYZ  LGSOG  K.                   [101]

Message 2

CWHPK  KXFLU  MKURY  XCOPH  WNJUW  KWIHL
OKZTL  AWRDF  GDDEZ  DLBOT  FUZNA  SRHHJ
NGUZK  PRCDK  YOOBV  DDXCD  OGRGI  RMICN
HSGGO  PYAOY  X.                   [101]

Message 3

WFWTD  NHTGM  RAAZG  PJDSQ  AUPFR  OXJRO
HRZWC  ZSRTE  EEVPX  OATDQ  LDOQZ  HAWNX
THDXL  HYIGK  VYZWX  BKOQO  AZQND  TNALT
CNYEH  TSCT.                       [99]

Message 4

TULDH  NQEZZ  UTYGD  UEDUP  SDLIO  LNNBO
NYLQQ  VQGCD  UTUBQ  XSOSK  NOXUV  KCYJX
CNJKS  ANGUI  FTOWO  MSNBQ  DBAIV  IKNWG
VSHIE  P                           [96]

Superimpose messages 1 and 2.

*     *      *
No. 1      PGLPN  HUFRK  SAUQQ  AQYUO  ZAKGA  EOQCN
No. 2      CWHPK  KXFLU  MKURY  XCOPH  WNJUW  KWIHL

*
No. 1      PRKOV  HYEIU  YNBON  NFDMW  ZLUKQ  AQAHZ
No. 2      OKZTL  AWRDF  GDDEZ  DLBOT  FUZNA  SRHHJ

*                       *      *
No. 1      MGCDS  LEAGC  JPIVJ  WVAUD  BAHMI  HKORM
No. 2      NGUZK  PRCDK  YOOBV  DDXCD  OGRGI  RMICN

*
No. 1      LTFYZ  LGSOG  K.                   [101]
No. 2      HSGGO  PYAOY  X.                   [101]

The number of comparisons is 101 x 0.0667 = 7 coincidences
which is less than the observed 8.  Nice start but
suspicious.  Shifting one letter to right the number of
coincidences is 4. One more shift = 3.  Then:

*      *    *
No. 1      PGLPNHUFRKSAUQQAQYUOZAKGAEOQCN
No. 2         CWHPKKXFLUMKURYXCOPHWNJUWKW

*                       *
No. 1      PRKOVHYEIUYNBONNFDMWZLUKQAQAHZ
No. 2      IHLOKZTLAWRDFGDDEZDLBOTFUZNASR

*        **
No. 1      MGCDSLEAGCJPIVJWVAUDBAHMIHKORM
No. 2      HHJNGUZKPRCDKYOOBVDDXCDOGRGIRM

*
No. 1      LTFYZLGSOGK.
No. 2      ICNHSGGOPYAOYX.         [98]

Now 98 x 0.0667 = 6.5366   versus 9 coincidences or 30% more
than the first comparison.  The first test was accidental.
The jump is normal from incorrect to correct.  The correct
superimposition is either 100% correct or incorrect.

Friedman suggests that tests be made first to the right and
then to the left, one letter at a time for best efficiency.
[FRE3]

It is possible to systematize our investigation by testing
three or four messages at a time.

We make a diagram where the number of coincidences are
tallied with all three messages:

1     2     3
-----------------
1|   x     9     3
|
2|   x     x     3
|
3|   x     x     x

The number of tallies in cell 1-2 is 9 as examined.  A column
which shows identical letters in messages 1 and 3 yields a
tally in 1-3, between 2 and 3 goes to 2-3 and so forth.  Only
when a superimposition yields three identical letters in a
column is a tally to be recorded in 1-3 or 1-2 (3
coincidences.

So adding message 3 to the investigation:

*
No. 1      PGLPNHUFRKSAUQQAQYUOZAKGAEOQCN
No. 2         CWHPKKXFLUMKURYXCOPHWNJUWKW
No. 3      WFWTDNHTGMRAAZGPJDSQAUPFROXJRO

*   *            *
No. 1      PRKOVHYEIUYNBONNFDMWZLUKQAQAHZ
No. 2      IHLOKZTLAWRDFGDDEZDLBOTFUZNASR
No. 3      HRZWCZSRTEEEVPXOATDQLDOQZHAWNX

*      *
No. 1      MGCDSLEAGCJPIVJWVAUDBAHMIHKORM
No. 2      HHJNGUZKPRCDKYOOBVDDXCDOGRGIRM
No. 3      THDXLHYIGKVYZWXBKOQOAZQNDTNALT

No. 1      LTFYZLGSOGK.
No. 2      ICNHSGGOPYAOYX.
No. 3      CNYEHTSCT.

so:

1     2     3
-----------------
1|   x     9     3
|
2|   x     x     3
|
3|   x     x     x

Successive number of columns are examined and coincidences
(of messages 1 and 3 and 2 and 3) are tabulated.  We find:

Combination  Total Number  Number of Coincidences
of                                  Delta
Comparisons   Expected  Observed       %

1 - 3        99           ~ 7        3           -57
2 - 3        96           ~ 6        3           -50
1- 2- 3      293           ~ 20      15           -21

A correct superimposition for one of the three combinations
may yield such good results as to mask  the bad results for
the other two combinations.

We shift message 3 one space to the right with the following
results:

*
No. 1      PGLPNHUFRKSAUQQAQYUOZAKGAEOQCN
No. 2         CWHPKKXFLUMKURYXCOPHWNJUWKW
No. 3       WFWTDNHTGMRAAZGPJDSQAUPFROXJR

*   *               *   *
No. 1      PRKOVHYEIUYNBONNFDMWZLUKQAQAHZ
No. 2      IHLOKZTLAWRDFGDDEZDLBOTFUZNASR
No. 3      OHRZWCZSRTEEEVPXOATDQLDOQZHAWN

*    *
No. 1      MGCDSLEAGCJPIVJWVAUDBAHMIHKORM
No. 2      HHJNGUZKPRCDKYOOBVDDXCDOGRGIRM
No. 3      XTHDXLHYIGKVYZWXBKOQOAZQNDTNAL

*    *
No. 1      LTFYZLGSOGK.
No. 2      ICNHSGGOPYAOYX.
No. 3      TCNYEHTSCT.

1     2     3
-----------------
1|   x     9     10
|
2|   x     x     7
|
3|   x     x     x

Combination  Total Number  Number of Coincidences
of                                  Delta
Comparisons   Expected  Observed       %

1 - 3        99           ~ 7       10           +43
2 - 3        97           ~ 6        6             0
1- 2- 3      294           ~ 20      25           +25

The results are very good.  We add the fourth message.

No. 1      PGLPNHUFRKSAUQQAQYUOZAKGAEOQCN
No. 2         CWHPKKXFLUMKURYXCOPHWNJUWKW
No. 3       WFWTDNHTGMRAAZGPJDSQAUPFROXJR
No. 4        TULDHNQEZZUTYGDUEDUPSDLIOLNN

No. 1      PRKOVHYEIUYNBONNFDMWZLUKQAQAHZ
No. 2      IHLOKZTLAWRDFGDDEZDLBOTFUZNASR
No. 3      OHRZWCZSRTEEEVPXOATDQLDOQZHAWN
No. 4      BONYLQQVQGCDUTUBQXSOSKNOXUVKCY

No. 1      MGCDSLEAGCJPIVJWVAUDBAHMIHKORM
No. 2      HHJNGUZKPRCDKYOOBVDDXCDOGRGIRM
No. 3      XTHDXLHYIGKVYZWXBKOQOAZQNDTNAL
No. 4      JXCNJKSANGUIFTOWOMSNBQDBAIVIKN

No. 1      LTFYZLGSOGK.
No. 2      ICNHSGGOPYAOYX.
No. 3      TCNYEHTSCT.
No. 4      WGVSHIEP.

1     2     3     4
----------------------
1|   x     9     10    7
|
2|   x     x     7     7
|
3|   x     x     x     5
|
4|   x     x     x     x

Combination  Total Number  Number of Coincidences
of                                  Delta
Comparisons   Expected  Observed       %

1 - 3        96           ~ 6        7           +16
2 - 3        95           ~ 6        7           +16
3 - 4        96           ~ 6        5           -16
1,2,3,4       581           ~39       44           +10

This is actually the correct group of superimpositions.
Testing another message 4 movement to right shows us the
picture.

No. 1      PGLPNHUFRKSAUQQAQYUOZAKGAEOQCN
No. 2         CWHPKKXFLUMKURYXCOPHWNJUWKW
No. 3       WFWTDNHTGMRAAZGPJDSQAUPFROXJR
No. 4         TULDHNQEZZUTYGDUEDUPSDLIOLN

No. 1      PRKOVHYEIUYNBONNFDMWZLUKQAQAHZ
No. 2      IHLOKZTLAWRDFGDDEZDLBOTFUZNASR
No. 3      OHRZWCZSRTEEEVPXOATDQLDOQZHAWN
No. 4      NBONYLQQVQGCDUTUBQXSOSKNOXUVKC

No. 1      MGCDSLEAGCJPIVJWVAUDBAHMIHKORM
No. 2      HHJNGUZKPRCDKYOOBVDDXCDOGRGIRM
No. 3      XTHDXLHYIGKVYZWXBKOQOAZQNDTNAL
No. 4      YJXCNJKSANGUIFTOWOMSNBQDBAIVIK

No. 1      LTFYZLGSOGK.
No. 2      ICNHSGGOPYAOYX.
No. 3      TCNYEHTSCT.
No. 4      NWGVSHIEP.

1     2     3     4
----------------------
1|   x     9     10    3
|
2|   x     x     7     3
|
3|   x     x     x     2
|
4|   x     x     x     x

Combination  Total Number  Number of Coincidences
of                                  Delta
Comparisons   Expected  Observed       %

1 - 3        96           ~ 6        3           -50
2 - 3        96           ~ 6        3           -50
3 - 4        96           ~ 6        2           -83
1,2,3,4       582           ~39       33           -18

SUBSEQUENT SOLUTION STEPS

These four messages were enciphered by a long keying
sequence. We now have found the correct superimposition of
the four messages. Therefore, the text has been reduced to
monoalphabetic columnar form and can be solved.  What was not
given on this example was that the enciphering device was a
U. S. Army Cipher Disk and that the key was intelligent as
well as the alphabets are reversed standard.

It doesn't matter to the Kappa test what kind of cipher
alphabets were used or whether or not the key is random or
intelligent.  We try our favorite technique - the probable
word on message 1 of DIVISION.

Ciphertext      P G L P N H U F R K S A U Q Q
Assumed Plain   D I V I S I O N
Resultant Key   S O G X F

nope, shift one letter right.

Ciphertext      P G L P N H U F R K S A U Q Q
Assumed Plain   . D I V I S I O N
Resultant Key   . J T K

nope, shift one more, and one and finally to the end with no
resultant intelligent key.

Ciphertext      P G L P N H U F R K S A U Q Q
Assumed Plain           R E G I M E N T N O
Resultant Key           E L A N D O F T H E

which suggests LAND of T(HE) which yields REGIMENT NO. More
assumptions yield an E before LAND and the cipher text
yielding IS for the plain.  The process continues one letter
at a time and checking the cipher versus the plain for
reconstructive clues.

We can use all four messages to gives us clues by multiple
superimposition.

Key                     E L A N D O F T
No 1 Ciphertext      P G L P N H U F R K S A U Q Q
Plain                   R E G I M E N T

No 2 Ciphertext            C W H P K K X F L U M K
Plain                   I E L D T R A I

No 3 Ciphertext        W F W T D N H T G M R A A Z
Plain                   L I N G K I T C

No 4 Ciphertext          T U L D H N Q E Z Z U T Y
Plain                   T I T A N K G U

We see  No. 2 gives us FIELD TRAIN, No 3 has ROLLING KITCHEN,
and No 4 with ANTITANK GUN.  These words yield additional
letters.  If the key is unintelligent text we use the
messages against each rather than against the key.

UNKNOWN SEQUENCES

The previous example assumed a known cipher alphabet.  When
it is not known, Data for solution by indirect symmetry by
detection of isomorphs cannot be expected, for isomorphs may
not be produced by the system. Solution can be reached only
if there is sufficient text to permit analysis of columns for
superimposition diagram. Large amount of text yields
repetitions and the basis for probable word assumption.
After establishment of a few values for cipher text letters
does indirect symmetry come into play.  Each column requires
15 -20 letters minimum. These can be studied statistically
and if two columns have similar characteristics, they may be
combined using the cross product test.

RUNNING KEY PRINCIPLE

The running - key principle may be interesting in principle
but difficult in practice. Mistakes in encipherment or
transmission, essentially decrease the likely hood of the
correct decipherment. The running Key does improve
cryptographic security but the mechanical details involved in
the production, reproduction, and distribution of such keys
represents a formidable challenge - enough to destroy the
effectiveness of the system for practical purposes
(voluminous communication).

Suppose a basic unintelligible, random sequence of keying
characters which is not derived from the interaction of two
or more shorter keys and which NEVER repeats is employed only
ONCE as a key for encipherment.  Can such a cryptogram be
solved. No. No method of attack will solve this because the
system is not uniquely solvable.

Two things are required for solution: the logical answer must
be offered and it must be unique. The Bacon-Shakespeare
"cryptographers tend to overlook the latter issue.
To attempt to solve a cryptogram enciphered as previously
described is like solving an equation in two unknowns with
absolutely no data available for solution but the solution
itself.  The key is one unknown and the plain text is the
other.  Any one quantity may be chosen and yield a viable
result without the required uniqueness constraint being
observed.  There are an infinite number of solutions
possible.

The problem is better defined when the running key
constitutes intelligent test, or if it is used to encipher
more than one message, or if it is the secondary result of
the interaction of two or more short primary keys which go
thru cycles themselves.   The additional information in these
cases are enough to meet the uniqueness constraint.

CROSS-PRODUCT TEST OR CHI [X]

The KAPPA test is used to prepare data for analysis. It
circumvents the polyalphabetic obstacle. It moves the
solution from polyalphabetic to monoalphabetic terms. The
solution can be reached if their is some cryptographic
relationship between the columns, or the letters can be
combined into a single frequency distribution.

The amount of data has to be sufficient for comparison
purposes and this depends on the type of cipher alphabets
involved.  Although the superimposition diagram may be
composed of many columns, often only a relatively small
number of different cipher alphabets are put into play.
The number of times that a secondary alphabet is employed is
directly related to the key text or number of keying elements
in the sequence.

In the running-key cipher using a long phrase or book as a
key, the key is intelligible text and it follows that the
secondary alphabets will be employed with frequencies
directly  related to the respective frequencies of occurrence
of letters of plain text. The key letter 'E' alphabet should
be most frequent, 'T' next and so forth. J, K, Q, X, Z are
improbable, so the cryptanalyst usually handles no more than
19-20 secondary alphabets.

It is possible to study the various distributions for the
columns of the superimposition diagram with the view of
assembling those distributions which belong to the same
cipher alphabet, say 'E', thus making the determination of
values easier in a combined distribution.

If the key is random text, and assuming sufficient text
within the columns, the columnar frequency distributions may
afford the opportunity to amalgamate a large number of small
distributions into a smaller number of larger distributions.
This is known as matching and we use the Cross-Product or Chi
Test, aka X test.

The Chi test is used to identify distributions which belong
to the same cipher alphabet.  It is used when the amount of
data is not very large.

DERIVATION OF CHI TEST [KULL]

The theory of monographic coincidence in plain text was
originally developed by Friedman and applied in his technical
paper written in 1925 dealing with his solution of messages
enciphered by a cryptographic machine known as the "Herbern
Electric Super-Code." The paper is among the Riverbank
Publications in 1934.

The probability of coincidence of two A's in plain text is
the square of the probability of occurrence of the single
letter A in such text.  Samething with B's through Z's.
The sum  of these squares for all letters of the alphabet as
shown in Table 15-2, is found to be 0.0667.  This is almost
double the combined probability of random text for hitting
two random text letters coincidentally or:

26 letters x 1/26 x 1/26 = 1/26 = 0.0385 = Kr

Table 15-2

Letter       Frequency in     Probability     Square of
1000 Letters     of Occurrence   Probability
Separately      of Separate
Occurrence
-----------------------------------------------------------
A          73.66          0.0737           0.0054
B           9.74           .0097            .0001
C          30.68           .0307            .0009
D          42.44           .0424            .0018
E         129.96           .1300            .0169
F          28.32           .0283            .0008
G          16.38           .0164            .0003
H          33.88           .0339            .0012
I          73.52           .0735            .0054
J           1.64           .0016            .0000
K           2.96           .0030            .0000
L          36.42           .0364            .0013
M          24.74           .0247            .0006
N          79.50           .0795            .0063
O          75.28           .0753            .0057
P          26.70           .0267            .0007
Q           3.50           .0035            .0000
R          75.76           .0758            .0057
S          61.16           .0612            .0037
T          91.90           .0919            .0084
U          26.00           .0260            .0007
V          15.32           .0153            .0002
W          15.60           .0156            .0002
X           4.62           .0046            .0000
Y          19.34           .0193            .0004
Z            .98           .0010            .0000
---------------------------------------------------------
Total         1,000.00        1.0000           0.0667

We have seen this value before as Kp.  It is the probability
that any two letters selected at random in a large volume of
normal English plain text will coincide.

Given a 50 letter plain-text distribution:

3   1 1 7 1   2 3     1 2 5 6     2 5 6 2   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

The number of pairings that can be made are n (n-1)/2 =

(50 x 49)/2 = 1,225 comparisons.  According to the theory of
coincidences, there should be 1,225 x 0.0667 = 81.7065 or
approximately 82 coincidences of single letters.  We look at
the distribution and finds there are 83 for a very close
agreement.  [N(N-1)/2]

3   1 1 7 1   2 3      1 2 5  6      2 5  6  2   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
3+0+0+1+21+0+0+1+3+0+0+0+1+10+15+0+0+1+10+15+1+0+1+0+0+0=83

If N is the total number of letters in the distribution, then
the number of comparisons is N(N-1)/2 and the expected number
of coincidences may be written:

.0067N(N-1)/2

or       (.0067N**2 - 0.0667N)/2      eq. I

If we let Fa = number of occurrences of A in the foregoing
distribution, the number of coincidences for letter A is
Fa(Fa-1)/2. Similarly for B, we have Fb(Fb-1)/2. The total
number of coincidences for the distribution is:

Fa(Fa-1)/2 +Fb(Fb-1)/2+...+Fz(Fz-1)/2.

Let Fa = any letter A..Z and d = the sum of all terms that
follow it. The distribution d(Fa**2-Fa)/2 represents the
actual coincidences.

Although derived from different sources we equate the terms.

d(Fa**2-Fa)/2 = (.0067N**2 - 0.0667N)/2

and dFa = N

d(Fa**2-Fa) = (.0067N**2 - 0.0667N)

dFa**2 - N  = (.0067N**2 - 0.0667N)

dFa**2  = .0067N**2 + 0.9333N         eg. II

Equation II tells us the sum of the squares of the absolute
frequencies of a distribution is equal to 0.0667 times the
square of the total number of letters in the distribution,
plus 0.933 times the total number of letters in the
distribution.  We let S2 replace dFa**2.

Suppose two monoalphabetic distributions pertain to the same
cipher alphabet. If they are to be correctly combined into a
single distribution, the latter must still be monoalphabetic.
We use subscripts 1 and 2 to indicate the distributions in
question.   So:

d(Fa1+Fa2)**2 = .0067(N1+N2)**2 + 0.9333(N1+N2)

expanding terms:

dFa1**2 +2dFa1Fa2 +dFa2**2 =0.0667(N1**2 +2N1N2 + N2**2) +
.9333N1 +.9333N2      eq. III

dFa1**2  = .0067N1**2 + 0.9333N1

dFa2**2  = .0067N2**2 + 0.9333N2

and rearranging:

.0667N1**2 +.9333N1 +2dFa1Fa2 + .0667 N2**2 + .9333N2 =

.0667(N1**2 +2N1N2 +N2**2) + .9333N1 +.9333N2

further reducing:

2dFa1Fa2 = 0.667 (2N1N2)

finally:

dFa1Fa2 = 0.667                      eq. IV
-------
N1N2

This equation permits the establishment of an expectant value
for the sum of products of the corresponding frequencies of
the two distributions being considered for amalgamation. The
Chi test or Cross-product test is based on Equation IV.

Given two distributions to be matched:

1 4   3   1     1     1     1     3 2 2 1   1 3   2
F1 - 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

2       3     1   1     1 1     3 1 1         1 2
F2 - 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 juxtapose the frequencies for convenience.

N1 = 26
Fa1    1 4   3   1     1     1     1     3 2 2 1   1 3   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
Fa2      2       3     1   1     1 1     3 1 1         1 2
N2 = 17
Fa1Fa2 0 8 0 0 0 3 0 0 1 0 0 0 0 0 1 0 0 9 2 2 0 0 0 0 0 4
d=30

N1N2 = 26 x 17 = 442

dFa1Fa2    30
-------  = --   = 0.0711
N1N2      442

or 442 x 0.0667 = 28.15 expected value versus 30. The two
distributions very probably belong together.

To point out the effectiveness of the correct Chi test
placement, we look at the example but juxtaposed one interval
to the left.

N1=26
1 4   3   1     1     1     1     3 2 2 1   1 3   2
F1 - 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
F2 - 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
2       3     1   1     1 1     3 1 1         1 2
N2=17
Fa1Fa2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 3 0 0
dFa1Fa2=2+3+2+3= 10

dFa1Fa2     10
--------  = ---- =  0.226
N1N2       442

Thus, if the two distribution pertain to the same primary
components then they are not properly superimposed.  The Chi
test may be applied also to cases where two or more frequency
distributions must be shifted relatively in order to find the
correct superimposition.  The problem determines whether we
use direct superimposition or shifted superimposition of the
second distribution in question.

APPLYING THE CHI TEST TO PROGRESSIVE-ALPHABET SYSTEM

We assume for this example that the secondary alphabets were
derived from the interaction of two identical mixed primary
components. The cipher alphabet is based on HYDRAYLIC...Z
sequence shifted one letter to the right for each encipher-
ment.  Based on Figure 15-1, the horizontal sequences are all
identical and shifted relatively. The letters inside the
square are plain-text letters.

Instead of letters in the cells of the square we tally the
normal frequencies of the letters occupying the respective
cells.  For the first 3 rows we have:

1 . . . 5 . . . . 10 . . . . 15 . . . . 20 . . . . . 26

A 7 3 4 8 3 1 12 3 2     3 8 7  3   6 9 1 1      3 2 4  8
B 112 3 2     3 8 7  3   6 9 1 1      3 2 4  8 7 3 8 3  1
C 3 112 3 2     3 8 7  3   6 9  1 1     3 2 4  8 7 3 4  8

The shift required in this case is 5 to the right to match up
A and B.  Note that amount of displacement, or number of
intervals, the B sequence must be shifted to make it match A
sequence corresponds exactly to the distance between the
letters A and B in the primary cipher component.

..... A U L I C B ......
0 1 2 3 4 5

The fact that the primary plain component is identical with
the primary cipher component is coincidental.  The
displacement interval is being measured on the cipher
component.

The Given Cipher message is written into a 26 column (26
alphabets) square rather than the standard 5 letter groups.

FIGURE 15-1

ALPHABET NO

1   5    10   15   20    26
A | AULICBEFGJKMNOPQSTVWXZHYDR
B | BEFGJKMNOPQSTVWXZHYDRAULIC
C | CBEFGJKMNOPQSTVWXZHYDRAULI
D | DRAULICBEFGJKMNOPQSTVWXZHY
E | EFGJKMNOPQSTVWXZHYDRAULICB
F | FGJKMNOPQSTVWXZHYDRAULICBE
C  H | HYDRAULICBEFGJKMNOPQSTVWXZ
I  I | ICBEFGJKMNOPQSTVWXZHYDRAUL
P  J | JKMNOPQSTVWXZHYDRAULICBEFG
H  K | KMNOPQSTVWXZHYDRAULICBEFGJ
E  L | LICBEFGJKMNOPQSTVWXZHYDRAU
R  M | MNOPQSTVWXZHYDRAULICBEFGJK
N | NOPQSTVWXZHYDRAULICBEFGJKM
O | OPQSTVWXZHYDRAULICBEFGJKMN
L  P | PQSTVWXZHYDRAULICBEFGJKMNO
E  Q | QSTVWXZHYDRAULICBEFGJKMNOP
T  R | RAULICBEFGJKMNOPQSTVWXZHYD
T  S | STVWXZHYDRAULICBEFGJKMNOPQ
E  T | TVWXZHYDRAULICBEFGJKMNOPQS
R  U | ULICBEFGJKMNOPQSTVWXZHYDRA
V | VWXZHYDRAULICBEFGJKMNOPQST
W | WXZHYDRAULICBEFGJKMNOPQSTV
X | XZHYDRAULICBEFGJKMNOPQSTVW
Y | YDRAULICBEFGJKMNOPQSTVWXZH
Z | ZHYDRAULICBEFGJKMNOPQSTVWX

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

A frequency distribution square is compiled, each column of
the text forming a separate distribution in columnar form in
the square.  See Figure 15-2.  Note the size of each
distribution on the right side of the square under N.

The Chi test is applied to the horizontal rows in the square.
Since the test is statistical, it is more reliable as the
size of the distribution increases. We choose the V and W
distributions because they have the greatest total number of
tallies at 53 and 52 occurrences, respectively.

Figure 15-2

1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26 N
A  1       1   1 4 1 3 1   1       3   2       3 3 1    25
B        6 3   3 7 1 1   1   1 2   1 2 1 8     1 4      43
C  2 3   2 1 3 1 1 1 1   1 2   4 2   1 5 2 6 4   2   1  45
D  1 4   4     2     2 7      1 1  2   1 3 3 1   1 1    34
E  2 3 2 1       4   2     1 4 2   3 2 1   2 1   1 3 1  35
F  2   4 2   3 7 1 1 2 1     6 3 9 3   2       2 1 1 1  51
G  3 6     1 1 1     1 1 4 2   1 4 3   1 1   3 2   3 2  39
H    5     7       4       1   3 4   2 6     2 2   2 1  38
I  4     2 3 2   2 2 1 3 1   1 4       1     3 2 8 4 2  45
J    1 4 3 4 4 3 6 1     3   4 2   1 3 2   4       2 2  50
K    3       2   3 3   4       6 2 2 2 2 1 2 2     2 1  37
L  2 2   1 1     1 2 2 7 4 1       2 1   1 1 1   3 1 1  33
M  2 1   1 3 1 5   1 3     2 1       2   4 7     3 1    37
N  3   2 5           1 7 1 3 2   3       1     1 1   4  34
O  2 3 1   6 1         2 2 1 5 4   2     1 3 1   2 2    38
P  4       2 9   1 1     1 1   1 1 1 9 5 1 2     1 3    43
Q      5 3 1   1 1 1 3   2 2     3     2 5 1 7 5   3    45
R  5 2 1 1 2   1 4 1 1 3 1   2 1   3 4   3 4 1 3   1 2  46
S  1   2       2     1     5 4 1   4   1       3 6 1 8  39
T  3 2 6 1   2     2 1 1 1 2     6 4     3     2 1   1  39
U  1   3 3 2 4 2   2     1 2 1   1   1   2 1 2 4 1      33
V  1   2     2 6 4 8     7     2 1 1 1 1 1   6 4    2 4 53
W  1 1 5 3   1     2 8 1 7 6   1     2 3   2 1 2    4 2 52
X    4   1 3 2 1   5     3 2 3 2 3 1 2     1        1 3 37
Y    1 1     3 3   1 4     4 2   1 4 2 4 3   5 1    2 3 44
Z      2 1     1 1   3 1   2 2     2 2     1   3 3    3 27
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26

The results of three relative displacements are given.

Test 1

FV  1   2     2 6 4 8     7     2 1 1 1 1 1   6 4   2 4
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FW    4 2 1 1 5 3   1     2 8 1 7 6   1     2 3   2 1 2
24. . 1 . . . 5 . . . .10 . . . .15 . . . .20 . . .
FVFW      4     1018  8    14    14 6   1      18     2 8

NV = 53, NW =52
dFVFW = 103

dFVFW = 103
-----   ---  = 0.037      nok.
NVNW    2756

Test 2

FV  1   2     2 6 4 8     7     2 1 1 1 1 1   6 4   2 4
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FW  2 3   2 1 2   4 2 1 1 5 3   1     2 8 1 7 6   1
. .20 . . . 24. . 1 . . . 5 . . . .10 . . . .15 . .
FVFW  2         4  16 16   35     2     2 8 1  36

NV = 53, NW =52
dFVFW = 122

dFVFW = 122
-----   ---  = 0.044      nok.
NVNW    2756

Test 3

FV  1   2     2 6 4 8     7     2 1 1 1 1 1   6 4   2 4
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FW  3   1     2 8 1 7 6   1     2 3   2 1 2   4 2 1 1 5
. 5 . . . .10 . . . .15 . . . .20 . . . . .26 1 . .
FVFW  3   2     4 48 4 56   7     4 3   2 1 2   24 8 2 20

NV = 53, NW =52
dFVFW = 190

dFVFW = 190
-----   ---  = 0.069      OK!
NVNW    2756

More tests would indicate that we have found the best
correlation for these two cipher alphabets. Therefore, the
primary cipher component has the letters V and W in these
positions.  The 4th cell of the W distribution must be placed
under the 1 st cell of the V distribution per Test 3.

1 2 3 4
. . . V . . W . . .

The next best row is F with 51 occurrences.  We must test
this row against V, W, and V+W.  Test 4,5 and 6 show the
correct superimpositions for the F row.  Note that  the
computer can be a big time help in this evaluation.

Test 4

FV  1   2     2 6 4 8     7     2 1 1 1 1 1   6 4   2 4
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FF  1 1 2 1     6 3 9 3   2       2 1 1 1 2   4 2   3 7
. .10 . . . .15 . . . .20 . . . . .26 1 . . . 5 . .
FVFF  1   4      36 12 72   14      2 1 1 1 2  24 8   6 28

NV = 53, NF =51
dFVFF = 212

dFVFW = 212
-----   ---  = 0.078
NVNF    2703

Test 5

FW  1 1 5 3   1     2 8 1 7 6   1     2 3   2 1 2   4 2
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FF    3 7 1 1 2 1     6 3 9 3   2       2 1 1 1 2   4 2
5 . . . .10 . . . .15 . . . .20 . . . . .26 1 . . .
FVFF    3 35    2      48 3 63 18 2       6   2 1 4  16 4

NW = 52, NF =51
dFWFF = 210

dFWFF = 210
-----   ---  = 0.078
NWNF    2703

Test 6

FV+W  4   3     414 515 6   8    4  4 1 3 2  3 10 6 1 3  9
1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
FF  1 1 2 1     6 3 9 3   2       2 1 1 1  2  4 2   3  7
. .10 . . . .15 . . . .20 . . . . . 26 1 . . . 5 . .
FV+W  4   6      84 15 35 18 16     8 1 3 21 6  40 12 9 63
*FF
N(V+W) = 105, NF = 51
dF(W+V)FF = 422

dF(W+V)FF = 422
--------    ---  = 0.079
N(W+V)NF    5355

This test yield the sequence:

1 2 3 4 5 6 7 8 9

V . . W . . . F .

As the work progresses, we use smaller and smaller
distributions. This decrease in information is
counterbalanced by the number of superimpositions being
reduced as the primary cipher alphabet comes to the surface.

The completely reconstructed primary cipher component (both
plain and cipher were specified as identical) is:

1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
V A L W N O X F B P Y R C Q Z I G S E H T D J U M K

In practice, the matching process would be interrupted after
a few letters of the primary component were retrieved and the
skeleton of a few words became apparent.

We ascertain the initial position for the primary cipher
component and decipher the cryptogram.

1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
1  W G J J M M M J X E D G C O C F T R P B M I I I K Z
W I T H T H E I M P R O V E M E N T S I N T H E A I

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

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

...... and so forth.

The interesting point is that all the tallies in the
frequency square were made of cipher letters occuring in the
cryptogram, and the tallies represented their actual
occurences.  We compared cipher alphabet to cipher alphabet.
The plain text letters were held as unknown through out the
process.

CRACKING THE PROGRESSIVE CIPHER USING INDIRECT SYMMETRY

What happens when we do not have enough data to foster the
statistical attack?  We can use indirect symmetry because of
certain phenomena arising from the mechanics of the
progressive cipher encipherment method itself.

Take:

Plain    HYDRAULICBEFGJKMNOPQSTVWXZ
Cipher   FBPYRCQZIGSEHTDJUMKVALWNOX

Encipher FIRST BATTALION by the progressive method sliding
the cipher component to the left one interval after each
encipherment.:

1 2 3 4 5 6 7 8 91011121314
Plain    F I R S T B A T T A L I O N
Cipher   E I C N X D S P Y T U K Y Y
Index    F E B C I L U A R D Y H Z X
shift(-)   1 2 3 4 5 6 7 8 910111213

Repeated letters in the text are two I's, three T's and two
A's. Lets look at them:

F I R S T B A T T A L I O N
1 2 3 4 5 6 7 8 91011121314
Plain    . I . . . . . . . . . I . .
Cipher   . I . . . . . . . . . K . .
Plain    . . . . T . . T T . . . . .
Cipher   . . . . X . . P Y . . . . .
Plain    . . . . . . A . . A . . . .
Cipher   . . . . . . S . . T . . . .

The two I's are 10 letters apart in both the plain and cipher
components.  Since the cipher component is displaced one step
after each encipherment, two identical letters n intervals
apart in the plain text must yield cipher equivalents which
are n intervals apart in the cipher component.  This leads to
the probable word and indirect symmetry attack on the
progressive cipher.

A second flaw concerns the repeated cipher letters. Look at
the three Y's.

1 2 3 4 5 6 7 8 91011121314
Plain    . . . . . . . . T . . . O N
Cipher   . . . . . . . . Y . . . Y Y

Reference to the plain component shows that the N O . . . T
is reversed in order with respect to the plain text.  The
intervals are correct.  Since the cipher component is shifted
one to the left each encipherment, two identical letters n
intervals apart in the cipher text must yield plain text
equivalents which are n intervals apart in the cipher
component.   If the cipher is displaced to the left than the
order of the plain is logically reversed.

the military greeting COMMANDING GENERAL FIRST ARMY (probable
words) the data yielded by this assumption is:

IKMKI  LIDOL  WLPNM  VWPXW  DUFFT
FNIIG  XGAMX  CADUV  AZVIS  YNUNL ...

1.......................26

Plain (assumed) COMMANDINGGENERALFIRSTARMY
Cipher          IKMKILIDOLWLPNMVWPXWDUFFTF

Set up the decryption square in Figure 15-3.

Figure 15-3

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     I
2                             K
3                         M
4                         K
5 I
6                            L
7       I
8                  D
9                            O
10             L
11             W
12           L
13                           P
14        N
15                                  M
16 V
17                       W
18          P
19                 X
20                                  W
21                                    D
22                                      U
23 F
24                                  F
25                          T
26                                                F

Applying indirect symmetry to the above square gives:

1 . . . 5 . . . .10 . . . .15 . . . .20 . . . . . 26
Plain  A     L I C   E F G   M N O     S             Y D R
Cipher     M K V . L W N O . F . P . . . . . I . . . . T
D . . . . . . . . . . M

Setting C (plain) = I (cipher) for the first encipherment,
the 8th value, I (plain) = D (cipher)  which yields D and
eventually X.  We use the partial sequences to unlock other
letters.  Using the word ARMY we open the gaps some more.

1 2 3 4 5 6 7 8 9 10 11 12
Plain      N I I G X G A M X  C  A  D
Cipher     . I L . . . . E O  .  .  R

The next word after ARMY might be WILL.  We then insert the
W in the plain and G in the Cipher.

The presence of MMM, WWW, FFF in the cipher might be a short
word used several time.. hmm how about THE?? replacing any
one of the triplets with THE, applying indirect symmetry, we
may have a wedge.

MACHINE CRYPTOGRAPHY

The principles discussed in the previous paragraph may be
used with progressive systems in which the interval is > 1
and with modifications to those intervals which are irregular
but follow a pattern such as 1-2-3, 1-2-3, ... or 2-5-7-3-1,
2-5-7-3-1- and so on. The latter type of progression is
encountered in certain mechanical cryptographs.  [FRE3]

THE PHI TEST h FOR MONOALPHABETICITY

The Chi test is based on the general theory of coincidences
and the probability constants Kp and Kr. Now two
monoalphabetic distributions when correctly combined will
yield a single distribution which still will be
monoalphabetic in character.  The Phi (h) test is used to
confirm that a distribution is in fact alphabetic.

DERIVATION Of PHI h TEST

number of pairs of letters for comparison purposes is:

N(N-1)/2    for N letters

from the discussion on the Chi (a) test we found that the
expected value of Fa(Fa-1)/2 +..+Fz(Fz-1) for A...Z is equal
to the theoretical number of coincidences of two letters to
be expected in N(N-1)/2  for N letters, which for normal
English plaintext is  Kp x N(N-1)/2 and for random text is Kr
x N(N-1)/2.

d Fi (Fi-1)    = E(hp)  = Kp x N(N-1)

for i= A to Z            for plain text

d Fi (Fi-1)    = E(hr)  = Kr x N(N-1)

for i= A to Z            for random text

E(a) means the average or expected value of the expression in
parenthesis, Kp = 0.0667 for normal English plain text, Kr =
0.0385 for random English text (26 letters).

Example 1:

Is the following enciphered monoalphabetically:

1     1 2 3 4 2     1       4 2   1           1   3  N=25
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(ao) = 1x0+1x0+2x1+3x2+4x3+2x1+1x0+4x3+2x1+1x0+1x0+3x2=
2+6+12+2+12+2+6 = 42     o = observed

E(ap) = Kp x N(N-1) = 0.0667 x 25 x 24 = 40    plain

E(ar) = Kr x N(N-1) = 0.0385 x 25 x 24 = 23.1  random

Since the E(ao) =42 is closer to E(ap) = 40, the distribution
is most likely monoalphabetic.

Example 2:

Y O U I J   Z M M Z Z  M R N Q C   X I Y T W   R G K L H

The distribution is

1       1 1 2 1 1 1 3 1 0 2 1 2   1 1   1 1 2 3 N=25
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

d Fi(Fi-1) = 18

Since E(ar) is closer to E(ao) the enciphement is probabably
polyalphabetic to suppress the frequency distribution. The
message was enciphered actually by 25 alphabets used in
sequence.

LOGARITHMIC WEIGHT: CHI SQUARED TEST

Gleason discusses an important application of the theory of
testing hypothesis. Given a number of messages, some of which
are transposed English text and some are flat text. We want
to develop a test for picking out the transpositions, and to
accomplish this is possible to frame a statistical hypothesis
concerning each message.  Gleason discusses a 5 step
procedure to 1) obtain probability information, 2) calculate
its critical region, 3) differentiate by weighted logs 4)
calculate the values of alpha and beta statistical inference
5) examine the normal distribution for given values of alpha
and beta.  The answer tells us how many letters to examine at
some level of certainty to determine if we are dealing with a
transposition.  Chapter 13 Problem 1 gives a reasonable look
at the process. [GLEA]  Problems 2 and 3 look at the concept
of Bayesian probability applied to transposition problems and
should be of interest.

WITZEND'S TABLES TO AID CRYPTARITHM SOLUTION

WITZEND has graciously produced several cryptarithmic tables
to aid in solution for problems involving bases from ten to
sixteen.  They are given as Tables 15 - 3 through 15 - 9 and
should ease the pain.

Table 15 - 3
DECIMAL - BASE 10

0  1  2  3  4  5  6  7  8  9
----------------------------
0 | 0  1  2  3  4  5  6  7  8  9
1 | 1  2  3  4  5  6  7  8  9 10
2 | 2  3  4  5  6  7  8  9 10 11
3 | 3  4  5  6  7  8  9 10 11 12
4 | 4  5  6  7  8  9 10 11 12 13
5 | 5  6  7  8  9 10 11 12 13 14
6 | 6  7  8  9 10 11 12 13 14 15
7 | 7  8  9 10 11 12 13 14 15 16
8 | 8  9 10 11 12 13 14 15 16 17
9 | 9 10 11 12 13 14 15 16 17 18

MULTIPLICATION

0  1  2  3  4  5  6  7  8  9
----------------------------
0 | 0  0  0  0  0  0  0  0  0  0
1 | 0  1  2  3  4  5  6  7  8  9
2 | 0  2  4  6  8 10 12 14 16 18
3 | 0  3  6  9 12 15 18 21 24 27
4 | 0  4  8 12 16 20 24 28 32 36
5 | 0  5 10 15 20 25 30 35 40 45
6 | 0  6 12 18 24 30 36 42 48 54
7 | 0  7 14 21 28 35 42 49 56 63
8 | 0  8 16 24 32 40 48 56 64 72
9 | 0  9 18 27 36 45 54 63 72 81

N     1   2    3     4     5      6      7       8       9
----------------------------------------------------
N Square 1   4    9    16    25     36     49      64      81
N Cube   1   8   27    64   125    216    343     512     729
N Fourth 1  16   81   256   625   1296   2401    4096    6561
N Fifth  1  32  243  1024  3125   7776  16807   32768   59049
N Sixth  1  64  729  4096 15625  46656 117649  262144  531441
N Sevnth 1 128 2187 16384 78125 279936 823543 2097152 4782969

X         2      4     5     5     5     5       6       8
Y         6      6     3     5     7     9       6       6
X * Y     12    24    15    25    35    45      36      48

Table 15 - 4
UNDECIMAL - BASE 11

1  2  3  4  5  6  7  8  9  A
----------------------------
1 | 2  3  4  5  6  7  8  9  A 10
2 | 3  4  5  6  7  8  9  A 10 11
3 | 4  5  6  7  8  9  A 10 11 12
4 | 5  6  7  8  9  A 10 11 12 13
5 | 6  7  8  9  A 10 11 12 13 14
6 | 7  8  9  A 10 11 12 13 14 15
7 | 8  9  A 10 11 12 13 14 15 16
8 | 9  A 10 11 12 13 14 15 16 17
9 | A 10 11 12 13 14 15 16 17 18
A |10 11 12 13 14 15 16 17 18 19

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A
----------------------------
1 | 1  2  3  4  5  6  7  8  9  A
2 | 2  4  6  8  A 11 13 15 17 19
3 | 3  6  9 11 14 17 1A 22 25 28
4 | 4  8 11 15 19 22 26 2A 33 37
5 | 5  A 14 19 23 28 32 37 41 46
6 | 6 11 17 22 28 33 39 44 4A 55
7 | 7 13 1A 26 32 39 45 51 58 64
8 | 8 15 22 2A 37 44 51 59 66 73
9 | 9 17 25 33 41 4A 58 66 74 82
A | A 19 28 37 46 55 64 73 82 91

N     1    2    3    4    5     6     7     8    9    A
-------------------------------------------------
N Square 1    4    9   15   23    33    45    59   74   91
N Cube   1    8   25   59  104   187   292   427  603  82A

Table 15 - 5
DUODECIMAL - BASE 12

1  2  3  4  5  6  7  8  9  A  B
-------------------------------
1 | 2  3  4  5  6  7  8  9  A  B 10
2 | 3  4  5  6  7  8  9  A  B 10 11
3 | 4  5  6  7  8  9  A  B 10 11 12
4 | 5  6  7  8  9  A  B 10 11 12 13
5 | 6  7  8  9  A  B 10 11 12 13 14
6 | 7  8  9  A  B 10 11 12 13 14 15
7 | 8  9  A  B 10 11 12 13 14 15 16
8 | 9  A  B 10 11 12 13 14 15 16 17
9 | A  B 10 11 12 13 14 15 16 17 18
A | B 10 11 12 13 14 15 16 17 18 19
B |10 11 12 13 14 15 16 17 18 19 1A

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A  B
-------------------------------
1 | 1  2  3  4  5  6  7  8  9  A  B
2 | 2  4  6  8  A 10 12 14 16 18 1A
3 | 3  6  9 10 13 16 19 20 23 26 29
4 | 4  8 10 14 18 20 24 28 30 34 38
5 | 5  A 13 18 21 26 2B 34 39 42 47
6 | 6 10 16 20 26 30 36 40 46 50 56
7 | 7 12 19 21 2B 36 41 48 53 5A 65
8 | 8 14 20 28 34 40 48 54 60 68 74
9 | 9 16 23 30 39 46 53 60 69 76 83
A | A 18 26 34 42 50 5A 68 76 84 92
B | B 1A 29 38 47 56 65 74 83 92 A1

N     1   2   3   4   5   6    7   8     9    A   B
---------------------------------------------
N Square 1   4   9  14  21  30   41   54   69   84   A1
N Cube   1   8  23  54  A5 160  247  368  569  874  92B

X         2      3     3     4     4     6       6       6
Y         6      4     8     3     6     2       4       6
X * Y    10     10    20    10    20    10      20      30

X         6      6     8     8     8     9       9       2
Y         8      A     3     6     9     4       8       1
X * Y    40     50    20    40    60    30      60       2

X         2      3     3     3     4     4       4       4
Y         7      1     5     9     1     4       7       A
X * Y    12      3    13    23     4    14      24      34

Table 15 - 6
TERDECIMAL - BASE 13

1  2  3  4  5  6  7  8  9  A  B  C
----------------------------------
1 | 2  3  4  5  6  7  8  9  A  B  C 10
2 | 3  4  5  6  7  8  9  A  B  C 10 11
3 | 4  5  6  7  8  9  A  B  C 10 11 12
4 | 5  6  7  8  9  A  B  C 10 11 12 13
5 | 6  7  8  9  A  B  C 10 11 12 13 14
6 | 7  8  9  A  B  C 10 11 12 13 14 15
7 | 8  9  A  B  C 10 11 12 13 14 15 16
8 | 9  A  B  C 10 11 12 13 14 15 16 17
9 | A  B  C 10 11 12 13 14 15 16 17 18
A | B  C 10 11 12 13 14 15 16 17 18 19
B | C 10 11 12 13 14 15 16 17 18 19 1A
C |10 11 12 13 14 15 16 17 18 19 1A 1B

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A  B  C
----------------------------------
1 | 1  2  3  4  5  6  7  8  9  A  B  C
2 | 2  4  6  8  A  C 11 13 15 17 19 1B
3 | 3  6  9  C 12 15 18 1B 21 24 27 2A
4 | 4  8  C 13 17 1B 22 26 2A 31 35 39
5 | 5  A 12 17 1C 24 29 31 36 3B 43 48
6 | 6  B 15 1B 24 2A 33 39 42 48 51 57
7 | 7 11 18 22 29 33 3A 44 4B 55 5C 66
8 | 8 13 1B 26 31 39 44 4C 57 62 6A 75
9 | 9 15 21 2A 36 42 4B 57 63 6C 78 84
A | A 17 24 31 3B 48 55 62 6C 79 86 93
B | B 19 27 35 43 51 5C 84 78 86 94 A2
C | C 1B 2A 39 48 57 66 75 84 93 A2 B1

N     1  2   3   4   5   6    7   8    9    A    B   C
-------------------------------------------------
N Square 1  4   9  13  1C  2A   3A  4C   63   79   94  B1
N Cube   1  8  21  4C  98 138  205 365  441  5BC  785 A2C

Table 15 - 7

1  2  3  4  5  6  7  8  9  A  B  C  D
-------------------------------------
1 | 2  3  4  5  6  7  8  9  A  B  C  D 10
2 | 3  4  5  6  7  8  9  A  B  C  D 10 11
3 | 4  5  6  7  8  9  A  B  C  D 10 11 12
4 | 5  6  7  8  9  A  B  C  D 10 11 12 13
5 | 6  7  8  9  A  B  C  D 10 11 12 13 14
6 | 7  8  9  A  B  C  D 10 11 12 13 14 15
7 | 8  9  A  B  C  D 10 11 12 13 14 15 16
8 | 9  A  B  C  D 10 11 12 13 14 15 16 17
9 | A  B  C  D 10 11 12 13 14 15 16 17 18
A | B  C  D 10 11 12 13 14 15 16 17 18 19
B | C  D 10 11 12 13 14 15 16 17 18 19 1A
C | D 10 11 12 13 14 15 16 17 18 19 1A 1B
D |10 11 12 13 14 15 16 17 18 19 1A 1B 1C

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A  B  C  D
-------------------------------------
1 | 1  2  3  4  5  6  7  8  9  A  B  C  D
2 | 2  4  6  8  A  C 10 12 14 16 18 1A 1C
3 | 3  6  9  C 11 14 17 1A 1D 22 25 28 2B
4 | 4  8  C 12 16 1A 20 24 28 2C 32 36 3A
5 | 5  A 11 16 1B 22 27 2C 33 38 3D 44 49
6 | 6  C 14 1A 22 28 30 36 3C 44 4A 52 58
7 | 7 10 17 20 27 30 37 40 47 50 57 60 67
8 | 8 12 1A 24 2C 36 40 48 52 5A 64 6C 76
9 | 9 14 1D 28 33 3D 47 52 5B 66 71 7A 85
A | A 16 22 2C 38 44 50 5A 66 72 7C 88 94
B | B 18 25 32 3D 4D 57 64 71 7C 89 96 A3
C | C 1A 28 36 44 52 60 6C 7A 88 96 A4 B2
D | D 1C 2B 3A 49 58 67 76 85 94 A3 B2 C1

N   1  2  3   4   5   6   7   8   9   A   B   C   D
-----------------------------------------------
N **2  1  4  9  12  1B  28  37  48  5B  72  89  A4  C1
N **3  1  8 1D  48  8D 116 1A7 288 3A1 516 6B1 8B6 B2D

X         2      4     6     7     7     7       7       7
Y         7      7     7     2     4     6       8       A
X * Y    10     20    30    10    20    30      40      50

X         7      8     A     C     2     4       6       7
Y         C      7     7     7     8     8       8       3
X * Y    60     40    50    60    12    24      36      17

X         7      7     7     7     7     8       A       C
Y         5      7     9     B     D     8       8       8
X * Y    27     37    47    57    67    48      5A      6C

Table 15 - 8
QUINDECIMAL - BASE 15

1  2  3  4  5  6  7  8  9  A  B  C  D  E
----------------------------------------
1 | 2  3  4  5  6  7  8  9  A  B  C  D  E 10
2 | 3  4  5  6  7  8  9  A  B  C  D  E 10 11
3 | 4  5  6  7  8  9  A  B  C  D  E 10 11 12
4 | 5  6  7  8  9  A  B  C  D  E 10 11 12 13
5 | 6  7  8  9  A  B  C  D  E 10 11 12 13 14
6 | 7  8  9  A  B  C  D  E 10 11 12 13 14 15
7 | 8  9  A  B  C  D  E 10 11 12 13 14 15 16
8 | 9  A  B  C  D  E 10 11 12 13 14 15 16 17
9 | A  B  C  D  E 10 11 12 13 14 15 16 17 18
A | B  C  D  E 10 11 12 13 14 15 16 17 18 19
B | C  D  E 10 11 12 13 14 15 16 17 18 19 1A
C | D  E 10 11 12 13 14 15 16 17 18 19 1A 1B
D | E 10 11 12 13 14 15 16 17 18 19 1A 1B 1C
E |10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A  B  C  D  E
----------------------------------------
1 | 1  2  3  4  5  6  7  8  9  A  B  C  D  E
2 | 2  4  6  8  A  C  E 11 13 15 17 19 1B 1D
3 | 3  6  9  C 10 13 16 19 1C 2A 2E 33 37 3B
4 | 4  8  C 11 15 19 1D 22 26 2A 2E 40 45 4A
5 | 5  A 10 15 1A 20 25 2A 30 35 3A 40 45 4A
6 | 6  C 13 19 20 26 2C 33 39 40 46 4C 53 59
7 | 7  E 16 1D 25 2C 34 3B 43 4A 52 5E 61 68
8 | 8 11 19 22 2A 33 3B 44 4C 55 5D 66 6E 77
9 | 9 13 1C 26 30 39 43 4C 56 60 69 73 7C 86
A | A 15 20 2A 35 40 4A 55 60 6A 75 80 8A 95
B | B 17 23 2E 3A 46 52 5D 69 75 81 8C 98 A4
C | C 19 26 33 40 4C 5E 66 73 80 8C 99 A7 B3
D | D 1B 29 37 45 53 61 6E 7C 8A 98 A7 B4 C2
E | E 1D 2C 3B 4A 59 68 77 86 95 A4 B3 C2 D1

N   1  2  3   4   5   6   7   8   9   A   B   C   D   E
---------------------------------------------------
N **2  1  4  9  11  1A  26  34  44  56  6A  81  99  B4  D1
N **3  1  8 1C  44  85  E6 17D 242 339 46A 5DB 7A3 9B7 C2E

X         3      3     5     5     5     5       6       6
Y         5      A     3     6     9     C       5       A
X * Y    10     20    10    20    30    40      20      40

X         9      9     A     A     A     A       C       C
Y         5      A     3     6     9     C       5       A
X * Y    30     60    20    40    60    80      80      40

X         3      3     5     5     5     5       6       9
Y         6      B     4     7     A     D       B       6
X * Y    40     80    13    23    10    25      35      45
Table 15 - 9
SEXDECIMAL - BASE 16

1  2  3  4  5  6  7  8  9  A  B  C  D  E  F
-------------------------------------------
1 | 2  3  4  5  6  7  8  9  A  B  C  D  E  F 10
2 | 3  4  5  6  7  8  9  A  B  C  D  E  F 10 11
3 | 4  5  6  7  8  9  A  B  C  D  E  F 10 11 12
4 | 5  6  7  8  9  A  B  C  D  E  F 10 11 12 13
5 | 6  7  8  9  A  B  C  D  E  F 10 11 12 13 14
6 | 7  8  9  A  B  C  D  E  F 10 11 12 13 14 15
7 | 8  9  A  B  C  D  E  F 10 11 12 13 14 15 16
8 | 9  A  B  C  D  E  F 10 11 12 13 14 15 16 17
9 | A  B  C  D  E  F 10 11 12 13 14 15 16 17 18
A | B  C  D  E  F 10 11 12 13 14 15 16 17 18 19
B | C  D  E  F 10 11 12 13 14 15 16 17 18 19 1A
C | D  E  F 10 11 12 13 14 15 16 17 18 19 1A 1B
D | E  F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C
E | F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D
F |10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E

MULTIPLICATION

1  2  3  4  5  6  7  8  9  A  B  C  D  E  F
-------------------------------------------
1 | 1  2  3  4  5  6  7  8  9  A  B  C  D  E  F
2 | 2  4  6  8  A  C  E 10 12 14 16 18 1A 1C 1E
3 | 3  6  9  C  F 12 15 18 1B 1E 21 24 27 2A 2D
4 | 4  8  C 10 14 18 1C 20 24 28 2C 30 34 38 3C
5 | 5  A  F 14 19 1E 23 28 2D 32 37 3C 41 46 4B
6 | 6  C 12 18 1E 24 2A 30 36 3C 42 48 4E 54 5A
7 | 7  E 15 1C 23 2A 31 38 3F 46 4D 54 5B 62 69
8 | 8 10 18 20 28 30 38 40 48 50 58 60 68 70 78
9 | 9 12 1B 24 2D 36 3F 48 51 5A 63 6C 75 7E 87
A | A 14 1E 28 32 3C 46 50 5A 64 6E 78 82 8C 96
B | B 16 21 2C 37 42 4D 58 63 6E 79 84 8F 9A A5
C | C 18 24 30 3C 48 54 60 6C 78 84 90 9C A8 B4
D | D 1A 27 34 41 4E 5B 68 75 82 8F 9C A9 B6 C3
E | E 1C 2A 38 46 54 62 70 7E 8C 9A A8 B6 C4 D2
F | F 1E 2D 3C 4B 5A 69 78 87 96 A5 B4 C3 D2 E1

N  1  2  3  4  5  6   7   8   9   A   B   C   D   E   F
-----------------------------------------------------
N **2 1  4  9 10 19 24  31  40  51  64  79  90  A9  C4  E1
N **3 1  8 1B 40 7D D8 157 200 2D9 3E8 533 6C0 895 AB8 D2F

LECTURE 14 SOLUTIONS

14-1. Multiplication (Two words,  0-1) original by EDNASANDE

WOMEN X MEN = UTNNLM + TIWENO + NWTWNN  = NLSMTUWM

0123456789
SLOWMINUET

14-2. Division  (Two words, 0 -9)               MORDASHKA

ATOM / ASK = N; - GNC = IS

O123456789

14-3. Multiplication. (No word, 0-1)             FOMALHAUT

ASAP X  MAB = RITMT  + TMPRY  + PDBYD  =PAYDIRT

0123456789
DBARTMPIYS

14-4. Unidecimal multiplication. (Two words 0-X)  WALRUS

TOUGH X DIG = IDIGDN  + NYYDNG  + UIHDOU  =  DDCUUILN

0123456789X
CLOUDYNIGHT

LECTURE 15 PROBLEMS - Taken from OP- 20 -G course:

15-1.   Naval Text.  Recover Keys.

J Z S S W B P D Z Z L F O M E K Q P D J H C K U M C

A B C O O X M Y S I I G B S G G Y V D S W A J O Q E

K U P W K N J K C C H W O Z Q Q B P Y N V J J O Q E

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

D H U V N K V K C Y Y A L R Q O O Q D N Z C G L R E

K F H Q R N J B.

15-2.  Naval Text.

A U V Z I S Z F B F Y E I R B I O W A O Y J L B L D

D G K U I T T Z B D B E Q I O C J R F W X D Y H G M

S P P I S W Y P F V S Y G G S H Q K L A L Z A Q F N

U T C Q H D G Y L B Z P D V C S J N W G N T P T M S

H J T W C K O C M X Z P Z R R U Y I W H H M E Z F L

O C F I S W L P D N W T Z H H T I R L Y I P N Q F N

U T C Q H D G Y L B Z P D V C S J N W G N T P T M E

O S V B W J B L V X Z P Z R R U Y I W H H P L P F T

R B P G X B U L V N W J P R H I H F Q X L N B L P S

H J T W I J T T Q W E E Q F O I I Z P M B J Q P Y M

D U Q W A T Z O W D C L Z Q M P U K.

REFERENCES / CRYPTOGRAPHIC RESOURCES [updated 01 July 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.

[ANDE] D. Andelman, J. Reeds, On the cryptanalysis of rotor
and substitution-permutation networks. IEEE Trans. on
Inform.  Theory, 28(4), 578--584, 1982.

[ANGL] D. Angluin, D. Lichtenstein, Provable Security in
Crypto-systems: a survey. Yale University, Department
of Computer Science, #288, 1983.

[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.

[AUT4] UBET,"Auto-Transposition Cipher," SO62, The
Cryptogram, American Cryptogram Association, 1962.

[AUT5] BARGE,"Decrypting the Auto-Transposition Cipher,"
ND63, The Cryptogram, American Cryptogram Association,
1963.

[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] Anonymous, "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.

[BAZ1] OZ,"Bazeries Cipher," MA59, The Cryptogram, American
Cryptogram Association, 1959.

[BAZ2] ALII KIONA,"Bazeries Cipher," F35, The Cryptogram,
American Cryptogram Association, 1935.

[BAZ3] ZANAC,"A Poker Player's Method to Solve Bazeries
Ciphers," JF82, The Cryptogram, American Cryptogram
Association, 1982.

[BAZ4] HI-FI,"Bazeries Ciphers Revisited," SO64, The
Cryptogram, American Cryptogram Association, 1964.

[BAZ5] MACHIAVELLI,"Bazeries Cipher - Dutch," ND71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZ6] MACHIAVELLI,"Bazeries Cipher - English," JF71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZ7] MACHIAVELLI,"Bazeries Cipher - French," JF71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZ8] MACHIAVELLI,"Bazeries Cipher - German," MA71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZ9] MACHIAVELLI,"Bazeries Cipher - Italian," JA71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZA] MACHIAVELLI,"Bazeries Cipher - Portuguese," SO71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZB] MACHIAVELLI,"Bazeries Cipher - Spanish," MJ71, The
Cryptogram, American Cryptogram Association, 1971.

[BAZC] MACHIAVELLI,"Bazeries Cipher - Unknown Language,"
MJ72, The Cryptogram, American Cryptogram Association,
1972.

[BAZD] HANO,"Bazeries Cipher - Swedish," JA81, The
Cryptogram, American Cryptogram Association, 1981.

[BAZE] D. STRASSE,"Bazeries Cipher - Esperanto," SO74, The
Cryptogram, American Cryptogram Association, 1974.

[BAZ5] MACHIAVELLI, "Equivalents of 'e' in the Bazeries
Cipher" SO72, The Cryptogram, American Cryptogram
Association, 1972.

[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.

[BEKE] H.  Beker, F. Piper, Cipher Systems. Wiley, 1982.

[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)

[BEN1] John Bennett, Analysis of the Encryption Algorithm
Used in the WordPerfect Word Processing Program.
Cryptologia 11(4), 206--210, 1987.

[BERG] H. A. Bergen and W. J.  Caelli, File Security in
WordPerfect 5.0. Cryptologia 15(1), 57--66, January
1991.

[BETH] T.  Beth, Algorithm engineering for public key
algorithms.  IEEE Selected Areas of Communication,
1(4), 458--466, 1990.

[BIF1] ESP, "4-Square Method for C. M. Bifid," SO92, The
Cryptogram, American Cryptogram Association, 1992.

[BIF2] GALUPOLY, "6X6 Bifid," JA62, The Cryptogram, American
Cryptogram Association, 1962.

[BIF3] DR. CRYPTOGRAM, "Bifid and Trifid Cryptography," MJ59,
The Cryptogram, American Cryptogram Association, 1959.

[BIF4] TONTO, "Bifid Cipher," JJ45, The Cryptogram, American
Cryptogram Association, 1945.

[BIF5] GOTKY, "Bifid Cipher with Literal Indices Only," FM47,
AM47, The Cryptogram, American Cryptogram Association,
1947.

[BIF6] SAI CHESS, "Bifid-ian Timesaver," ON48, The
Cryptogram, American Cryptogram Association, 1948.

[BIF7] LABRONICUS, "Bifid Period by Pattern," ND89, The
Cryptogram, American Cryptogram Association, 1989.

[BIF8] TONTO, "Bifid recoveries," ON50, The Cryptogram,
American Cryptogram Association, 1950.

[BIF9] GIZMO, "Bifid Period Determination Using a Digraphic
Index of Coincidence," JF79, The Cryptogram, American
Cryptogram Association, 1979.

[BIFA] GALUPOLY, "Bifid with Conjugated Matrices," JF60, The
Cryptogram, American Cryptogram Association, 1960.

[BIFB] XAMAN EK, "Bifid Workshop, Part 1 - Encoding a Bifid,"
MA93, The Cryptogram, American Cryptogram Association,
1993.

[BIFC] XAMAN EK, "Bifid Workshop, Part 2 - Problem Setup,"
MJ93, The Cryptogram, American Cryptogram Association,
1993.

[BIFD] XAMAN EK, "Bifid Workshop, Part 3 - Tip Placement,"
JA93, The Cryptogram, American Cryptogram Association,
1993.

[BIFE] XAMAN EK, "Bifid Workshop, Part 4 - Solving a Bifid,"
SO93, The Cryptogram, American Cryptogram Association,
1993.

[BIFF] DUBIOUS and GALUPOLY, " Chi-Square Test for Bifids,"
JA60, The Cryptogram, American Cryptogram Association,
1960.

[BIFG] FIDDLE, "C. M. Bifid, Simplified Solution," MJ73, The
Cryptogram, American Cryptogram Association, 1973.

[BIFH] ZYZZ, "Conjugated Matrix Bifid, Modified Solving
Technique," SO92, The Cryptogram, American Cryptogram
Association, 1992.

[BIFI] X.GOTKY, "Delastelle Bifid Cipher," AS45, The
Cryptogram, American Cryptogram Association, 1945.

[BIFJ] D.MORGAN, "Finding the Period in a Bifid," JJ46, The
Cryptogram, American Cryptogram Association, 1946.

[BIFK] S-TUCK, "Finding the Period in a Bifid," AM46, The
Cryptogram, American Cryptogram Association, 1946.

[BIFL] S-TUCK, "Finding the Period in Bifids," ON44, The
Cryptogram, American Cryptogram Association, 1944.

[BIFM] ROGUE, "General Probabilities of Part Naturals in
Bifid, Trifid" JA70, The Cryptogram, American
Cryptogram Association, 1970.

[BIFN] B.NATURAL, "In Line Bifid Method," MA62, The
Cryptogram, American Cryptogram Association, 1962.

[BIFO] ABC, "Short Cut in a Bifid," SO61, The Cryptogram,
American Cryptogram Association, 1961.

[BIFP] ROGUE, "Specific Probabilities of Part Naturals in
Bifid, Trifid" SO70, The Cryptogram, American
Cryptogram Association, 1970.

[BIFQ] ROGUE, "Split Half Method  For Finding A Period of
Bifid," MA71, The Cryptogram, American Cryptogram
Association, 1971.

[BIFR] ABC, "Twin Bifids - A Probable Word Method," JA62, The
Cryptogram, American Cryptogram Association, 1962.

[BIFS] GALUPOLY, "Twin Bifids," MJ60, JA60, The Cryptogram,
American Cryptogram Association, 1960.

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

[BIHS] E. Biham and A. Shamir, Differential cryptanalysis of
DES-like cryptosystems. Journal of Cryptology, vol.
4, #1, 3--72, 1991.

[BISH] E. Biham, A. Shamir, Differential cryptanalysis of
Snefru, Khafre, REDOC-II, LOKI and LUCIFER. In
Proceedings of CRYPTO '91, ed. by J. Feigenbaum, 156-
-171, 1992.

[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.

[BOYA] J. Boyar, Inferring Sequences Produced by Pseudo-
Random Number Generators. Journal of the ACM, 1989.

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

[BRAG] G. Brassard, Modern Cryptology: a tutorial.  Spinger-
Verlag, 1988.

[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.

[BRIK] E.  Brickell, J. Moore, M. Purtill, Structure in the
S-boxes of DES. In Proceedings of CRYPTO '86, A. M.
Odlyzko ed., 3--8, 1987.

[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.

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

[BROP] L. Brown, J. P ieprzyk, J. Seberry, LOKI - a
cryptographic primitive for authentication and secrecy
applications. In Proceedings of AUSTCRYPT 90, 229--
236, 1990.

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

[BRO1] L. Brown, A proposed design for an extended DES,
Computer Security in the Computer Age.  Elsevier
Science Publishers B.V. (North Holland), IFIP, W. J.
Caelli ed., 9--22, 1989.

[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.

Cryptography," SO55, The Cryptogram, American
Cryptogram Association, 1955.

American Cryptogram Association, 1991.

Cryptogram, American Cryptogram Association, 1989.

[CAEL] H.  Gustafson, E. Dawson, W. Caelli, Comparison of
block ciphers. In Proceedings of AUSCRYPT '90, J.
Seberry and J. Piepryzk eds., 208--220, 1990.

[CAMP] K. W. Campbell, M. J. Wiener, Proof the DES is Not a
Group. In Proceedings of CRYPTO '92, 1993.

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

[CARJ] John Carrol and Steve Martin, The Automated
Cryptanalysis of Substitution Ciphers. Cryptologia
10(4), 193--209, 1986.

[CARL] John Carrol and Lynda Robbins, Automated Cryptanalysis
of Polyalphabetic Ciphers.  Cryptologia 11(4), 193--
205, 1987.

[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.

[CHE1] ABAKUSAN, " A tip for Checkerboard Solution," AS40,
The Cryptogram, American Cryptogram Association, 1940.

[CHE2] X.GOTSKY, " On the Checkerboard, AS44,The Cryptogram,
American Cryptogram Association, 1944.

[CHE3] QUARTERNION, "Straddling Checkerboard, " MA76, The
Cryptogram, American Cryptogram Association, 1976.

[CHE4] PICCOLA, "The Checkerboard Alphabet, " DJ34, The
Cryptogram, American Cryptogram Association, 1934.

[CHE5] SI SI, "The Hocheck Cipher Examined, " JA90, The
Cryptogram, American Cryptogram Association, 1990.

[CHE5] SI SI, "The Checkerway Cipher Examined, " MJ90, The
Cryptogram, American Cryptogram Association, 1990.

[CHE6] GEMINATOR, "The Homophonic Checkerboard, " MA90, The
Cryptogram, American Cryptogram Association, 1990.

[CHE6] GEMINATOR, "The Checkerway Cipher, " JF90, The
Cryptogram, American Cryptogram Association, 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.

[CROT] Winter, Jack, "Solving Cryptarithms,"  American
Cryptogram Association, 1984.

[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
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[CRY5] FAUSTUS, "Science of Cryptanalysis,The " JA91, The
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[CRY6] BEAU NED, "Semi-Systems in Crypt-Cracking," FM36, The
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[CRY7] Y.NOTT, "Systems Of Systems," ON35, The Cryptogram,
1935.

[CULL] Cullen, Charles G., "Matrices and Linear
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[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:
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1979.

[DAVI] Da Vinci, "Solving Russian Cryptograms", The
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[DAVJ] M. Davio, J. Goethals, Elements of cryptology. in
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[DEAC] Deacon, R., "The Chinese Secret Service," Taplinger,
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[DEAU] Bacon, Sir Francis, "De Augmentis Scientiarum," tr. by
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[DELA] Delastelle, F., Cryptographie nouvelle, Maire of
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[DENN] Denning, Dorothy E. R.," Cryptography and Data

[DEVO] Deavours, Cipher A. and Louis Kruh, Machine
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[DEV1] Deavours, C. A., "Breakthrough '32: The Polish
Solution of the ENIGMA,"  Aegean Park Press, Laguna
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[DEV2] Deavours, C. A. and Reeds, J.,"The ENIGMA,"
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[DEV3] Deavours, C. A.,"Analysis of the Herbern Cryptograph
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[DEV4] Deavours, C. A., "Cryptographic Programs for the IBM
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[DEVR] HOMO SAPIENS, "De Vries Cipher," SO60, The Cryptogram,
The American Cryptogram Association, 1960.

[DIG1] DENDAI, "Digrafid, A Footnote to Tip Placement," SO84,
The Cryptogram, The American Cryptogram Association,
1984.

[DIG2] B. NATURAL, "Digrafid, Cipher solution," MJ61, The
Cryptogram, The American Cryptogram Association, 1961.

[DIG3] KNUTE, "Digrafid Cipher," SO60, The Cryptogram, The
American Cryptogram Association, 1960.

[DIG4] THE RAT, "The Buzzsaw, an Enhanced Digrafid," JA83,
The Cryptogram, The American Cryptogram Association,
1983.

[DIG5] BERYL, "Digrafid, Cipher," SO93, The Cryptogram, The
American Cryptogram Association, 1993.

[DIFF] W. Diffie, M. Hellman, Privacy and Authentication: An
introduction to cryptography. IEEE proceedings, 67(3),
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[DIF2] W. Diffie, The first ten years of public key
cryptography.  IEEE proceedings, 76(5), 560--577,
1988.

[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
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[EDUC] OZ, "Educational Cryptography," MA89, The Cryptogram,
The American Cryptogram Association, 1989.

[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!]

[ELLI] Carl M. Ellison, A Solution of the Hebern Messages.
Cryptologia, vol. XII, #3, 144-158, Jul 1988.

[ENIG] Tyner, Clarence E. Jr., and Randall K. Nichols,
"ENIGMA95 - A Simulation of Enhanced Enigma Cipher
Machine on A Standard Personal Computer," for
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[EPST] Epstein, Sam and Beryl, "The First Book of Codes and

[EQUI] THE OAK, "An Equi-Frequency Cipher System," JA55, The
Cryptogram, The American Cryptogram Association, 1955.

[ERSK] Erskine, Ralph, "Naval Enigma: The Breaking of
Heimisch and Triton," Intelligence and National
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[EVEN] S. Even, O. Goldreich, DES-like functions can generate
the alternating group. IEEE Trans. on Inform. Theory,
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[EVES] , Howard, "An Introduction to the History of
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[EYRA] Eyraud, Charles, "Precis de Cryptographie Moderne'"
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[FEI1] H. Feistel, Cryptography and Computer Privacy.
Scientific American, 228(5), 15--23, 1973.

[FEI2] H. Feistel, H, W. Notz, J. Lynn Smith. Some
cryptographic techniques for machine-to-machine data
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1975.

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

[FIDD] FIDDLE, (Frederick D. Lynch, Col.) "An Approach to
Cryptarithms," ACA Publications, 1964.

[FID1] FIDDLE, " The International Chess Cable Code," MJ55,
The Cryptogram, American Cryptogram Association, 1955.

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

[FIRE] FIRE-O, "A Tool for Mathematicians: Multiplicative
Structures," The Cryptogram, Vol. XXXVI, No 5, 1977.

[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.

[FOR1] VULPUS, "Four-Square Cipher," JA63, The Cryptogram,
The American Cryptogram Association, 1963.

[FOR2] FIDDLE, "Further Comments on Solution of Four-Square
Ciphers by Probable Word Method," FM50, The
Cryptogram, The American Cryptogram Association, 1950.

[FOR3] GALUPOLY, "Numerical Four-Square Cipher," MA62, MJ62,
The Cryptogram, The American Cryptogram Association,
1962.

[FOR4] SAI CHESS, "Sharpshooting the Four-Square Cipher,"
AM49,JJ49,   The Cryptogram, The American Cryptogram
Association, 1949.

[FOR5] B. NATURAL, "Solution of Type II-X Four-Square
Cipher," MJ62, The Cryptogram, The American Cryptogram
Association, 1962.

[FOR6] FIDDLE, "Solutionof Four-Square Ciphers by Probable
Word Method," DJ49, The Cryptogram, The American
Cryptogram Association, 1949.

[FOWL] Fowler, Mark and Radhi Parekh, " Codes and Ciphers,
- Advanced Level," EDC Publishing, Tulsa OK, 1994.
(clever and work)

[FRAA] Friedman, William F. , "American Army Field Codes in
The American Expeditionary Forces During the First
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[FRAB] Friedman, W. F., Field Codes used by the German Army
During World War. 1919.

[FRAN] Franks, Peter, "Calculator Ciphers," Information
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[FRA1] SI SI, "Analysis and Optimization of the Fractionated
Morse Cipher," ND81, The Cryptogram, The American
Cryptogram Association, 1981.

[FRA2] B. NATURAL, "Elementary Study of the Fractionated
Morse Cipher," AS51, The Cryptogram, The American
Cryptogram Association, 1951.

[FRA3] X.GOTKY, "Fractionated Morse Cipher," AM50, The
Cryptogram, The American Cryptogram Association, 1950.

[FRA4] CROTALUS, "Fractionated Morse Frequencies Reissued,"
MA93, The Cryptogram, The American Cryptogram
Association, 1993.

[FRA5] RIG R. MORTIS, "Fractionated Morse Keyword Recovery,"
MA60, The Cryptogram, The American Cryptogram
Association, 1960.

[FRA6] LAMONT CRANSTON, "Fractionated Morse Made Easy," JA92,
The Cryptogram, The American Cryptogram Association,
1992.

[FRA7] MOOJUB, "General Break For Fractionated Morse," AS51,
The Cryptogram, The American Cryptogram Association,
1951.

[FRA8] FIDDLE, "Periodic Fractionated Morse," AS54, The
Cryptogram, The American Cryptogram Association, 1954.

[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.

[GARO] G. Garon, R. Outerbridge, DES watch: an examination of
the sufficiency of the Data Encryption Standard for
financial institutions in the 1990's.  Cryptologia,
vol.  XV, #3, 177--193, 1991.

[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

[GOOD] I. J.  Good, Good Thinking: the foundations of
probability and its applications. University of
Minnesota Press, 1983.

[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)

[HELL] M. Hellman, The mathematics of public key
cryptography.  Scientific American, 130--139, 1979.

[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.

[HUNT] D. G. N. Hunter and A. R. McKenzie, Experiments with
Relaxation Algorithms for Breaking Simple Substitution
Ciphers. Computer Journal 26(1), 1983.

[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.

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Not only well written, clear to understand but as
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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.]

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[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
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[NIH1] PHOENIX," Computer Column: Nihilist Substitution,"
MJ88,  The Cryptogram, American Cryptogram
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[NIH2] PHOENIX," Computer Column: Nihilist Substitution,"
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[ORAN] The ``Orange Book'' is DOD 520 0.28-STD, published
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Write to Department of Defense,  National Security
20755-6000, and ask for the Trusted Computer System
Evaluation Criteria. Or call 301-766-8729.  The
``Orange Book'' will eventually be replaced by the
U.S. Federal Criteria for Information Technology
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and active federal standards.

[OTA]  "Defending Secrets, Sharing Data: New Locks and Keys
for Electronic Information," Office of Technology
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[PORT] Barker, Wayne G. "Cryptograms in Portuguese," Aegean
Park Press, Laguna Hills, CA., 1986.

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Pocket Books, New York, N.Y., 1960.

[POUN] Poundstone, William, "Biggest Secrets," Quill
Publishing, New York, 1993. ( Explodes the Beale
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[PRIC] Price, A.,"Instruments of Darkness: the History of
Electronic Warfare, London, Macdonalds and Janes,
1977.

[PRI1] W. Price, D. Davies, Security for computer networks.
Wiley, 1984.

[PROT] "Protecting Your Privacy - A Comprehensive Report On
Eavesdropping Techniques and Devices and Their
Corresponding Countermeasures," Telecommunications
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[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.
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[RAND] Randolph, Boris, "Cryptofun," Aegean Park Press, 1981.

[RB1]  Friedman, William F., The Riverbank Publications,
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[RB3]  Friedman, William F., The Riverbank Publications,
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[REED] J. Reeds, `Cracking' a Random Number Generator.
Cryptologia 1(1), 20--26, 1977.

[REE1] J. A. Reeds and P. J. Weinberger, File Security and
the UNIX  Crypt Command. AT&T Bell Laboratories
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[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma
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[RELY] Relyea, Harold C., "Evolution and Organization of
Intelligence Activities in the United States," Aegean
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[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'",
Bulletin Trimestriel de l'association des Amis de
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[RHEE] Rhee, Man Young, "Cryptography and Secure
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Obtaining Digital Signatures and Public Key
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Analysis," 1330 Copper Peak Lane, San Jose, Ca. 95120-
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[ROBO] NYPHO, The Cryptogram, Dec 1940, Feb, 1941.

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Axis Radio-Intelligence in the Battle of the Atlantic,
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[ROHW] Rohwer Jurgen,  "Critical Convoy Battles of March
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[ROH1] Rohwer Jurgen, "Nachwort: Die Schlacht im Atlantik in
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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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[RYP7] PIT, "Cryptarithm Crutch," JA80, The Cryptogram,
1980.

[RYP8] DENDAI, DICK, "Cryptarithm Ccub root," ND76, The
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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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1943.

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[RYPI] FIDDLE, "Exhausitive for Three," JF59, The Cryptogram,
1959.

[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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[RYPN] CROTALUS, "Make Your Own Arithmetic Tables In Other
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[RYPQ] FIRE-O, "Multiplicative Structures," MJ70, The
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[RYPR] CROTALUS, "Solving A Division Cryptarithm," JA73, The
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[RYPS] CROTALUS, "Solving A Multiplication Cryptarithm,"
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[RYPT] PHOENIX, "Some thoughts on Solving Cryptarithms,"
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[RYPU] CROTALUS, "Square Root Cryptarithms," SO73, The
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