## Lesson 11: Polyalphabetic Substitution Systems II Cryptanalysis Of Viggy's Family

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CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI

May 05, 1996
Revision 0

LECTURE 11

POLYALPHABETIC SUBSTITUTION SYSTEMS II
CRYPTANALYSIS OF VIGGY'S FAMILY

SUMMARY

In Lectures 11-12, we continue our course schedule with a study
of fascinating cipher systems known as the "Viggy" based on
multiple alphabets - Polyalphabetic Substitution systems.

We will continue developing our subject via an overview based
on the Op-20-GYT course notes (Office of Chief Of Naval
Operations, Washington) [OP20].  We will revisit polyalphabetic
cipher systems using Friedman's detailed analysis.  We will
cover the Viggy, Variant, PORTA systems and other family
members.  [FRE4], [FRE5], FRE6], [FRE7], [FRE8].  We will take
material from ACA's Practical Cryptanalysis Volume V by William
G. Bryan on "Periodic Ciphers - Miscellaneous: Volume II"
[BRYA] and Sinkov's [SINK] text to discover Viggy's secrets.
We will look at [ELCY's] treatment of these systems.

In Lecture 12, we will describe the difficult aperiodic
polyalphabetic case and give a diagram of topics considered in
Lectures 10 - 12.  [FR3]  We will complete the Viggy family.
I will also cover decimation processes in detail.

I have again updated our Resources Section with many references
on these systems - focusing on the cryptanalytic attack and
areas of historical interest.  Kahn has some wonderful stories

ZEN CRYPTO

In Lectures 1- 10,  I have purposely stayed away from the
heavier mathematics of cryptography (subject to change).
Everything I am presenting can and has been reduced to
mathematical models and computerized for ease of work.  For my
readers who can not live without the math diet, there are
plenty of guru' s like [SCHN] and [SCH2] to have breakfast
with.  There are plenty of computer aids at the Crypto Drop Box

BUT those who embark on a course of 'only the computer' do this
without knowing the real effort -the brain power - the
shortcuts - the tradecraft - the historical implications,  in
my opinion, have lost the real heart of Cryptography.  The 'ah
ha's of inspiration are what make the difference.  First, there
is a fundamental problem in that computer models do not apply
to all variant cases.  Simple changes to the system can fool
even the most adept computer program.  For example, placing
clever nulls will defeat many a statistical based model.

Second, we lose the sense of urgency that was required for
wartime cryptography.  If President Kennedy's Playfair message
[ that's right it was not English as in the movie PT-109] on
the back of a coconut had been intercepted and deciphered by
the Japanese [which they very capable of doing], we might not
have had the graceful light of his Presidency or who knows the
moon landings.  As another case in point, the solution of
ENIGMA during the mid - final Atlantic Campaigns of World War
II, reduced the operational effectiveness of the U-Boat to one
day and hence saved allied tonnage and warships suppling
Europe.  The American and British Crypee's 'thought' more like
their German counterparts than their counterparts.  Computer
solutions were bulky, machine dependent [ the solution "stops"]
and not reliable until 1945.  People made the difference.

SOLVING A PERIODIC POLYALPHABETIC CIPHER

There are three fundamental steps to solve a Periodic cipher.

1) Determine the period.  This sets up the correct geometrical
positioning of ciphertext alphabets.

2) Identify the Cipher System and reduce or consolidate the
multiple alphabet distribution into a series of
monoalphabetic frequency distributions.

3) Solve the monoalphabetic distributions by known principles.
We have covered this in Lectures 1-3 and Lecture 10.

Friedman presents a more detailed and eloquent version of this
procedure in [FR7].

THE LONG AND SHORT OF KASISKI

Step one is finding the period.  Bryan reminds us that there
are at least two ways to find the period.  The short approach
makes use of the distances between patent cipher text
repetitions and factors the differentials.  The long approach
is used when there are no patent repetitions to factor.  In
this case we set up a possibilities matrix and factor every
combination looking for the highest probable common factor.
[BRYA]

As an example of the first case take:

10            20            30            40
BGZEY  DKFWK  BZVRM  LUNYB  QNUKA  YCRYB  GWMKC  DDTSP

50            60            70            80
OFIAK  OWWHM  RFBLJ  JQFRM  PNIQA  VQCUP  IFLAZ  HKATJ

90          100            110          120
UVVQE  EKESZ  DUDWE  KKESL  IZQAT  SBYUZ  UUVAZ  IXYEZ

130          140
JFTAJ  EMRAS  QKZSQ  FOPHM  W.

We tabulate the repetitions and the cipher text letter
differences between repetitions.

Delta        Factors
BG 29          -
RM 45         3,5,9
KA 53          -
MR 77         7,11
QA 39         3,13
VQ 17          -
AZ 40         4,5,8,10
AT 26         13
UV 31         -
EK 9          3,9
KES 10        5,10      .... this trigraph more important
SQ 4          4              than QA or AT digraphs.
Suggest that the period is
either 5 or 10. Practice dictates
that the larger number is the
proper.

But suppose there are no repeats or those that do exist do not
establish a period. What then?

Given:
10             20           30            40
RNQJH  AUKGV  WGIVO  BBSEJ  CRYUS  FMQLP  OFTLC  MRHKB

50            60            70             80
BUTNA  WXZQS  NFWLM  OHYOF  VMKTV  HKVPK  KSWEI  TGSRB

90            100           110           120
LNAGJ  BFLAM  EAEJW  WVGZG  SVLBK  IXHGT  JKYUC  HLKTU

MWWK.

We set up the following vertical tally.  We note the
actual position of every letter.

A  6 45 83 89 92 115
B  16 17 40 41 80 86 104
C  21 35
D  ---
E  19 74 91 93
F  26 32 52 60 87
G  9 12 77 84 98 100 109
H  5 38 57 66 108 116
I  13 75 106
J  4 20 85 94 111
K  8 39 63 67 70 71 105 112 118 124
L  29 34 54 81 88 103 117
M  27 36 55 62 90 121
N  2 44 51 82
O  15 31 56 59
P  30 69
Q  3 28 49
R  1 22 37 79
S  18 25 50 72 78 101
T  33 43 64 76 110 119
U  7 24 42 114 120
V  10 14 61 65 68 97 102
W  11 46 53 73 95 96 122 123
X  107
Y  23 47 58 113
Z  48 99

Now we take each difference and every difference in each case.
For example, A45-6, 83-6,89-6,92-6,115-6; and 83-45,89-45,92-
45,115-45; and 89-83,92-83,115-83; and 92-89,115-89, and 115-
92.  Then we factor these differences, setting up a matrix
(Table 11-1) of potential periods from 3 -12 inclusive and
total the tabulations for each factor in each of the letters of
the alphabet.  The highest column total represents the period.
The number is correct more than 98 per cent of the time.

Table 11-1

3  4  5  6  7  8  9  10  11  12
-------------------------------
A    3  1     1  1     1   1   2   1
B    9  7  4  5  3  7  4   2   1   2
C       1  1     1  1      1
D
E    1  1  1  1         1      1   1
F    2  3  3  1  2  1   1   1  1
G    5  5  4  1  4  3   2   1  3   1
H    6  3  2  2  3  1   1   2  1
I    1
J    3  1  2  1  1  1   3   1
K    13 10 4  9  8  5   3   1   2   3
L    4  3  4  1  4  1   3   1   2
M    4  2  3  2  6      3   1   1
N    1  1  1  1  3  1       1
O    1  3  1     1  1           1
P    1
Q    1     1     1
R    5  1  1  3  2      1           1
S    4  4  2  3  2  1   1   1   1
T    4  3  1  1  2      1   1   2   2
U    5  1  2  5  1  2   3   1   2   2
V    5  6  2  2  1  2   3       1   1
W    9  4  5  3  8  1   4   4   3   1
X
Y    2  2  3  2  1  2       1   3   1
Z    1
---------------------------------
87  61 47  43  57  30  35  21  25  16    Columns total
X     3  4   5   6   7   8   9  10  1  112     times period
----------------------------------
261 244 235 258 399 240 315 210 275 192    Total
===

The period is 7.

WHAT CIPHERS MAKE UP THE VIGGY FAMILY?

The Viggy (or more correctly the Vigenere) Family is group of
ciphers.  Included in this group are: Vigenere, Variant,
Beaufort, Gronsfeld, Porta, Portax, and Quagmires I-IV.
Other ciphers may be included in the group.  They are Nihilist
Substitution, Auto - Key, Running Key and Interrupted ciphers.
Bryan includes the Tri-square, the periodic Fractionated
Morse, the Seriated Playfair and the Homophonic in the same
class of ciphers.

These ciphers were invented at different times by different
authors, sometimes with confusion of authorship, and in
different countries.  They are similar in that they represent
permutations of the same cryptographic concept and can be
cracked with the same general methodology, albeit with slight
variations in procedure.  What is also interesting is that
these ciphers can be viewed in tableaux form, in slide form or
matrix form.

The theory of polyalphabetic substitution is simple. The
encipherer has at his disposal several simple substitution
alphabets, usually 26.  He uses one such alphabet to encipher
only one letter, another alphabet for the second letter,
and so forth, until some preconcerted plan has been followed.
The earliest known ciphers of this kind, the Porta (1563), the
Vigenere (1586) used tableau's for encipherment, in which all
the alphabets were written out in full below each other. The
Gronsfield (1655) had a mental key, and the Beaufort (1857)
which came two hundred years later, again used the tableaux.
The process was reduced to strips or slides in 1880 at the
French military academy of Saint-Cyr.  The polyalphabetic
deciphering slides now bear that name.   [ELCY]

To know thoroughly any of these ciphers is to understand the
fundamental principles of all.  Lets look at the papa bear.

THE VIGENERE CIPHER

The father of the Viggy family is the Vigenere Cipher.  Like
most of the periodic ciphers, the 'Viggy' is actually a series
of monoalphabetic substitutions such as Aristocrats, and since
a keyword is used, under each letter of the keyword, there is a
separate simple substitution cipher - each one different- ,
using all the letters, in such a manner, that the resulting
cipher is a combination of several such substitutions.

Attributed to Blaise de Vigenere, the cipher named for him was
invented by him in 1586.  In his "Traicte des Chiffres"
he did invent an autokey system which used both a priming key
and did not recommence his plaintext key with each word, nut
kept it running continuously.  He described a second autokey
system which was more open but still secure.  Both systems were
forgotten and were re-invented in the 19th century.  Historians
have credited Vigenere with the simpler polyalphabetic
substitution system.  Legend grew around this cipher that it
was "impossible of translation" as late as 1917. [KAHN]

The original Viggy was composed of an enciphering and
deciphering tableaux.  Letters were enciphered and deciphered
one letter at a time.  The modern Vigenere tableaux is
shown in Figure 11-1.

Figure 11-1

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

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

The normal alphabet at the top of the tableaux is for plaintext
and the keyletters are shown at the extreme left under the 'A'
of the top row.  Where the two lines intersect in the body of
Figure 11-1, the ciphertext is found.

For example using the keyword TENT, we encipher "COME AT ONCE"

we have: TENT       TENT
----       ----
COME       VSZX   (ciphertext)
ATON       TXBG
CE         VI--

The enciphering and deciphering problem are done as a group of
letters to improve speed and accuracy of the process.

Another way to look at this is that the Viggy is really a two
dimensional slide problem.  We can construct (or purchase for
about \$2.00 from ACA) a set of two Saint-Cyr slides that
operate the same way as the tableaux shown in Figure 11-1.
What is useful is that each slide bears the standard normal
alphabet from A-Z with high frequency letters colored or
shaded.  Each slide is a double-alphabet to allow flexibility.

Figure 11-2

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
GHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEF
*                         *

Figure 2 shows the Saint- Cyr slide at a key of G.  Check with
Figure 11-1 to see that the results are the same for Nplain =
Tcipher or Iplain = Ocipher.

The practical use of the Saint Cyr slide is that the whole
column of plaintext is enciphered as a unit.  So C A C would be
enciphered as V A V, plaintext O T E becomes S X I, etc.
This eliminates mistakes.   The cipher is taken off in 5 letter
groups by rows, so we would have VSZXT XBGVI for our previous
example.

Friedman points out that the sliding components produce the
same type of cipher with the circular disks like the old U. S.
Army version.  [FRE7]

Koblitz [KOBL]  describes the Viggy as follows:

For some fixed k, regard blocks of k letters as vectors in
(Z/NZ)**k. Where N is the N-letter alphabet and a digraph
integer correspondence exists between modulo N**2 array
and it is a vector mapping.  Choose some fixed vector b
which exists in the plane (Z/NZ)**k which can be remembered
by a key word and encipher by means of the vector translation
C = P +b where C is the ciphertext message unit and P is the
plaintext message unit which is a k-tuple of the integers
modulo N.

The object is to guess N and k, break up the ciphertext in
blocks of k letters and performs a frequency analysis on the
first letter of each block to determine the first component of
b and then proceeds onto the second letter
in the block, etc.

Konheim's description is worse than Koblitz's. [KONH]

Seberry and Pieprzyk describe the Viggy as made up of
key sequence k= k1...kd where ki , (i=1,d) gives the amount of
shift in the ith alphabet, fi(a) = a+ki(mod n) and the
ciphertext is described as fi**(-1) = (ki -c) mod n so that

fi(a) = [(n-1)-a +(ki +1) ] mod n             [SEAB]

The latter four descriptions are boring - even to my
engineering background.  They also do not hold water for
randomized alphabets or tableauxs with disruption areas in
place.  These represent discontinuities in the mathematical
function.  They are discontinuous and tractable.  Or
differentiable if the model is such.  SCYER's program may have
solved the discontinuity integer problem by area limits or
module limits.   When he publishes the procedure, maybe he will
tell us.

WHICH WAY ?

Does it matter with the Viggy,  that we encipher S by B (B
alphabet or Key B) to find cipher T or encipher B by S (S
alphabet or Key S) to find T?  No. This is an interesting
characteristic not shared by all in the Viggy family.  It may
be its downfall.

For instance, the message:

Send Supplies To Morley's Station

enciphered with the repeating key, BED under the original
method of encipherment as might be described by Blaise de
Vigenere would be:

Key   : BEDB  EDBEDBED  BE  DBEDBED  BEDBEDB
Plain : SEND  SUPPLIES  TO  MORLEYS  STATION
Cipher: TIQE  WXQTOJIV  US  PPVOFCV  TXDUMRO

The modern Saint-Cyr slide encipherment of the above would be:

Key        B E D     B E D     B E D
Plain      S E N     D S U     P P L
Cipher     T I Q     E W X     Q T O

I E S     T O M     O R L
J I V     U S P     P V O

E Y S     S T A     T I O
F C V     T X D     U M R

N
O

which gives:

5         10          15          20          25
T I Q E W   X Q T O J   I V U S P   P V O F C   V T X D U

30
M R O X X    (two ending nulls and a bad choice at that)

With the Saint Cyr slide, we would encipher S, I, E, N; then
D, T, S, and finally P, O , T by setting the B key on the
bottom slide under the A key of the top slide and reading off
the equivalents.                            [SINK], [ELCY]

DECIPHERMENT BY PROBABLE WORD

Refer to Figure 11-3:

Figure 11-3

Deciphering with the Key:

Key   :  B E D B E D B E D B E D  ........
Cipher:  T I Q E W X Q T O J I V  ........
Plain :  S E N D S U P P L I E S  ........

Deciphering with the Message:

Plain :  S E N D S U P P L I E S  ........  (trial key)
Cipher:  T I Q E W X Q T O J I V  ........
Key   :  B E D B E D B E D B E D  ........  (true  key)

Figure 11-3 indicates a possible solution method.  The message
fragment works well as a trial key, and if applied in the
same manner as the true key, the true original key will be
revealed.  The Vigenere Cipher works equally well in reverse.
It is this peculiarity that portends the use of a probable word
attack.

Suppose we have the cryptogram:

U S Z H L    W D B P B    G G F S ...

which we suspect that the presence of the word SUPPLIES.
We decipher the first 8 letters using this probable word as a
trial key, and obtain the jumbled series: C Y K S A O Z J,

which is unsatisfactory.  We next drop the first U, and obtain
group  : A F S W L V X X.  We fail again on the third and
fourth trials.  The fifth decipherment obtains the series
TCOMETCO.  We see the TCO repeats and the key word COMET.
[ELCY]

F. R. Carter of the ACA shows us a more organized approach in
Figure 11-4:

Figure 11-4

Cryptogram Fragment: U S Z H L W D B P B G G F S ......

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

Look down at an angle between the stars to find the key word
COMET.  The first letter S was used to decipher every possible
key letter which can produce S.  The entire row of equivalents
were produced at the same time.  The resulting rows of
decipherment indicate all the possible keyletters that could
produce S, then U, then P, and so on.   Carter actually
shortened the procedure to three full rows and then partials
thereafter.  He assumes that the keyword is readable and

DECIPHERMENT BY PROBABLE TRIGRAM SEQUENCE

For the case where we have no probable word or the sequence is
a list of usual trigrams THE, AND, THA, ENT, ION, TIO.  The key
fragments deciphered by these will be short and numerous, some
correct and some incorrect to bring out the repeating key
sequence.  A secondary worksheet is used to test the various
fragments as keys.  If any one of them is a fragment of the
original key, it must bring out fragments of plaintext at
regular intervals.

A scheme like Carters can be used with the trigrams THE, AND..
replacing the word SUPPLIES.   Refer to Figure 11-5.

Given:
10                    20              26
L N F V E  O L N V M  R N G Q F  H H R N H  I R V F E  B

The cipher text is only 26 letters long.  Every letter except
the final two might begin a cipher trigram.  So we have 24
cipher trigrams.  Write them out in full on two worksheets.

Figure 11-5

ION                Trial 1

LNF NFV FVE VEO EOL OLN LNV NVM VMR MRN RNG NGQ
AZS FRI XHR NQB WAY GXA DZI FHZ NYE EDA JZT FSD
---
GQF QFH FHH HHR HRN RNH NHI HIR IRV RVF VFE FEB
YCS IRU XTU ZTE ZDA ZJU FTV ZUE ADI JHS NRR XQO

EDA                Trial 2

LNF NFV FVE VEO EOL OLN LNV NVM VMR MRN RNG NGQ
HKF JCV BSE RBO ALL KIN HKV JSM RJR ION NKC JDQ
---
GQF QFH FHH HHR HRN RNH NHI HIR IRV RVF VFE FEB
CNF MCH BEH DER DON NKH JEI DFR EOV NSF RCE BBB

Trial 1 tests for THA, THE, AND fail but ION gives us FRI and
WAY. But anyone of these 24 decipherments on the second row
might be a fragment of the original key.  Trial 2 fails to
confirm FRI or WAY but test of key-fragment EDA yields ION.
If this sequence is actually a portion of the original key,
then the plaintext will be brought out at some constant
distance apart.  The point we found the trigram is the tenth
cryptogram letter; that is every trigram presents only one new
letter so to find a completely different trigram in either
direction, we must count backwards or forwards a distance of
three trigrams.

Beginning at the tenth trigram we examine every third trigram
in both directions.  The following is found: HKF, RBO, HKV,ION,
CNF, DER,JEI, NSF.  These are incoherent. This would be
equivalent to a period of three - not likely.  Try every fourth
decipherment: JCV,KIN,ION,MCH,NKH,NSF. Not usable for a
consecutive sequence, continuously written cryptogram.
Trying the decipherments at a proposed period of 5, we get ALL,
ION, BEH, DFR.  This possibility is good.  We try to
decipher the T before ION and get the letter C.  We now have
four letters in our key C E D A.  With a little anagraming we
have the word D A * C E.  A probable word FRIDAY comes to mind.

BRYAN'S SAINT-CYR 'HITS' METHOD

William G. Bryan shows us how to use the high frequency letters
on the Saint-Cyr slide to good use.

Given the Viggy with a known period of 7 based on a similar
effort used in Table 11-1:

PXIZH  GVGEU  UOXIX  MYEEJ  ZCOCM  OWZCL  FMTOR  ISIGH  LKWPS

MSIDX  WCFBR  KPYXO  PRJIL  HFMCR  IHUDU  LVRLJ  FVVVS  HTYFR

RGPHQ  WIIBL  XQXMM  TDVGU  EITFM  QEEJH  WUHFW.

We reset the problem in groups of 7:

1234567
PXIZHGV
GEUUOXI
XMYEEJZ
COCMOWZ
CLFMTOR
ISIGHLK
WPSMSID
XWCFBRK
PYXOPRJ
ILHFMCR
IHUDULV
RLJFVVV
SHTYFRR
GPHQWII
BLXQXMM
TDVGUEI
TFMQEEJ
HWUHFW

Now each column represents a separate simple substitution
cipher.  They will not produce consecutive plaintext, but
merely show isolated letters in that particular substitution,
to be coupled with those letters that fall on either side in
other substitutions, to make a true plain text sequence. Here's
where the underlined high-frequency letters on the slide come
in:

We go down column 1 and tabulate all the letters which
appear\more than once. P-2, G-2, X-2, C-2, I-3, T-2. We
rearrange them in their normal sequence = C G I P T X.
The lower slide is moved successively so that the first letter
C is under the high frequency letters, in turn, A E H I N O R S
T, and a reading is made of the number of 'hits' , the number
of other cipher text letters G I P T X that fall below the high
frequency letters.  If they do then the letter under A of the
top slide is the key letter for that column.  If they don't
further trials are necessary.

High frequency letters don't always show up. Some times medium
frequency letters may be required.  So with C under A: G-E, I-
G,P-N, T-R, X-V; With C under E:G-I, I-K, P-R, T-V, X-Z; With C
under the H: G-L, I-N, P-U, T-Y, X-C; with C under the I: G-
M,I-O,P-V, T-Z, X-D; and with C under the N: G-R, I-t, P -A, T-
E, X-I (six hits); and we have found the setting. So we set P
under the A in the top slide, and decipher the entire column A
R I N N T H I A T T C D R, and write it into a blank column as
column 1.

passable results at P and U, Column 4 seems to go with Y,
column 5, setting B has 4 hits, Column 6 has 5 hits indicating
an E, and Column 7, R gives six hits.

The keyword thus recovered is P P Y B E R.  We choose to
decipher the ending B E R as the ending of a keyword to
produce:

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

These are almost all good fragments.  The GHT must have an I or
U before it.  Since cipher letter G is involved, we place the G
under the I which results in the Y we already had and putting G
under the U gives us M under the A, we choose the latter.

Now we have  MBER has a key fragment.  Deciphering column 4
with M adds N I I S A A U A T C T R T M E E U E V to the
evidence.

There are several possibilities NGCE preceded by an O, UGHT
preceded by an O, TANT preceded by an OR;  TLYA preceded by an
N; UTAR preceded by an  O or A; and EWIV preceded by R/H.

With the Viggy cipher, remember to read the setting for the
keyword letter below the A of the Stationary slide; and the
plain text appears on the same slide as this A, while the
cipher text is in the lower slide.

VIGENERE COMPUTER SOLUTION IS QUICKER

At this juncture, I wondered how our Viggy solver at the CDB
would do on this problem.  I brought up my faithful computer
program and entered the cipher text into Vigenere.exe without
telling it the period and found the following:

The period was found within 1 second.  The trial keyword
was PLQMBER, which I assumed was PLUMBER.  Using PLUMBER as my
keyword,  it typed out the answer: "AMONG CERTAIN TRIBES OF
INDIANS IN ALASKA.. ends BUT ARE USED AS SLAVES."  The process
took less than 3 seconds of compute time on my 486/50.

I then rearranged the ciphertext with five nulls strategically
added.  The next pass gave me a period of nine and a gibberish
trial keyword.  So for well defined problems the computer is
less fun but a clear winner.  For the clever cryptographer,
the computer can be defeated.

PRIMARY COMPONENTS

We have seen that equivalents obtainable from use of square
tables may be duplicated by slides or revolving disks [FR2],
[FR7] or computer models.  Cryptographically, the results may
be quite diverse from different methods of using such
paraphenalia, since the specific equivalents obtained from one
method may be altogether different from those obtained from
another method.  But from the cryptanalytic point of view the
diversity referred to is of little significance.

There are, not two, but four letters involved in every case of
finding equivalents by means of sliding components;
furthermore, the determination of an equivalent for a given
plaintext letter is represented by two equations involving four
equally important elements, usually letters.

Consider this juxtaposition:

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

Question - what is the equivalent of Pplain when the Key letter
is K?  Answer - without further specification, the cipher
equivalent can not be stated.  Which letter do we set K against
and in which alphabet?  We have previously assumed that the K
cipher would be put against A in the plain. But this is only a
convention.

Figure 11-6

Index            Plain
*              *
1. Plain:                   ABCDEFGHIJKLMNOPQRSTUVWXYZ
2. Cipher:FBPYRCQZIGSEHTDJUMKVALWNOXFBPYRCQZIGSEHTDJUMKVALWNOX
*              *
Key              Cipher

With this setting Pplain = Zcipher.

The four elements are:

1.  The Key letter, 0k
2.  The index letter, 01
3.  The plaintext letter, 0p
4.  The cipher letter. 0c

The index letter is commonly the initial letter of the
component, but by convention only.  We will assume from now on
that 01 is the initial letter of the component in which it is
located.  Refer to Figure 11-6 to confirm this assumption.
The enciphering equations above are:

(I) Kk = A1 ; Pp = Zc     k=key, p=plain,
c=cipher, 1= initial

There is nothing sacred about the sliding components. Consider
Figure 11-6b.

Figure 11-6b

Index            Cipher
*              *
1. Plain:                   ABCDEFGHIJKLMNOPQRSTUVWXYZ
2. Cipher:FBPYRCQZIGSEHTDJUMKVALWNOXFBPYRCQZIGSEHTDJUMKVALWNOX
*              *
Key              Plain

thus           (II) Kk = A1; Pp = Kc

Since equations (I) and (II) yield different results even with
the same index, key and plain text letters, it is obvious that
a more precise formula is required.  Adding locations to these
equations does the trick.

(I)  Kk in component (2) =A1 in component (1); Pp in component
(1) = Zc in component (2).

(II) Kk in component (2) =A1 in component (1); Pp in component
(2) = Zc in component (1).

In shorthand notation:

(1)  Kk/2 = A1/1; Pp/1 + Zc/2
(2)  Kk/2 = A1/1; Pp/2 + Zc/1

Employing two sliding components and four letters implies
twelve different resulting systems for the same set of
components and twelve enciphering conditions.  These
constitute the Viggy Family:

Table 11-2

(1) 0k/2=01/1; 0p/1=0c/2        (7)  0k/2=0p/1; 01/2=0c/1
(2) 0k/2=01/1; 0p/2=0c/1        (8)  0k/2=0c/1; 01/2=0p/1
(3) 0k/1=01/2; 0p/1=0c/2        (9)  0k/1=0p/2; 01/1=0c/2
(4) 0k/1=01/2; 0p/2=0c/1        (10) 0k/1=0c/2; 01/1=0p/2
(5) 0k/2=0p/1; 01/1=0c/2        (11) 0k/1=0p/2; 01/2=0c/1
(6) 0k/2=0c/1; 0p/1=0p/2        (12) 0k/1=0c/2; 01/2=0p/1

The first two equations (1) and (2) define the Vigenere type of
encipherment and are widely used.  Equations (5) and (6) define
the Beauford type and Equations (9) and (10) define the
Delastelle type of encipherment.  [FR7]

FURTHER REMARKS ON REPETITIONS

I have said that the three steps in the cryptanalysis of
repeating key systems are : 1) Find the length of the period,
2) Allocate or distribute the letters of the ciphertext into
their respective alphabets, thereby reducing the polyalphabetic
text to monoalphabetic terms, and 3) analysis of the individual
monoalphabetic distributions to determine the plain text values
of their cipher equivalents in each distribution or alphabet.

As a direct result of using a repeating key (no matter how
long) certain phenomena are manifested externally to the
cryptogram.  Regardless of what system is used, identical plain
text letters enciphered by the same cipher alphabet with single
equivalents must yield identical cipher letters.  This happens
each time the same key letter is used to encipher identical
plaintext letters.

Since the number of columns or positions with respect to the
key are limited, and there is a normal redundancy in the
language, it follows that there will be in a message of fair
length many cases where identical plain text letters must fall
into the same column.  This will be enciphered by the same
cipher alphabet, resulting in many repetitions.  There are two
types of repetitions: causal and accidental (random)
repetitions.  The former we can trace back to the key. The
latter occurs when different plaintext letters fall in
different columns and by chance produce identical cipher text
letters.

Accidental repetitions will occur frequently with individual
letters, less frequently with digraphs (because the accident
must occur twice in succession, much less in the case of
trigraphs and very much less in the case of a tetragraph.
The probability of chance repetition decreases significantly as
the repetition increases in length.  Friedman has developed
statistical tables based on the binomial and Poisson
distributions to determine the individual and cumulative
probabilities for expected number of repetitions in n letter
text to occur x or more times in samples of random text.

The use of these tables is important.  They tell us when
we are dealing with cryptographically maneuvered text versus
random noise designed to fool the listener.  They indicate
what may be a hoax (Beale or Bacon - Shakespeare controversies)
versus valid enciphered text.

Tables 11-3 to 11-6 show the above theory.

Table 11-3

Number          Expected Number of Digraphs Occurring
of                  Exactly x Times
Letters E(2)  E(3)  E(4)  E(5)  E(6)  E(7)  E(8)  E(9)  E(10)
--------------------------------------------------------------
100     6.21  .298  .011
200     21.8  2.12  .154  .009
300     42.5  6.23  .683  .060  .004
400     65.3  12.8  1.87  .220  .022  .002
500     88.1  21.6  3.97  .582  .071  .008
600    110.   32.3  7.11  1.25  .184  .023  .003
700    129.   44.3  11.4  2.35  .403  .059  .008  .001
800    145.   57.1  16.8  3.96  .777  .130  .019  .003
900    158.   70.1  23.2  6.16  1.36  .257  .043  .006   .001
1000   169.   83.0  30.6  9.03  2.21  .466  .085  .014   .002

Table 11-4

Number    Expected Number of Trigraphs Occurring
of                  Exactly x Times
Letters E(2)  E(3)  E(4)
--------------------------
100     .269  .001
200     1.10  .004
300     2.48  .014
400     4.40  .033
500     6.85  .064
600     9.81  .111  .001
700    13.3   .175  .002
800    17.3   .261  .003
900    21.8   .371  .005
1000   26.8   .505  .008

Table 11-5

Number    Expected Number of Tetragraphs Occurring
of                  Exactly x Times
Letters E(2)     E(3)
--------------------------
100     .010
200     .043
300     .096
400     .171
500     .270
600     .389
700     .530
800     .693
900     .877
1000    1.08      0.001

Table 11-6

Number    Expected Number of Pentagraphs Occurring
of                  Exactly x Times
Letters E(2)
----------------
100
200     .002
300     .004
400     .007
500     .011
600     .015
700     .021
800     .027
900     .034
1000    .042

By way of illustration, of the use of these tables, from Table
11-3, we obseve that in a sample of 300 letters of random text,
we may expect 43 digraphs to occur twice, 6 digraphs to occur
three times and 1 digraph to occur four times.  If we sum the
values under E(2) through E(6) we have the cumulative
probability in the 300 letter sample.  The sum is 49.477, which
indicates that in a sample of 300 letters or so, 49 digraphs
will occur two or more times.

STATISTICAL PROOF OF THE MONOALPHABETICITY OF THE DISTRIBUTIONS

The second step in the solution of periodic ciphers is to
distribute the cipher text into the component monoalphabets.
The period once established tells us the number of cipher
alphabets.  By rewriting the message in groups corresponding to
the length of the key (period) in columnar fashion,  we
automatically have divided up the text so that letters
belonging to the same cipher alphabet occupy similar positions
in the groups or in the same columns.

If we make separate uniliteral frequency distributions for the
isolated alphabets, each of these resulting distributions is
therefore, a monoalphabetic frequency distribution.  Were this
not so, if they did not have the characteristic crest and
trough appearance including the expected number of blanks,
if the observed values of Phi are not sufficiently close to the
expected value of Phi plain, or do not yield I.C.'s in the
close vicinity of the expected value, then the entire analysis
is fallacious.

The I.C. values of these individual distributions may be
considered an index of correctness of the factoring process.
Both theoretically and practically, the correct hypothesis with
respect to these distributions will tend to conform more
closely to the expected I.C. of a monoalphabetic frequency
distribution.

Friedman demonstrates the above with an example:    [FR7]

Plaintext Message:

The artillery battalion marching in the rear of the advance
guard keeps its combat train with it insofar as practical.

Keyword BLUE using direct standard alphabets.

Cipher Alphabets

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

B L U E B L U E B L U E B L U E B L U E B L U E ...
T H E A R T I L L E R Y B A T T I L I O N M A R ...

Cipher Text

USYES  ECPMP  LCCLN  XBWCS  OXUVD  SCRHT
HXIPL  IBCIJ  USYEE  GURDP  AYBCX  OFPJW
JEMGP  XVEUE  LEJYQ  MUSCX  JYMSG  LLETA
LEDEC  GBMFI

Friedman gives a useful formula for monographic I.C. of a 26
character text:

I.C.  =  26 sum f(f-1)/N(N-1) = Phi(o) / Phi (r)

and since Phi (p) for English is 0.0667N (N-1)

and Phi (r) = 0.0385 N ( N-1)  where N is the total number of
elements in the distribution.  I.C. for English plain = 1.73
and 1.0 for random text.  We may apply the I.C. test to the
distributions of periodic polyalphabetic  ciphers to confirm
the monoalphabeticity of their character.  This also confirms
the period length and correctness.  if the correct period is
assumed, then the Phi test applied to each of the alphabets
should approximate closely and consistently the value of Phi(p)
and conversely, if the incorrect period is assumed, then the
Phi(o) should approximate the value of Phi(r).  Deviation from
this hypothesis must be statistically significant.  [FR7]

So we break down the four alphabets:

4 1 4 1 1 1 1 1 3     1   1 1     1 1 4      Phi =42
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  I.C.=1.68

1   2   4   1         2 1     4     4 1     1 2 2 Phi=44
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  I.C.=1.91

1   5     1   1 1 1   5 2 1     1       2 1   1 2 Phi=46
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  I.C.=1.99

1   6   2   2 1     1   1 1   2 2     1 1 3 1 Phi=44
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  I.C.=1.91

It is seen that all these distributions are monoalphabetic
since their observed Phi's are closer to the Phi (p) = 40.
rather than Phi (r) = 23.  Any other period assumed at four
or a multiple of four, will not yield monoalphabetic
distributions.

In light of the foregoing principles, we now look at two
additional cryptanalytic techniques for the Viggy family.
The first compares the distributions to the normal and the
second is very important - completing the plain-component.

SOLUTION BY FITTING THE DISTRIBUTIONS TO THE NORMAL

Given message text A:

5         10         15         20         25
A.  A U K H Y  J A M K I  Z Y M W M  J M I G X  N F M L X
B.  E T I M I  Z H B H R  A Y M Z M  I L V M E  J K U T G
C.  D P V X K  Q U K H Q  L H V R M  J A Z N G  G Z V X E
D.  N L U F M  P Z J N V  C H U A S  H K Q G K  I P L W P
E.  A J Z X I  G U M T V  D P T E J  E C M Y S  Q Y B A V
F.  A L A H Y  P O I X W  P V N Y E  E Y X E E  U D P X R
G.  B V Z V I  Z I I V O  S P T E G  K U B B R  Q L L X P
H.  W F Q G K  N L L L E  P T I K W  D J Z X I  G O I O I
J.  Z L A M V  K F M W F  N P L Z I  O V V F M  Z K T X G
K.  N L M D F  A A E X I  J L U F M  P Z J N V  C A I G I
L.  U A W P R  N V I W E  J K Z A S  Z L A F M  H S

The period is 5 and the I.C. confirms this hypothesis.

We make uniliteral frequency distributions for the 5 alphabets
to determine if we have standard alphabets.

Alphabet 1     I.C. = 1.44
5 1 2 3 3   3 2 2 6 2 1   6 1 5 3   1   2   1     6
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

Alphabet 2     I.C. = 1.47
5   1 1   3   3 1 2 4 9 1   2 5     1 2 4 4     4 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

Alphabet 3     I.C. = 1.71
2 3     1       8 2 2 4 8 1   1 2     3 4 5 1 1   5
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

Alphabet 4     I.C. = 1.36
3 1   1 3 4 4 4     2 2 3 3 1 1   1   2   2 4 9 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

Alphabet 5     I.C. = 1.91
6 2 4   8 1 3   7   1 2 1 4 3     5 2 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

Except for possibly Alphabet 1, all are standard distributions.
It is clear that the Aplain for  alphabets 2,3,4,5 are H,I,T,E
cipher.  A little experimentation gets us Aplain in alphabet 1=
Wcipher.  The key word under Aplain is WHITE. The five complete
cipher alphabets are shown in matrix form in Figure 11-7.

Figure 11-7

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

Applying these values to the first groups of our message:

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

Look at the I.C.'s for these alphabets. The expected is
1.73. The third alphabet is almost exact. Three alphabets seem
low and one is high or are they?  Actually these deviations are
within one sigma of the samples of these sizes 55 tallies, so
the deviations are not abnormal.  The standard deviations may
be calculated with:

For plain text:

Sigma (O) = Sqrt[ (0.0048)N**3 + (.1101)N**2-
(.1149) N]

Sigma(I.C.)= 26/(N-1)sqrt(N) * sqrt[ (0.0048)N**2 +
(.1101)N- (.1149) ]

The more important deviation is from random rather than
observed:

Sigma(Phi) = 0.2720 sqrt[ N (N-1)]

Sigma(I.C.)= 7.0711/sqrt[N(N-1)]

where: sqrt is the square root function
The latter two equations apply to a 26 letter alphabet only.

Since simage is defined as a difference between the observed
and the expected number, divided by the standard deviation, it
may be shown that the I.C. of Alphabet 1 is 1.44-1.00/.13 =
3.38 sigma over random; for this type of distribution which
follows the Chi squared distribution, this amounts to 1 chance
in 300 of being random.

In the foregoing example, standard alphabets were used.
We could easily of used reversed standard alphabets. The U.S.
Army Cipher Disk produces just this type of cipher. It is known
as the Beaufort Cipher.  The direction of the crests and
troughs is reversed when fitting the distributions to the
normal.

SOLUTION BY COMPLETING THE PLAIN-COMPONENT SEQUENCE

When direct standard alphabets are used we can mechanically
solve the cipher by completing the plain component.  The plain
text reappears on only one generatrix and this generatrix is
the same for the whole message.  It is the only generatrix that
yields intelligible text.  This same process can be modified to
work with the alphabets of a Viggy. In this case the correct
generatrix should be distinguishable from the others because it
shows a more favorable assortment of high frequency letters,
and thus can be selected by eye from the whole set of
generatrixes.

Using the previous example, we let the first ten cipher letters
in each alphabet be set down in a horizontal line and the
assumption is made that the alphabets are direct standard with
normal sequences.  See Figure  11-8.

We use the following selection rules:

1. Circle all low frequency letters J, K, Q, X, Z and discard
any row that has two or more of these letters in it.

2. We weight the eight highest frequency letters (ETANORISH)
as 1 and the remaining letters as 0. The sum of the weights
is recorded at the side of each row.

3. Select the highest score.  This works 8 out of 10 times.
The correct answer is 10 out of 10 if we examine the top
three scores.   Friedman presents the statistical proof for
this method in FRE7].

This method works regardless of the key (which might be a
number) as in the Gronsfeld Cipher.

Figure 11-8

Gen./   Alphabet 1    Alphabet 2    Alphabet 3     Alphabet 4
1      AJZJNEZAIJ  2 UAYMFTHYLK  2 KMMIMIBMVU     HKWGLMHZMT
2      BKAKOFABJK    VBZNGUIZML    LNNJNJCNWV   5 ILXHMNIANU
3    0 CLBLPGBCKL  4 WCAOHVJANM    MOOKOKDOXW     JMYINOJBOV
4    0 DMCMQHCDLM    XDBPIWKBON  2 NPPLPLEPYX     KNZJOPKCPW
5  * 7 ENDNRIDEMN    YECQJXLCPO    OQQMQMFQZY     LOAKPQLDQX
6    7 FOEOSJEFNO    ZFDRKYMDQP  7 PRRNRNGRAZ   3 MPBLQRMERY
7    2 GPFPTKFGOP    AGESLZNERQ  7 QSSOSOHSBA     NQCMRSNFSZ
8      HQGQULGHPQ  5 BHFTMAOFSR  6 RTTPTPITCB  *8 ORDNSTOGTA
9    5 IRHRVMHIQR  4 CIGUNBPGTS    SUUQUQJUDC   4 PSEOTUPHUB
10     JSISWNIJRS    DJHVOCQHUT  4 TVVRVRKVED     QTFPUVQIVC
11     KTJTXOJKST  4 EKIWPDRIVU  3 UWWSWSLWFE     RUGQVWRJWD
12     LUKUYPKLTU    FLJXQESJWV    VXXTXTMXGF     SVHRWXSKXE
13     MVLVZQLMUV    GMKYRFTKXW  1 WYYUYUNYHG   3 TWISXYTLYF
14   4 NWMWARMNVW    HNLZSGULYX    XZZVZVOZIH     UXJTYZUMZG
15     OXNXBSNOWX  4 IOMATHVMZY  5 YAAWAWPAJI     VYKUZAVNAH
16   3 PYOYCTOPXY    JPNBUIWNAZ    ZBBXBXQBKJ   3 WZLVABWOBI
17     QZPZDUPQYZ    KQOCVJXOBA  2 ACCYCYRCLK     XAMWBCXPCJ
18     RAQAEVQRZA  1 LRPDWKYPCB    BDDZDZSDML     YBNXCDYQDK
19   5 SBRBFWRSAB    MSQEXLZQDC *8 CEEAEATENM     ZCOYDEZREL
20   4 TCSCGXSTBC *6 NTRFYMARED  2 DFFBFBUFON   4 ADPZEFASFM
21   2 UDTDHYTUCD  5 OUSGZNBSFE  2 EGGCGCVGPO   4 BEQAFGBTGN
22   4 VEUEIZUVDE  4 PVTHAOCTGF  0 FHHDHDWHQP   2 CFRBGHCUHO
23   2 WFVFJAVWEF  1 QWUIBPDUHG    GIIEIEXIRQ   3 DGSCHIDVIP
24     XGWGKBWXFG    RXVJCQEVIH    HJJFJFYJSR     EHTDIJEWJQ
25     YHXHLCXYGH    SYWKDRFWJI    IKKGKGZKTS     FIUEJKFXKR
26     ZIYIMDYZHI    TZXLESGXKJ  2 JLLHLHALUT     GJVFKLGYLS

Alphabet 5
1      YIMXXIRMEG
2      ZJNYYJSNFH
3      AKOZZKTOGI
4    2 BLPAALUPHJ
5      CMQBBMVQIK
6    4 DNRCCNWRJL
7      EOSDDOXSKM
8    5 FPTEEPYTLN
9      GQUFFQZUMO
10   4 HRVGGRAVNP
11   4 ISWHHSBWOQ
12     JTXIITCXPR
13     KUYJJUDYQS
14     LVZKKVEZRT
15   3 MWALLWFASU
16     NXBMMXGBTV
17   3 OYCNNYHCUW
18     PZDOOZIDVX
19     QAEPPAJEWY
20     RBFQQBKFXZ
21   4 SCGRRCLGYA
22   3 TDHSSDMHZB
23  *8 UEITTENIAC
24     VFJUUFOJBD
25     WGKVVGPKCE
26     XHLWWHQLDF

The high frequency generatrixes are selected and their letters
are juxtaposed in columns, the consecutive letters of
intelligible plain text present themselves.  If reversed
standard alphabets are used, we must convert the cipher letters
of each isolated alphabet into their normal, plain component
equivalents, and then proceed as in the case of direct standard
alphabets.

For Alphabet 1, generatrix 5..  E N D N R I D E M N
For Alphabet 2, generatrix 20.. N T R F Y M A R E D
For Alphabet 3, generatrix 19.. C E E A E A T E N M
For Alphabet 4, generatrix 8..  O R D N S T O G T A
For Alphabet 5, generatrix 23.. U E I T T E N I A C

(Read down the columns for plain text.)

Friedman describes a graphical method for generatrix
development in [FR7] and [FR8].

Time to move on to other family members.  We shall identify the
systems and peculiarities of each, but remember that the
solution techniques presented for the papa bear apply equally
well to the children and cousins.

VARIANT CIPHER

The Variant Cipher is just that, a variant of the Vigenere,
except that if the Viggy procedure is followed through, a
peculiar keyword appears, like JYUWFT.  Going back to the
slides, In the Variant, the plaintext appears in the opposite
slide from the one containing the key letter: Vigenere below
the 'A' and Variant above the 'A'.  The application of the high
frequency letters is the same.  The keyword is obtained in a
different fashion.  For the simple encipherment of  COME AT
ONCE with the keyword TENT:

T E N T     T E N T
-------     -------
C O M E     J K Z L
A T O N     H P B U
C E - -     J A - -

The setting of the slides for say , the initial T of the
keyword is:

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

The decipherment of a Variant is the same as a Vigenere.

VARIANT SOLUTION BY COMPUTER

>From our trusty CDB, I found Variant.exe and applied it to the
following cryptogram:

UALOT SILKH RWEBN NRHNL THURD VPVCH DLSUC OABSM YMXFO QAUBR
NFHFR IBAOH YTMWT ENJVQ UPZHF AQWGZ MVHTB OENJD IGIMF SULUA
BPMLZ RNFNX SMJTG DJHAF EKKSZ QWDZQ CLVRN FZXBZ WISTJ LMRNH
RZ.

The solution was found in two steps with a period of 7, keyword
"RABBVTS" which is RABBITS, and reads: Lamp black is
extensively in the manufacture of printing inks, as a pigment
for oil painting and also for waxing and lacquering of leather
as well as in darkening  a furniture polish.  Total time 2 or
3 minutes.

BEAUFORT CIPHER

A third member of the Viggy family, the Beaufort, and while the
same procedure is applied, the slides (or tables)  are
different.  One is a normal alphabet, extending double length
A-Z; the other is reversed, double length Z-A.  So if I = T at
one setting, then T=I at the same setting.  It does not matter
what the index for the key is, the results are the same.

So:

ABCDEFGHIJKLMNOBQRSTUVWXYZABCDEFGHIJKL
TSRQPONMLKJIHGFEDCBAZYWXVUTSRQPONMLKJI
*                         *

Again the simple example.

T E N T     T E N T
-------     -------
C O M E     R Q B P
A T O N     T L Z G
C E - -     R A --

BEAUFORT SOLUTION BY COMPUTER NEEDS WORK

I found BEAUFORT.exe at the CDB and applied it two the
following message:

LDYUP AKUPT LVDTO BXUFW SERZP QMQPD NITHA NXUHE UGZTG HMGSM
SRCUF LBQPZ XRYOB FDMNZ TGCUP QQUFB PANAQ HBOON XOOQP DJCJK
TPFDV TBRKL TTSZG ODUFB TETEL POIEB HRTSM DBGGA YUT.

Not so successful this time.  It croaked at period = 6.
The best i could get was "light-" I then reran the program with
a wider key range and found that the true period was 10.  After
some trial and error,
the keyword is LIGHTHOUSE and the message starts:

A fine head land of granite pierced by a natural arch on..
Solution time 15 minutes with at least two wrong trails.

RELATIONSHIPS

LEDGE points out some interesting relationships between the
Vigenere, Variant and Beaufort.  Let A=0, B=1, C=2 .. Z=25,
then:

O  Vigenere: Cipher Letter = Plaintext letter + keyletter
(modulo 26)

O  Variant:  Cipher letter = Plaintext letter - keyletter
(modulo 26)

O  Beaufort: Cipher letter = Keyletter - Plaintext letter
(modulo 26)

Suppose plain text = B and Key = C.  Since B=1 and C=2,
Vigenere ciphertext = 1 + 2 = 3 or D; For Variant ciphertext
1-2=-1 +26 = 25 = Z.

For Vigenere and Variant if key letter = A, since A=0,the
cipher text = plain text.  If we reconstruct a cipher assuming
it is a Vigenere, but it is actually a Variant, we will get the
true plain text but strange keyword.  By subtracting the
Variant equation from the Vigenere equation and setting cipher
text (Viggy) = ciphertext (Variant) and similarly plaintext
(Viggy) = plaintext (Variant), we get the keyletter (Variant)
= - keyletter(Vigenere) the same relationship as that between
ciphertext and plaintext when the keyletter is A in the
Beaufort (since A=0).  Hence, we encipher our strange keyword
with the A Beaufort alphabet to get the Variant key.  The same
holds true if we have a Variant and assume it a Viggy.

If we have a Vigenere and a fragment of the same message
enciphered with the same key in Variant (or visa versa) then,

a. Plaintext = (Ciphertext(Variant)) +
Ciphertext(Vigenere))/2(modulo 13)

b. Key  = (Ciphertext(Vigenere) - Ciphertext(Variant))/2
(modulo 13)

If we have a Vigenere and a fragment of a Beaufort for the same
key and plaintext or visa versa then,

c. Plaintext = (Ciphertext(Vigenere)) -
Ciphertext(Beaufort))/2(modulo 13)

d. Key  = (Ciphertext(Vigenere) +
Ciphertext(Beaufort))/2(modulo 13)

In equations a-d, two answers are produced because modulo 13
will give one number from 0-12 and another 13-25.  Solution is
by inspection.

PORTA (aka NAPOLEON'S TABLE)

Table 11-7 defines the PORTA Cipher.  In this table the
alphabets are all reciprocal, for example Gplain(Wkey) =
Rcipher, Rplain(Wkey)=Gcipher. They are called complementary
alphabets. Either of two letters may serve as a key letter
indifferently: Gplain(Wkey) or Gplain(Xkey) = Rcipher.

Table 11-7

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

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

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

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

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

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

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

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

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

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

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

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

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

The Porta Cipher permits 13 different ways to disguise a plain
letter.

Again our simple encipherment:

T E N T    T E N T
C O M E    Y M S N
A T O N    W E I E
C E - -    Y T - -

A peculiarity of this system  is that since half the alphabet
is represented by the half of the alphabet, there never will be
found the letters A-M  of the plaintext appearing as A-M in the
ciphertext; no N-Z plaintext appearing as the N-Z ciphertext.
This helpful in placing a tip. THE shows up as a (A-M) (N-Z)
(N-Z) combination.    [BRYA]

Table 11-8 shows a different view of the PORTA Cipher

Table 11-8

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

Using the message text A from page 20 as an example with key
word WHITE , the distribution of 5 alphabets is:

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

4 2 5     1   3   4 4     1 2 3 1 2 4 9 1   2 5
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

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

5 2 2 2           4 3 2 1 6 2 4   9 1 3   7   1
5.   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

Now we can divide the M and N distributions, and each half may
be used to fit a normal distribution.  In alphabet 1, the
sequence CDEFGHIJ cipher may easily be recognized as NOPQRSTU
plain; this would fix the keyletters as WX, and therefor the
A...Mplain sequence should begin with Ycipher.  In alphabets
2,3, and 5 the RSTplain sequence may be  spotted at BCDcipher,
ABCcipher, and CDEcipher, respectively, whereas in alphabet 4,
if Ncipher = Eplain, then Ecipher = Nplain; therefore the
original assumptions for the first halves will be confirmed by
the goodness of fit of the distributions for the second halves.
The keys fore these 5 alphabets are derived as (W,X), (G,H)
(I,J), (S,T), and (E,F); from these letters we get WHITE.

In completing the plain component sequence for the Porta
encipherment, the cipher letters are first converted to their
Porta plain-component equivalents and then these letters are
used for the decipherment.  EXCEPT, cipher letters A-M are
completed in a downward direction and cipher letters N-Z are
completed in an upward direction.

Reference [FR7] gives the example:

P K T F F  C D V I T   O B V Z X  C V R E E  G I V J E
T P R K T  O Q C F L   P B V P X  ....

The conversion process and plain component completion of the
first three alphabets are shown below using the generatrix
elimination and weighting scheme developed earlier:

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

The generatrixes with the highest scores are the correct ones.

MODIFIED PORTA

Just as the Vigenere table consisting of direct standard
alphabets has its complementary table of reversed standard
alphabets, a variant of the Porta table can be constructed
where the lower halves  of the sequences run  in opposite
direction to the upper half. For example,

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

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

PROBABLE WORD METHOD OF SOLUTION FOR PORTA

The probable word method is very easy way to attack a Porta
cipher.  Let 1 = any letter in the A-M sequence, and 2 equal
any letter in the N-Z sequence.

P K T F F  C D V I T   O B V Z X  C V R E E  G I V J E
2 1 2 1 1  1 1 2 1 2   2 1 2 2 2  1 2 2 1 1  1 1 2 1 1

T P R K T  O Q C F L   P B V P X  ....
2 2 2 1 2  2 2 1 1 1   2 1 2 2 2

Use the probable word INFANTRY, which has the class notation of
12112222, but in encipherment is reversed to 21221111 pattern.
At position 15,  X C V R E E G I,  we find:

plain       I N F A N T R Y
cipher      X C V R E E G I

key         E W G I S E W G
derived     F X H J T F X H

Read diagonally, we see WHITE repeated.

COMPUTER SOLUTION OF PORTA

At the trusty CDB is a program called PORTA.exe.  Using it on
the following cipher message found a period of 9 with a
possible key of KL/IJ/CD/MN/AB/OP/OP/EF/QR.  I came up with the
keyword LIDNAOOER

EYWRR  MOTJJ  QOHFA  LTYQV  SQFPG  EPWTG  RVGUC  DVVBT  EMLMN
BYSOE  OHFKW  YARQL  PEBSB  ETVXM  WVBCV  XRTIT  JJAMX  EHADX
VCAXN  MMWZR  WALFY  BTJSP  RTLLP  LZDVD  FZHGE  PBKQR  RUKWQ
AEAOP  Y

and behold the message cracked to:

While the Romans used leeks in the culinary depart..

The process took less than two minutes but did not yield the
actual keyword or require it.

GRONSFELD

The GRONSFELD Cipher uses a numerical key and restricts the
Viggy table to just ten alphabets.  We can construct a slide
with one normal alphabet and numbered one like this:

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

One half the digits are used for encipherment and the other
half for decipherment.  For example the key is derived as
follows:

C O N S T I T  U  T  I O N
1 6 4 8 9 2 10 12 11 3 7 5

The first duplicate letter carries the lower number.

So back to:

6 2 3 4      6 2 3 4
C O M E      I Q P I
A T O N      G V R R
C E - -      I G - -

Slide method: put the 0 over the C, take the letter to the
right in juxtaposition of the 6 = I, same for A which is G
and so on.  We decipher by looking to the left.

A typical decipherment might look like this for the test word
"YOUR":

0 2 4 7         0 2 4 7         0 2 4 7         0 2
T S V H Y Q B V Y I G L M G U X A S R M F K C I A A O V I Z
-----------------------------------------------------------
S R U G Y O U R X F H K M E N T Z R Q L F I V E Z Z N U I X
-------         -------         -------         ---
R Q T F         W G E J         Y Q P K         Y Y M T
Q P S E         V F D I         X P O J         W W K R

T S V H Y Q B V Y I G L M G U X A S R M F K C I A A O V I Z
-----------------------------------------------------------
Y     9 0   3   0   8     8     2       7   4   2 2
O         2   7             6     4                 0
U           7   4             3                       1
R             4                 9

LECTURE 11 PROBLEMS

11.1  Viggy.

SYCVT  HFXEQ  DPTLN  KTGMP  FHMPA  SRVIT  LSEXH  DPITX
KELIQ  WDXEC  VNLIP  HPWXD  XXIXH  UTRIH.

11.2  Beaufort.

SXSXZ  IYLEQ  AWEQF  EZEPP  QZQRD  VANKH  HLZJX  OQSEU
YSOVS  SZKLE  DRMRU  THTUW  SCLOX  NEHLA  OPEEU  GAZIA
UUOQG  OJX.

11.3  Variant.

JQRSB  YBKNF  WWTGK  UXDTK  ZAOAA  MCVJU  KBCEX  GUYLB
UASWY  TIENQ  XLPYX  CWASU  VAKOM  XIGIK  XHWZT  SWGOP
WRTSJ  NAWG.

11.4 Gronsfeld.

ZRWQU  IKLMS  IXAWI  UQMWP  KFQEL  RBWJG  XHIXT  NLVKS  ZHVHS
ZRUEK  KWPIM  GSXIA  XVUEL  RHZPI  SLBWT  NHU.

11.5  Viggy or Beaufort; same message and key starts ONOIHT.

ORQGX  HPNKW  QQCHI  ABIFZ  NQCHR  VLVLU  HYUDT  MCYJN  WAUHP
HLVIN  BZCCB  GCGKZ  JNLMM  WTVLY  DYCCV  JPUVG  KLKQX  YTTKI
XOQYB  JJMHJ  BYHQY  LFQWF  NRYUC  XCECN  GPCBW  TPAXE  ABKGC
PVHKL  OIKQW  TPKOW  KNCMM  HFFAV  A.

Thanks to JOE O for a fine analysis of all three problems.

QQ-1  QUAGMIRE I  Travelogue. (Ends:SINGOUTOFTHESEA) RHIZOME

1234567  1234567  1234567  1234567  1234567  1234567  1234567
THEFIRS  TIMEaVI  SITOREX  CLAIMSA  HROMANT  ICVENIC  ESINKIN
KKQHPQR  KTYOiTA  TLGAWBM  XORKTAT  BSOOIYI  CGICEJV  UCYZRJP

ALNSFRZ  UCQDXIS  TDRBFYS  YTFDZBD  USQWKMT  CPPDOAI  CAAKEHK

UAYFHQA  TLNIFSI  SIGJHAS  V.

QQ-1 Quagmire I Solution.

VERDICT/nose. Period =7.
The first time visitor exclaims "Ah, romantic Venice sinking
into the sea." The seasoned traveler exclaims,"Ah, stinking
Venice rising out of the sea.

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

QQ-2  QUAGMIRE III Tedious.   (CRYPTANALYTIC METHODS)
DOPPELSCHACH
Period= 6

12345  61234  56123  45612  34561  23456  12345  61234  56123
THETI  MEREQ  UIRED  BYS.......
PNATV  SJBAQ  WGMTR  BZYLU  ACACR  GBNTQ  FGGCN  APNID  ULMVD

SCEPB  AMCQF  BBPVR  EOBSL  AFSAN  HFYVV  MCYTF  LEMAO  MFHVU

KBAAU  ATTEA  NGOHU  GTQEX  ISUGU  SAKCC  TLIRT  TLSZM  PBMGV

APYRV  YIIGL  WGNUF  JFROG  SNQGN  HBOTU  TACUO  JUVQH  HUGWW

WBIMT  WNHVO  GTLSZ  MPYQZ  BNCEN  UWLC.

HARDER/decorative. Period = 6. The time required by some
cryptanalytic methods  grows extremely rapidly as key length or
message length increases.  All possible keys for a columnar
transposition instead of making an entry by building up a
from a pair of columns is an example.

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

QQ-3  QUAGMIRE IV  Economics Lesson.     EDNASANDE

THEEC  ONOMY  OFTHE  NATIO ..........
TDNSE  PMBSV  FURMQ  UFYSJ  PAGGY  FVIKT  GYVLV  FBTPH  IIIAD

HVIUY  QSAFA  VQVFU  HPIHE  BIXNN  HBSTN  IRMQH  IIIAD  OVIXT

CTNOW  EOJOZ  BOWBU  ONLFN  GOBJS  HBOQS  VZMOU  JSFQH  SAHPS

JBBJT  AAMIE  XILRA  TOTVL  TUAML  FLNEJ  PPMNT  XHVQV  FCYSB

JODNF  XJSFT  UIUTM  ONKDO  UMMSB  NWUL.

EXCHANGE/stock/MARKET.  The economy of the Nation is built
on supply and demand, the result of inflation. Recession
is a temporary falling off of business activity during a
period when such activity has been generally increasing..

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

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[ANDR] Andrew, Christopher, 'Secret Service', Heinemann,
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[ANN1] Anonymous., " Speech and Facsimile Scrambling and
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[ASA ] "The Origin and Development of the Army Security
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[ASHT] Ashton, Christina, "Codes and Ciphers: Hundreds of
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[ASIR] Anonymous, Enigma and Other Machines, Air Scientific
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[AUG1] D. A. August, "Cryptography and Exploitation of Chinese
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[BLK]  Blackstock, Paul W.  and Frank L Schaf, Jr.,
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[BODY] Brown, Anthony - Cave, "Bodyguard of Lies", Harper and
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[COLP] Collins Gem Dictionary, "Portuguese," Collins Clear Type
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[COLR] Collins Gem Dictionary, "Russian," Collins Clear Type
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[COPP] Coppersmith, Don.,"IBM Journal of Research and
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[EIIC] Ei'ichi Hirose, ",Finland ni okeru tsushin joho," in
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[ELCY] Gaines, Helen Fouche, Cryptanalysis, Dover, New York,
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[ENIG] Tyner, Clarence E. Jr., and Randall K. Nichols,
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[EPST] Epstein, Sam and Beryl, "The First Book of Codes and

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[FREB] Friedman, William F., "Cryptology," The Encyclopedia
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[FRSG] Friedman, William F., "Solving German Codes in World War
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[FR1]  Friedman, William F. and Callimahos, Lambros D.,
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[FR2]  Friedman, William F. and Callimahos, Lambros D.,
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[FR3]  Friedman, William F. and Callimahos, Lambros D.,
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[FR4]  Friedman, William F. and Callimahos, Lambros D.,
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[FR6]  Friedman, William F. Military Cryptanalysis - Part II,
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[FR7]  Friedman, William F. and Callimahos, Lambros D.,
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[FR8]  Friedman, William F. and Callimahos, Lambros D.,
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[FRE]  Friedman, William F. , "Elements of Cryptanalysis,"
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[FREA] Friedman, William F. , "Advanced Military Cryptography,"
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[FREB] Friedman, William F. , "Elementary Military
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[FR22] Friedman, William F., The Index of Coincidence and Its
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[FRAN] Franks, Peter, "Calculator Ciphers," Information
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[FR8]  Friedman, W. F., "Cryptography and Cryptanalysis
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[FRZM] Friedman, William F.,and Charles J. Mendelsohn, "The
Zimmerman Telegram of January 16, 1917 and its
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[GAR3] Gardner, Martin, "New Mathematical Diversions from
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[GAR4] Gardner, Martin, "Sixth Book of Mathematical Games from
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[GARL] Garlinski, Jozef, 'The Swiss Corridor', Dent, London
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[GAR1] Garlinski, Jozef, 'Hitler's Last Weapons', Methuen,
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[GE]   "Security," General Electric, Reference manual Rev. B.,
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[GERH] Gerhard, William D., "Attack on the U.S, Liberty,"
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[GERM] "German Dictionary," Hippocrene Books, Inc., New York,
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[GLEN] Gleason, Norma, "Fun With Codes and Ciphers Workbook,"
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[GLE1] Gleason, Norma, "Cryptograms and Spygrams," Dover, New
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[GLEA] Gleason, A. M., "Elementary Course in Probability for
the Cryptanalyst," Aegean Park Press, Laguna Hills, CA,
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[GLOV] Glover, D. Beaird, "Secret Ciphers of the 1876
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[GODD] Goddard, Eldridge and Thelma, "Cryptodyct," Marion,
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[GORD] Gordon, Cyrus H., " Forgotten Scripts:  Their Ongoing
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[GRA1] Grandpre: "Grandpre, A. de--Cryptologist. Part 1
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[GRA2] Grandpre: "Grandpre Ciphers", ROGUE, The Cryptogram,
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[GRA3] Grandpre: "Grandpre", Novice Notes, LEDGE, The
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[GREU] Greulich, Helmut, "Spion in der Streichholzschachtel:
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[GROU] Groueff, Stephane, "Manhattan Project: The Untold Story
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[GUST] Gustave, B., "Enigma:ou, la plus grande 'enigme de la
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[GYLD] Gylden, Yves, "The Contribution of the Cryptographic
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[HA]   Hahn, Karl, " Frequency of Letters", English Letter
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[HELD] Held, Gilbert, "Top Secret Data Encryption Techniques,"
Prentice Hall, 1993.  (great title..limited use)

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

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

[HIDE] Hideo Kubota, " Zai-shi dai-go kokugun tokushu joho
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[HILL] Hill, Lester, S., "Cryptography in an Algebraic
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[HIL1] Hill, L. S. 1929. Cryptography in an Algebraic
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[HIL2] Hill, L. S.  1931.  Concerning the Linear
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[HINS] Hinsley, F. H.,  "History of British Intelligence in the
Second World War", Cambridge University Press,
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[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
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[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
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[HITT] Hitt, Parker, Col. " Manual for the Solution of Military
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[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,
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cryptographic resource materials. )

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

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

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

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

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

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

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

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

[HYDE] H. Montgomery Hyde, "Room 3603, The Story of British
Intelligence Center in New York During World War II",
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[IBM1] IBM Research Reports, Vol 7., No 4, IBM Research,
Yorktown Heights, N.Y., 1971.

[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
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[JOHN] Johnson, Brian, 'The Secret War', Arrow Books,
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Cryptographic Properties of Arabic, Proceedings of the
Third Saudi Engineering Conference. Riyadh, Saudi
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[KAHN] Kahn, David, "The Codebreakers", Macmillian Publishing
Co. , 1967.

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

[KAH2] Kahn, David, "An Enigma Chronology", Cryptologia Vol
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[KAH3] Kahn, David, "Seizing The Enigma: The Race to Break the
German U-Boat Codes 1939-1943 ", Houghton Mifflin, New
York, 1991.

[KARA] Karalekas, Anne, "History of the Central Intelligence
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[KASI] Kasiski, Major F. W. , "Die Geheimschriften und die
Dechiffrir-kunst," Schriften der Naturforschenden
Gesellschaft in Danzig, 1872.

[KAS1] Bowers, M. W., {ZEMBIE} "Major F. W. Kasiski -
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[KATZ] Katzen, Harry, Jr., "Computer Data Security,"Van
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[KERC] Kerckhoffs, "la Cryptographie Militaire, " Journel des
Sciences militaires, 9th series, IX, (January and
February, 1883, Libraire Militaire de L. Baudoin &Co.,
Paris.  English trans. by Warren T, McCready of the
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[KOBL] Koblitz, Neal, " A Course in Number Theory and
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[KONH] Konheim, Alan G., "Cryptography -A Primer" , John Wiley,
1981, pp 212 ff.

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

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

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

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

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

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

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

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

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

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

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

[LAN2] Langie, Andre, and E. A. Soudart, "Treatise on
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[LATI] BRASSPOUNDER, "Latin Language Data, "The Cryptogram,"
July-August 1993.

[LAUE] Lauer, Rudolph F.,  "Computer Simulation of Classical
Substitution Cryptographic Systems" Aegean Park Press,
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[LEAR] Leary, Penn, " The Second Cryptographic Shakespeare,"
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[LEA1] Leary, Penn, " Supplement to The Second Cryptographic
Shakespeare," Omaha, NE [from author]  1994.

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

[LENS] Lenstra, A.K. et. al. "The Number Field Sieve,"
Proceedings of the 22 ACM Symposium on the Theory of
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[LEN1] Lenstra, A.K. et. al. "The Factorization of the Ninth
Fermat Number," Mathematics of Computation 61 1993, pp.
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[LEWF] Lewis, Frank, "Problem Solving with Particular Reference
to the Cryptic (or British) Crossword and other
'American Puzzles', Part One," by Frank Lewis,
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[LEW1] Lewis, Frank, "The Nations Best Puzzles, Book Six,"
by Frank Lewis, Montserrat, January 1990.

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

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

[LEWY] Lewy, Guenter, "America In Vietnam", Oxford University
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[LEVI] Levine, J.,  U.S. Cryptographic Patents 1861-1981,
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[LEV2] Levine, J.  1961.  Some Applications of High-
Speed Computers to the Case n =2 of Algebraic
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[LEV3] Levine, J. 1963.  Analysis of the Case n =3 in Algebraic
Cryptography With Involuntary Key Matrix With Known
Alphabet.  Journal fuer die Reine und Angewante
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[LISI] Lisicki, Tadeusz, 'Dzialania Enigmy', Orzet Biaty,
London July-August, 1975; 'Enigma i Lacida',
Przeglad lacznosci, London 1974- 4; 'Pogromcy
Enigmy we Francji', Orzet Biaty, London, Sept.
1975.'

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

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

[LYSI] Lysing, Henry, aka John Leonard Nanovic, "Secret
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[MACI] Macintyre, D., "The Battle of the Atlantic," New York,
Macmillan, 1961.

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[MAGN] Magne, Emile, Le plaisant Abbe de Boisrobert, Paris,
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[MANN] Mann, B.,"Cryptography with Matrices," The Pentagon, Vol
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[MANS] Mansfield, Louis C. S., "The Solution of Codes and
Ciphers", Alexander Maclehose & Co., London, 1936.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[MM]   Meyer, C. H., and Matyas, S. M., " CRYPTOGRAPHY - A New
Dimension in Computer Data Security, " Wiley
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[MODE] Modelski, Tadeusz, 'The Polish Contribution to the
Ultimate Allied Victory in the Second World War',
Worthing (Sussex) 1986.

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

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

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

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

[NIBL] Niblack, A. P., "Proposed Day, Night and Fog Signals for
the Navy with Brief Description of the Ardois Hight
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[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
Languages," ACA-L, August 18, 1995.

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

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

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

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

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

[NIC7] Nichols, Randall K., "Arabic Contributions to
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[NIC8] Nichols, Randall K., "U.S. Coast Guard Shuts Down Morse
Code System," The Cryptogram, SO95, ACA publications,
1995.

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

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

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

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

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

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

[NSA1] NMasked Dispatches: Cryptograms and Cryptology in
American History, 1775 -1900. Series 1, Pre World War I
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[OHAV] OHAVER, M. E., "Solving Cipher Secrets," Aegean Park
Press, 1989.

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1973.

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Unit One, Problem Solving and Logical Thinking,
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Manual For Cryptarithms," Unit One, Problem Solving and
Logical Thinking, University of Oklahoma, Norman, Ok.
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[OP20] "Course in Cryptanalysis," OP-20-G', Navy Department,
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[OTA]  "Defending Secrets, Sharing Data: New Locks and Keys for
Electronic Information," Office of Technology
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Dover, 1961.

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Ventura, Ca. 93003, 1994.

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[POPE] Pope, Maurice, "The Story of Decipherment: From Egyptian
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[PORT] Barker, Wayne G. "Cryptograms in Portuguese," Aegean
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[POR1] Aliandro, Hygino, "The Portuguese-English Dictionary,"
Pocket Books, New York, N.Y., 1960.

[POUN] Poundstone, William, "Biggest Secrets," Quill
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[PRIC] Price, A.,"Instruments of Darkness: the History of
Electronic Warfare, London, Macdonalds and Janes, 1977.

[PROT] "Protecting Your Privacy - A Comprehensive Report On
Eavesdropping Techniques and Devices and Their
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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.
Merriam Co., Norman, OK. 1982.

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

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

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

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

[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma
Cipher" published in vol 6, #1, Jan 1982 Cryptologia pp
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[RELY] Relyea, Harold C., "Evolution and Organization of
Intelligence Activities in the United States,"
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[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'", Bulletin
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[RHEE] Rhee, Man Young, "Cryptography and Secure Commun-
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[RIVE] Rivest, Ron, "Ciphertext: The RSA Newsletter 1, 1993.

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Obtaining Digital Signatures and Public Key
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[ROAC] Roach, T., "Hobbyist's Guide To COMINT Collection and
Analysis," 1330 Copper Peak Lane, San Jose, Ca. 95120-
4271, 1994.

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

[ROHE] Jurgen Rohwer's Comparative Analysis of Allied and Axis
Radio-Intelligence in the Battle of the Atlantic,
Proceedings of the 13th Military History Symposium, USAF

[ROHW] Rohwer Jurgen,  "Critical Convoy Battles of March 1943,"
London, Ian Allan, 1977.

[ROH1] Rohwer Jurgen, "Nachwort: Die Schlacht im Atlantik in
der Historischen Forschung, Munchen: Bernard and Graefe,
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[ROH2] Rohwer Jurgen, et. al. , "Chronology of the War at Sea,
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[ROH3] Rohwer Jurgen, "U-Boote, Eine Chronik in Bildern,
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[ROOM] Hyde, H. Montgomery, "Room 3603, The Story of British
Intelligence Center in New York During World War II",
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[ROSE] Budge, E. A. Wallis, "The Rosetta Stone," British Museum
Press, London, 1927.

[RSA]  RSA Data Security, Inc., "Mailsafe: Public Key
Encryption Software Users Manual, Version 5.0, Redwood
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[RUNY] Runyan, T. J. and Jan M. Copes "To Die Gallently",
Westview Press 1994, p85-86 ff.

[RYSK] Norbert Ryska and Siegfried Herda, "Kryptographische
Verfahren in der Datenverarbeitung," Gesellschaft fur
Informatik, Berlin, Springer-Verlag1980.

Tokyo: Charles E. Tuttle Co., 1969.

[SACC] Sacco, Generale Luigi, " Manuale di Crittografia",
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[SALE] Salewski, Michael, "Die Deutscher Seekriegsleitung,
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[SANB] Sanbohonbu, ed., "Sanbohonbu kotokan shokuinhyo." NIDS
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[SAPR] Sapir, E., "Conceptual Categories in Primitive
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[SASS] Sassoons, George, "Radio Hackers Code Book", Duckworth,
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[SCHN] Schneier, Bruce, "Applied Cryptography: Protocols,
Algorithms, and Source Code C," John Wiley and Sons,
1994.

[SCH2] Schneier, Bruce, "Applied Cryptography: Protocols,
Algorithms, and Source Code C," 2nd ed., John Wiley and
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[SCHU] Schuh, fred, "Master Book of Mathematical Recreation,"
Dover, 1968.

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

[SEBE] Seberry, Jennifer and Joseph Pieprzyk, "Cryptography: An
Introduction to Computer Security," Prentice Hall, 1989.
[CAREFUL!  Lots of Errors - Basic research efforts may
be flawed - see Appendix A pg 307 for example.]

[SHAN] Shannon, C. E., "The Communication Theory of Secrecy
Systems," Bell System Technical Journal, Vol 28 (October
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[SHIN] Shinsaku Tamura, "Myohin kosaku," San'ei Shuppansha,
Toyko, 1953.

[SHUL] Shulman, David, "An Annotated Bibliography of
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[SIC1] S.I. Course in Cryptanalysis, Volume I, June 1942,
Aegean Park Press, Laguna Hills , CA.  1989.

[SIC2] S.I. Course in Cryptanalysis, Volume II, June 1942,
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[SIG1] "International Code Of Signals For Visual, Sound, and
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[SIMM] Simmons, G. J., "How To Insure that Data Acquired to
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[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
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[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret
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[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I-
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[SURV] Austin, Richard B.,Chairman,  "Standards Relating To
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[THEO] Theodore White and Annalee Jacoby, "Thunder Out Of
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[THOM] Thompson, Ken, "Reflections on Trusting Trust,"
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[TILD] Glover, D. Beaird, Secret Ciphers of The 1876
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[TURN] Turn, Rein, "Advances in Computer Security," Artec
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[YAR3] Yardley, H. O., "The Education of a Poker Player, Simon
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[YOKO] Yukio Yokoyama, "Tokushu joho kaisoka," unpublished
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[YOUS] Youshkevitch, A. P., Geschichte der Mathematik im
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[YUKI] Yukio Nishihara, "Kantogan tai-So Sakusenshi," Vol 17.,
unpublished manuscript, National Institute for Defense
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[ZIM]  Zim, Herbert S., "Codes and Secret Writing." William
Morrow Co., New York, 1948.

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

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