## Lesson 10: Polyalphabetic Substitution Systems I Viggy's Family And Quagmires I - IV Applications Of The Principals Of Symmetry

```                CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI

April 6, 1996
Revision 0

LECTURE 10

POLYALPHABETIC SUBSTITUTION SYSTEMS I
VIGGY'S FAMILY AND QUAGMIRES I - IV
APPLICATIONS OF THE PRINCIPALS OF SYMMETRY

SUMMARY

In Lecture 10, we return to our course schedule with a study of
fascinating cipher systems based on multiple alphabets
-Polyalphabetic Substitution systems.  What is amazing about
these systems is how long they remained secure.  The Viggy
systems (my name for Vigenere) was considered unbreakable for
over 200 years.  Along comes Major Kasiski, and poof, we have
recreational cryptography.

I think the best way to introduce the subject is via an
overview based on the Op-20-GYT course notes (Office of Chief
Of Naval Operations, Washington) [OP20].  From there, I will
bring in MASTERTON's dissolution of QUAGMIRES I-IV.  [MAST]

In Lecture 11, we will revisit polyalphabetic cipher systems
and the polygraphic cases using Friedman's detailed analysis.
We will cover the PORTA system and other family members.  I
will cover decimation processes in detail. [FRE4], [FRE5],
FRE6], [FRE7], [FRE8]

In Lecture 12, we will describe the aperiodic polyalphabetic
case and give a diagram of topics considered in Lectures 10 -
12.  [FR3]

I have updated our Resources Section with many references on
these systems - focusing on the cryptanalytic attack and those
of historical interest. Kahn has some interesting stories about
the Viggy family. [KAHN]

POLYALPHABETIC SUBSTITUTION

A cipher system which employs two or more cipher alphabets and
includes a method for designating which cipher alphabet is to
be used for the encipherment of each plain-text letter, is
called a polyalphabetic substitution system.  Cipher systems
employing variant values may appear to use more than one
alphabet, but they have characteristics of mono-alphabetic
substitution and are properly classified as such.

Polyalphabetic substitution systems consists of two general
types; periodic and non-periodic.

(a)   In the periodic type the text of a message is divided
into definite, regular groups or cycles of letters which are
enciphered with identical portions of the key.  Periodic
systems are further subdivided as follows:

(1)   Multiple Alphabet Ciphers in which any number of
cipher alphabets are used in order designated by a
prearranged key.

(2)   Progressive Alphabet Ciphers in which a primary
cipher alphabet and its 25 secondary alphabets are
used either in regular succession, sliding the
components one letter at a time, or in irregular
order according to a prearranged shift.

(b)   In the non-periodic type there are no cyclic repetitions
of the key.

The cipher alphabets employed in multiple alphabet substitution
systems may be constructed by any number of methods.  As an
example, the QUAGMIRE IV uses both vertical and horizontal
keywords.

Example:

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

Here the plain component is a normal sequence, and the cipher
component are identical keyword sequences.  The same keyword
sequences may be used in both the plain cipher components, or
different sequences may be used.  The key which determines the
setting of the cipher alphabets against the plain component
(RED) may be any prearranged word or phrase.  Also, each cipher
alphabet may be assigned a number and the alphabets used in
accordance with a prearranged numerical key.

The process of enciphering a message with the multiple alphabet
system above would appear as follows:

Cipher Alphabet No.

1-2-3-1-2-3-1-2-3-1-2-3-1-2-3-1-2-3-1-2-3-1-2-3

Plain  -  M Y C O U R S E Z E R O T H R E E Z E R O A T T
Cipher -  I Z G S V P F L B W R X G B P W L B W R X R U N

1-2-3-1-2-3-1-2-3-1-2-3-1-2-3-1-2-3

Plain  -  H I R T E E N T H I R T Y T H R E E
Cipher -  Z D P G L J L U O P R N O U O D L J

In order to reduce the chances of encipherment by the wrong
alphabet, the plain text is often written so that the letters
designated by the key for encipherment by each alphabet are
placed in the same vertical column.

Note the repetitions in the plain text which begin at the same
point in the key produce repetitions in the cipher text, while
others [may not] do not.  Friedman discusses accidental
repetitions in [FR7].

PRINCIPLES OF FACTORING

Major Friedrich W. Kasiski (1805-1881) was a career officer in
East Prussia's 33 Infantry Regiment.  He is credited with a
revolutionary insight regarding polyalphabetic repeating key
systems - that the conjuction of a repeated portion of the key
with the repetition in the plaintext produces a repetition in
the ciphertext.  Like causes produce like effects.  The
interval between plaintext or ciphertext repetitions is noted
throughout the cryptogram, factored and the commonality of the
factor is a good indication of the key and number of alphabets
used to encipher the original methods.  The fall of the
Vigenere family is attributed to Kasiski's examination.  [KASI]
[KAS1], [KAHN]

If there are several long repetitions in the cipher text of an
unknown system, the intervals between the initial letters of
these repetition have a common factor, this factor represents
the number of alphabets used to encipher the message and the
exact number of repetitions of the key.

A simple example:

Given the cryptogram:

IZGSV   PFLBW   RXGBP   WLBWR   XRUNZ

DPGLJ   LUOPR   NOUOD   LJ

Factoring:

Repetition   Interval  Factors   Common Factor(s)

LBWRX          9         3,3            3
LJ            12         2,2,3          3
UO             6         2,3            3

The "period" or common factor is three and this is the number
of alphabets employed.

Digraph and trigraph repetitions may be the result of chance
instead of plain text repetitions.  [FR7] discusses in detail.

When factoring results in more than one common factor we shall
use the highest common factor and check with frequencies of the
expected alphabets to see how close to normal they are.  Only
short messages fail to lead to the correct determination of the
number of cipher alphabets employed in the system.  When
factoring fails on a longer message, an aperiodic cipher may
have been employed.

SOLUTION OF A MULTIPLE ALPHABET CIPHER

Phamplet Number 7, Office of Operations Cryptanalysis, Office
of the Chief of Naval Operations, Washington, 1930 [OP20]
prepared this problem for discussion.

From:           A B  (Black Force Commander)
To:             CD, EF, GH, IJ (Black Ships)
Time Groups:    0013-2300 April 1930
Remarks:        Cruiser transmitter.

Cryptogram written out in worksheet format:

Alpha. -  1 2 3 4 5 6 7 8 9 10  Alpha. - 1 2 3 4 5 6 7 8 9 10

1         K P T X S L I C T M    16      M V H A W A D G G Z

2         I A M C B B N M S Z    17      Y F A R Q V K M M Q

3         M J K A Q J B F Z A    18      K F M P S L G X A H

4         J G M B S L N P H H    19      E F W K G C B F T H

5         E E J Z W N C L O W    20      S V C B B U A H S S

6         Z F S A A S Z D E P    21      K P K D E C G O H Z

7         Z X C D J D D H A J    22      L V O D S C O C H A

8         O D B K A H P L G H    23      G V W B Z C A M O Z

9         A J M K T V A M K H    24      M J K A Q J B F J H

10        M B C A A C N W S Z    25      X B H A A V A K O S

11        Z D W I J K G M C X    26      K P K G U L T J O Q

12        M V X X U N B W Z T    27      D F Q Q J K K M H Z

13        I Y N C P O G H H W    28      H V H A E P Z W Q R

14        L G T B W P L V T T    29      O P L A U L B M O Z

15        O B O X J L R M H Z    30      M J K A Q J B F

Collateral Information:

The Black and Blue Fleets are engaged in war maneuvers in the
Caribbean Sea.  The Fleets are not in contact.  The location of
the enemy (the Black Fleet) is unknown.  The message in
question was intercepted by the Blue Flagship at 0015 on 14
April 1930.  The operator had reason to believe that a cruiser
sent the message.

The composition of the Black Fleet is as follows:

Battleships                   Cruisers

West Virginia (flag)          Trenton (flag)
Tennessee                     Richmond
New Mexico                    Memphis
Mississippi
California

Destroyers                    Air Force

Litchfield (flag)             Saratoga (flag)
Preble                        Langley
Pruitt                        Gannet
Noa
Decatur                       Submarine Force
Sicard
Hulbert                       Argonne (flag and tender)
V-1, V-2, V-3
William B. Preston

Factoring:

Repetition       Interval          Factors

ZMJKAQJBF          210             2,3,5,7,10
ZMJKAQJBF          270             2,3,3,5,10
ZMJKAQJBF           60             2,2,3,5,10
MHZMVHA            120             2,2,2,3,5,10
ZMV                 40             2,2,2,5,10
ZMV                160             2,2,2,2,2,5,10
KPK                 50             2,5,5,10

The highest common factor is 10; the period and number of
alphabets used is 10, so the sequence repeats itself after
each 10 letters.

"Lining-up" is one of the basic operations of solution.
We group the message in lines of ten letters. The letters in
each column are enciphered by the same alphabet.  Checking the
frequency tables, each alphabet resembles a single alphabet.

Frequency Tables

#1     #2    #3   #4    #5    #6    #7    #8   #9    #10
A 1    A 1   A 1  A 9   A 4   A 1   A 4   A    A 2   A 2
B      B 3   B 1  B 4   B 2   B 1   B 6   B    B     B
C      C     C 3  C 2   C     C 5   C 1   C 2  C 1   C
D 1    D 2   D    D 3   D     D 1   D 2   D 1  D     D
E 2    E 1   E    E     E 2   E     E     E    E 1   E
F      F 5   F    F     F     F     F     F 4  F     F
G 1    G 2   G    G 1   G 1   G     G 4   G 1  G 2   G
H      H     H 3  H     H     H 1   H     H 3  H 6   H 6
I 2    I     I    I 1   I     I     I 1   I    I     I
J 1    J 4   J 1  J     J 4   J 3   J     J 1  J 1   J 1
K 4    K     K 5  K 1   K     K 2   K 2   K 1  K 1   K
L 2    L     L 1  L 1   L     L 6   L 1   L 2  L     L
M 7    M     M 4  M     M     M     M     M 8  M 1   M 1
N      N     N 1  N     N     N 2   N 3   N    N     N
O 3    O     O 2  O     O     O 1   O 1   O 1  O 5   O
P      P 4   P    P 1   P 1   P 2   P 1   P 1  P     P 1
Q      Q     Q 1  Q 1   Q 4   Q     Q     Q    Q 1   Q 2
R      R     R    R 1   R     R     R 1   R    R     R 1
S 1    S     S 1  S     S 4   S 1   S     S    S 3   S 2
T      T     T 2  T     T 1   T     T 1   T    T 3   T 2
U      U     U    U     U 3   U 1   U     U    U     U
V      V 6   V    V     V     V 3   V     V 1  V     V
W      W     W 3  W     W 3   W     W     W 3  W     W 2
X 1    X 1   X 1  X 3   X     X     X     X 1  X     X
Y 1    Y 1   Y    Y     Y     Y     Y     Y    Y     Y
Z 3    Z     Z    Z 1   Z 1   Z     Z 2   Z    Z 2   Z 9
30     30    30   30    30    30    30    30   29    29

SOLUTION BY KNOWN-WORD METHOD

When ample collateral information is available, the known-word
attack is the easiest and potentially the quickest method of
solution.  From the given data, the message is presumably from
the Commander of a cruiser division to his four cruisers,
giving orders for scouting operations of the cruiser division.

The words most likely to appear are:

Scouting    Scouting line       Trenton      Latitude
Speed       Scouting speed      Richmond     Hundred
Distance    Scouting distance   Memphis      Numbers
Position    Commence scouting   Enemy        Times/Dates

Our concern is not with guessing words but standardizing the
solution.

The Known-Word" method applied in two ways:

(1) Start at a particular point in the cryptogram indicated by
the repetitions, symmetrical sequences, and try to fit the
known-word at this point.   This is called the "Obvious
Location Method."

(2) Start with a "Known-word" and find a place where it will
fit.  This may be called the "Obvious Word Method."

The best method to use depends on the circumstances. In this
problem both methods apply.

OBVIOUS LOCATION

The long repetitions are words or phrases, important to the
subject of the message, and may be known-words.  They are
excellent points of attack.  The beginning of the message or
the end of the message are usually good points of attack.

The second longest repetition is the right length for Trenton,
Memphis, or Hundred; furthermore it links in the letters of the
longest repetition.

Original Assumptions -

MHZ MVHA     lines 15-27  TRENTON is best assumption.
TRE NTON
MEM PHIS
HUN DRED

Check

MOZ MJKAQJBF  lines 24, 30     MOZ MJKAQJBF  could be
T E N  N      Excellent        TEE NHUNDRED  excellent
M M P  S      Poor             THE E--N ---  poor
H N D  D      Poor

Check
MCZ MVX       lines 1-12
TWE NTY       excellent
M M PH        poor
H V DP        poor

Check the values of TEEN HUNDRED and TRENTON

Line 2-3       12345678910     12345678910
IAMCBBNMSZ      MJKAQJBFZA
T E      NHUNDRED
suggests            ATTE      NHUNDRED

Line 23-24     GVWBZCAMOZ      MJKAQJBFDI
T     TEE      NHUNDRED
suggests         THIR
FOUR
FIF
SIX
ATSEVEN
EIGH

Lines 29-30    OPLAULBMOZ      MJKAQJBF--
N  ETEE      NHUNDRED
suggests          NINETEE      NHUNDRED

It is possible that all the above assumptions are incorrect but
they are too good to ignore.  We enter the above values into
the cryptogram to see if skeletons of words appear.

Possibilities are indicated below:

Lines 19-20     12345678910     12345678910
EFWKGCBFTH      SVCBBUAHSS
ED         T      T
SPEEDFI      FTEENKNOTS
SI      X

Line 19 ED could be Speed.. building on that we have other
possibilities.

Lines 21-22     KPKDECGOHZ      LVODSCOCHA
U     RE       T      R
COURSETHRE      ETHREEZERO

Lines 11-12     ZEWIJKGMCZ      MVXXUNBWZT
T E      NT    E
TWE      NTYMILES
T             THREE
FIVE

TRENTON is the most obvious break.  Check letter-combinations
of frequencies to see which of the three chosen words fitted
best.

HZ =1      ZMV=1    ZM =4   HA=1
RE         ENT      EN      ON      Trenton is only assumption
EM         MPH      MP      IS
UN         NDR      ND      ED

Frequency    869  7639
Cipher       MHZ  MVHA

Frequency    XXX  XXXX      X = high frequency
Plain        TRE  NTON
- = intermediate frequency
Frequency    -X-  --XX
Plain        MEM  PHIS      O + low frequency

Frequency    --X  -XX-
Plain        HUN  DRED

OBVIOUS WORD METHOD - LOCATION BY FREQUENCIES

One method of fixing the location of an obvious word is by
frequencies, provided the obvious word has one or more letters
of very low frequency.  The word should be 10 or more letters
to be practical.

The possibilities are RENDEZVOUS  and MARBLEHEAD.

First, frequencies are written over each letter of the
cryptogram.  The Known-word is put on a card and slid over the
cryptogram until it fits with the very low frequency letters
and neighbors.  This method is rather tedious and painful, but
good in a pinch.

OBVIOUS WORD METHOD - LOCATION BY SYMMETRY OR REPETITIONS

Location of words by symmetry is commonly employed when dealing
with single key ciphers.  With double key ciphers its
application depends much on chance.  If the alphabets are
repeated in the key or the key is short, we employ a limited
form of symmetry.

With a non repeating key or very long key, this method fails.
With a fairly short key we employ this method provided:

(1)  We assume a word or phrase longer than the key, and
(2)  This word or phrase happens to contain a letter repeated
at an interval equal to the length of the key.

For our sample problem, one of our choices might be

10 letter key -    SCOUTINGDISTANCE

Therefore, any place in the cryptogram where two successive
lines have common letters in the same column is a possible
location of our word.  Failure to find this location,
eliminates the possibility of this word.

Table one partially shows the ciphertext where repeated letters
are ten spaces apart.  Of the twelve possibilities for the word
"SCOUTINGDISTANCE" some are eliminated by frequencies of the
letters C,G,C, others by letter combinations and the balance by
test.  All fail.

Our Navy students would try the scouting line of cruisers as:

4             3                   1          2
2             1          OR       3          4
(flag)

These names might appear as follows:

HMONDTRENT      OR         TRENTONRIC
ONMARBLEHE                 HMONDMEMPH

These can be checked against Table I and cross checked by
frequency or digram analysis.

We have a little luck at Line 14 - 15 - 16

Line 14             LGTBWPLVTT
--MEMPHISR

Line 15             OBOXJLRMHZ
ICHMONDTRE

NTONMARBLE

check

Line 29             OPLAULDMOZ         Line 11        MOZ
I  N N T E                        I E
NINETEE                        TWE

Line 30             MJKAQJBF           Line 12        MVX
NHUNDRED                          NT
NTY

OBVIOUS LOCATION METHOD

Table I gives a list of obvious locations.  We suspect
the word COURSE  followed by a ZERO and ONE TWO or THREE.

Some possibilities are:

COURSEZERO             COURSETHRE
FOUR                   EZERO

COURSEONET             COURSETHRE
WO                     EONE

COURSEZERO             (promising but no check)
FOUR

COURSETHRE
ETHREE                 (checks with #9 in Table I)

Assumption

Line 21         KPKDECGOHZ        Line 26   S KPKGULT
COU
S COUTING

Line 22         LVODSCOCHA
ETHREEZERO

Both assumptions are entered into the cryptogram.

TABLE I

Lines                                         Reference

6-7              ZFSAASZDEPZXCDJD                1
8-9              KAHPLGHAJMKTVAMK                2
8-9              HAJMKTVAMKHMBCAA                3
10-11            ZZDWIJKGMCZMVXXU                4
17-18            FARQVKMMQKFMPSLG                6
18-19            FPMSLGXAHEFWKGCB                7
18-19            HEFWKGCBFTHSVCBB                8
21-22            DECGOHZLVODSCOCH                9
21-22            CGOHZLVODSCOCHAG                10
21-22            HZLVODSCOCHAGVWB                11
22-23            VCDSCOCHAGVWBZCA                12
22-23            COCHAGVWBZCAMOZM                13
24-25            AQJBFJHXBHAAVAKO                14
25-26            OSKPKGULTJOQDFQQ                15
28-29            AEPZWQROPLAULBMO                16
29-30            AVLBMOZMJKAQJBF                 17

TABLE II

12345678910     12345678910     12345678910    12345678910
COURSEZERO      COURSETHRE      COURSEONE      COURSETWO
ZERO            EZERO           ERO      Z     ERO      Z
ONE              ONE            NE       O     NE       O
TWO              TWO            WO       T     WO       T
THREE            THREE          HREE     T     HREE     T
FOUR             FOUR           OUR      F     OUR      F
FIVE             FIVE           IVE      F     IVE      F
SIX              SIX            IX       S     IX       S
SEVEN            SEVEN          EVEN     S     EVEN     S
EIGHT            EIGHT          IGHT     E     IGHT     E
NINE             NINE           INE      N     INE      N

COURSEZERO       COURSETHRE     COURSEONET     COURSETWOT
FOUR             EZER           WO             WO
EONE
ETHREE

DISCOVERY OF THE SYSTEM

We study the values assumed previously:

Value      Alphabets       Value        AlphabetS
C=E        3,6,8           H=O, O=H     3,6,8
O=H        3,8             N=L,L=N      3,6,8
H=O        3,8             K=U, U=K     3,6,8
B=E        4,7             N=A,A=N      4,7
A=N        4,7             S=E,E=S      5

The common values indicate that alphabets 3,6, and 8 are
identical and similarly so are 4 and 7.   Five reciprocal
values are noted without inconsistencies.  Seven different
alphabets are used.  The alphabets are probably reciprocal.

If the seven alphabets are Secondary (derived from the same
cipher component set against the same plaintext but in
different alignments) a short cut solution is possible. We can
next combine the alphabets into one system.

We have enough clear text to solve the cryptogram - I leave the
balance to the student.

Alpha. -  1 2 3 4 5 6 7 8 9 10  Alpha. - 1 2 3 4 5 6 7 8 9 10

1         K P T X S L I C T M    16      M V H A W A D G G Z
C O   M E N   E                N T O N     R     E

2         I A M C B B N M S Z    17      Y F A R Q V K M M Q
T   N   A T T E                    D   S T

3         M J K A Q J B F Z A    18      K F M P S L G X A H
N H U N D R E D   O            C   T   E N T Y   I

4         J G M B S L N P H H    19      E F W K G C B F T H
T E E N A   R I                S S P E E D   I

5         E E J Z W N C L O W    20      S V C B B U A H S S
R     L   N E                T E E N K N O T S

6         Z F S A A S Z D E P    21      K P K D E C G O H Z
N                        C O U R S E T H R E

7         Z X C D J D D H A J    22      L V O D S C O C H A
E R     R O                E T H R E E Z E R O

8         O D B K A H P L G H    23      G V W B Z C A M O Z
S   O   N   I            A T S E V E N T E E

9         A J M K T V A M K H    24      M J K A Q J B F J H
H T S     N T   I            N H U N D R E D   I

10        M B C A A C N W S Z    25      X B H A A V A K O S
N   E N   E A S T E                O N     N U E S

11        Z D W I J K G M C X    26      K P K G U L T J O Q
S     U T T W E            C O U T I N   R E
12        M V X X U N B W Z T    27      D F Q Q J K K M H Z
N T Y M I L E S                          U S T R E

13        I Y N C P O G H H W    28      H V H A E P Z W Q R
I     H T O R              N T O N S     S

14        L G T B W P L V T T    29      O P L A U L B M O Z
E     E                          O N N I N E T E E

15        O B O X J L R M H Z    30      M J K A Q J B F
H M   N   T R E            N H U N D R E D

TABLE III
DECIPHERING TABLE

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       G   K   L                 M
2                     J             P         V
3               C     O             H     J W   K       X
4               B               X A       D K
5             Q S       U         B   G     E     Z
6               C           U N   L
7         N     B                 A           G           O
8             F C     O             H       W M
9               O                         H   S        C
10              Z       H           A       S

TABLE IV
ENCIPHERING TABLE

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       G   K   L                 M
2                     J             P         V
3-6-8         F C     O     U N   L H     J W M K       X
4-7     N       B               X A       D K G           O
5             Q S       U         B   G     E     Z
9               O                         H   S        C
10              Z       H           A       S

Op-20-G gives us the quick and dirty of the problem.  We need
to understand what equivalent cipher alphabets are and how the
multiple alphabet system lends itself to reconstruction.

EQUIVALENT CIPHER ALPHABETS

Any sequence containing 26 letters may be rearranged so that
all the letters which are originally separated by equal
intervals will also be spaced at equal intervals in the new
related sequences.  Including the original sequence, a total of
of six related sequences may be constructed.  [Friedman expands
on this principle in FR7.]

Example:

1   3   5   7   9  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

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

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

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

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

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

In this example, a normal alphabet sequence has been re-spaced
to form five related sequences.  In constructing them, the
original sequence is regarded as a circle and the letters are
counted off in equal intervals, then written in adjacent
positions to form a related sequence.

Only the odd intervals from 3 - 11 can be used in re-spacing a
26 letter sequence to form different related sequences.
{primes}  Even intervals will produce only 13 letter sequences,
and the interval 13 can not be used.  Odd intervals from 15-25
will produce identical sequences with those from 1-11 but in
reversed direction.  (like the Porta)

Cipher alphabets may be re-spaced to form equivalent cipher
alphabets by the same process as that applied to construct
related sequences.

Example:

Original Cipher Alphabet

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

Equivalent Cipher Alphabet

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

An equivalent cipher alphabet can not be distinguished from the
original cipher alphabet unless a systematic construction or
some outside information is available to identify the original
one.  The secondary alphabets generated by shifting the points
of coincidence of the plain and cipher components are the same
alphabets regardless of which equivalent cipher alphabet has
been shifted.

Example:

Original Cipher Alphabet

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

Equivalent Cipher Alphabet

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

The secondary alphabet of this example has been derived by
shifting the cipher component of the original alphabet of the
previous paragraph, and the equivalent secondary cipher
alphabet by shifting the cipher component of the equivalent
alphabet of the previous paragraph.

The number of spaces each cipher component has been shifted is
not the same in each case, yet the plain and cipher values
correspond exactly.   This illustrates the most important
principle of symmetry in the secondary alphabets.

RECONSTRUCTION OF MULTIPLE ALPHABET SYSTEMS

When the same sequence has been used for each of the cipher
components of a multiple alphabet system, there are definite
relationships between the individual cipher values which may be
used in recovering other cipher values after a few have been
identified through analysis.

(a) When the plain component is originally a normal sequence
the cipher sequences will be recovered in their original order
and new values may be placed in the various cipher components
as soon as their relative positions have been established.

(b) When the plain and cipher components are originally the
same mixed sequence, the plain component enters into the
reconstruction in the same manner as the other cipher
component.

(c) The reconstruction of a multiple alphabet system in
which the plain component is a different mixed sequence from
that used in the cipher components, requires a relatively large
number of values for analysis.

The principles are explained by another example in which the
plain and cipher components are different mixed sequences:

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

The interval between letters of two cipher components, letters
which occur in the same vertical column, is equal to the amount
of displacement of one component from the other.

O (1) To N(2) is an interval of one, the amount of shift
between the cipher components (1) and (2).

E (3) to O (1) is the same interval as O (3) to U (1), and is
the same interval as U (3) to F (1), etc.

Thus a chain of letters, EOUF with current relative spacings
could be made from the vertical relationship alone, when the
order of plain component sequence is unknown.  A set of
equivalent alphabets might be the result of construction by
this means, but the original in this case would be recognized
when the proper spacing is found.

If the vertical relationship is used between components which
are displaced an even number of letters, such as ciphers (2)
and (3), a chain of 13 letters will result, and if the
components were originally displaced 13 letters, they would
show only reciprocal relationships.

APPLICATION OF SYMMETRY PRINCIPLES

Suppose the Enciphering table obtained during the solution of a
cryptogram appeared as follows:

Plain  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
Cipher 1 - Z U T   R   D A P     V   C W       G I         H
2 - X H Z N U     D O       W B V     E F G         T
3 - L     E P     W F     I K T J     U R S

Since the interval between R and P in the cipher sequence is
the same as that between P and F, we may arbitrarily assume
this interval to be one and build up a cipher sequence
accordingly.

The vertical columns remain unchanged.  We write:

0    E I       R in the third cipher           S E I
1    R P F     component appears under         G R P F U O
2    U O       S plain, so we continue   G R P F U O
3  R P F                                     G R P F U O

The progress of adding values to the plain and cipher sequences
progresses through the various stages:

0               T     S E I R B     Y
1               I S   G R P F U O E H      T
2        I S    G R P F U O E H     T
3             I S   G R P F U O E H      T

0          O     L T     S E I R B     Y   N C
1          W J   V I S   G R P F U O E H   C T   B Z
2    W J   V I S   G R P F U O E H   C T   B Z
3        W J   V I S   G R P F U O E H   C T   B Z

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

The intervals between E, F, G and between V, W, X in the cipher
sequence obtained above, indicate the equivalent alphabets have
been recovered which should be re-spaced by counting off every
third letter in the reverse direction.

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

CONTINUATION OF BLACK FORCE CRYPTOGRAM

A few more values are necessary in Table IV in order to
completely reconstruct the system used.

Line 1                          Line 18

Alpha    1 2 3 4 5 6 7 8 9 10   Alpha    1 2 3 4 5 6 7 8 9 10
Cipher   K P T X S L I C        Cipher   K F M P S L G X A H
Plain    C O   M E N   E        Plain    C   T   E N T Y   I
New          M       C          New            W

Line 3 to 5

Alpha    1 2 3 4 5 6 7 8 9 10   1 2 3 4 5 6 7 8 9 10    1
Cipher   M J K A Q J B F Z A    J G M B S L N P H H     E
Plain    N H U N D R E D   O        T E E N A   R I
New                      F      U R           P         L

Adding these new values to Table IV gives the following table
for use in reconstruction of the system:

TABLE IV
Revised
ENCIPHERING TABLE

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

The reciprocal relationship will be ignored.

On account of L and B being found in two vertical columns, a
good starting point is to assume that L and B are adjacent in
the cipher component.  Then we would have the following in the
cipher component:  GN, KI, MA, FQ,  CS, PQ, AND WE.

Using the PGN sequence in the first three cipher components,

PLAIN-          W T A           O R         P   L
1                 P G N                       W E
2                 V             P G N
3-6-8             M A           H J         P G N
4-7             P G N             D
5                                         P G N
9               C S               H J
10                            M A

Since HJ appears with the same interval as LB, then OC and SM
are also adjacent in the cipher sequence being constructed.

PLAIN-  H E W T A      S   O R       Z       N   P   L   U
1         L B P G N                    O C S M A   W E H J
2     H J     V        L B P G N
3-6-8   O C S M A      W E H J    V          L B P G N   K
4-7     L B P G N      K I   D       O C S M A
5     O C S M A      W E H J     V         L B P G N
9         O G S M A      W E H  J   V
10                 O C S M A

We combine the three partials:

PLAIN-  H E W T A   S   O R    Z       N   P   L   U
1         L B P G N              O C S M A   W E H J
2     H J     V     L B P G N
3-6-8   O C S M A   W E H J      V     L B P G N   K I  D
4-7     L B P G N   K I   D    O C S M A
5     O C S M A   W E H J      V     L B P G N
9         O G S M A   W E H  J     V
10        Z     O C S M A

I think you can see that most of the cipher sequence could be
obtained without considering the fact that the plain component
is the same sequence reversed.  The important point is that the
complete system may be reconstructed from relatively few values
obtained through analysis of the cryptogram.

The sequence used in this problem is randomly mixed, therefore
the original one can not be distinguished from a related one
which may be reconstructed.  The ten cipher components are set
with the key GUANTANAMO under the A plain.

FURTHER REMARKS

The same method used in determining which cipher values
probably represent vowels or consonants may be applied to poly-
alphabetic substitution ciphers as described in Lectures 1 and
2.  However, the values in each alphabet must be considered
with their respective prefixes and suffixes in adjacent
alphabets, in studying the frequencies of their combinations.

After the original sequences of a poly-alphabetic substitution
system are recovered, subsequent messages using these sequences
may be solved by a modified method.  The "generatrix frequency"
method was developed by W. F. Friedman and is described in FR7.

SOLVING CIPHER SECRETS

MASTERTON (Frank W. Lewis) was a personal 'pick' of William F.
Friedman.  His experience and book [MAST] is as insightful as
it is brilliant.  He takes us through the QUAGMIRE family. The
American Cryptogram Association calls the class of periodic
polyalphabetic substitution QUAGMIRES I, II, II, IV after the
terminology used for keying Aristocrats.  QUAGMIRES have a
mixed alphabet in at least one of the components.  QUAGMIRE I
uses a keyword-mixed plain component with a determined number
of normal cipher alphabets at different settings; QUAGMIRE II
uses a normal plain and various settings of the same mixed
cipher component; QUAGMIRE III employs the same mixed alphabet
for plain and cipher (juxtaposition repeated on a cycle); and
QUAGMIRE IV which has one mixed alphabet for plain and a series
of slides of another mixed alphabet for the cipher components.
[MAST]  The use of normal alphabets on a cycle, either direct
or reverse, is a weakness because the components are known and
are more vulnerable to solution.

QUAGMIRE I

We will take the QUAGMIRES in turn, making sure we understand
the method of encipherment and tricks of unraveling the text.

Lets build an alphabet  on the Keyword ENCIPHERMENT:

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

Let us take a NORMAL alphabet, with C under the first letter of
plain sequence.  This is cipher setting No 1.  Slide the normal
alphabet to I, under E, P, H, E, R to get:

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

I have numbered the alphabets for ease of use.  The initial
column keyword is standard practice.

To encipher the word regarding:  The first R is found in the
plain sequence, and the letter under it in alphabet 1 is I, we
after using the sixth alphabet.

QUAGMIRE I ATTACK

Given:

WBFWX  LWVPY  WICQJ  HJYDL  LNABF  JCQFB  BHMPA  XGKIU  CRHVK

YNEJO  VMDEJ  SPQPT  GLFFB  YOEYD  MIHYY  JJCPY  YDVIE  TOFXX

LWPSC  YTBKJ  ORCYZ  DBYDH  YHR.

The Cryptogram usually provides a tip:  "ILEANDTHENREPLIED. "
This will appear in the text someplace.

The repeat method of factoring doesn't work to well on this
example.  So assume 6, 7 or 8.  Write the crib based on those
cycles.

awh                awh               awh
ILEAND            ILEANDT          ILEANDTH
THENRE            HENREPL          ENREPLIE
PLIED             IED              D

We have added a possible text of awh to the crib.  The middle
crib has the I over an I 13 letters apart and the E's interval
of 6.   The stretch of cipher we want will have a repeat as:

----X------Y-----XY---.

The stretch "glffbYoeydmihYyjjcpYYdvie" fits the bill.  We
rewrite the cryptogram into a cycle of seven letters either in
columns or rows.  We fill in the tip and number the alphabets:

1234567  1234567  1234567  1234567  1234567  1234567  1234567
WBFWXLW  VPYWICQ  JHJYDLL  NABFJCQ  FBBHMPA  XGKIUCR  HVKYNEJ

1234567  1234567  1234567  1234567  1234567  1234567  1234567
OVMDEJS  PQPTGLF  FBYOEYD  MIHYYJJ  CPYYDVI  ETOFXXL  WPSCYTB
a  whILEAN  DTHENRE  PLIED

1234567  1234567  1
KJORCYZ  DBYDHYH  R.

We prepare a deciphering tableux, putting the plain values
above the normal cipher strip and using the plain E to start.

Plain  0         E
-----------------------------------------------------
Cipher 1
2
3
4 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 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
6
7 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

Since the fourth alphabet also has a plain L, we enter it on
the top line, and similarly place a plain N from the fifth
alphabet.  The N is confirmed by its appearance in the 7th
alphabet, so we know we are on the right track.

Since we have the plain L, the second alphabet comes in too and
hence the plain H and T.  This gives us the third alphabet and
the plain I.  There is more help.  Looking down the various
columns we find the Keyword COUNTRY which must have been placed
under the first letter of the plain sequence.   Snowballs.

Plain  0 A B C D E   H         R   T           P L   W I N G
-----------------------------------------------------
Cipher 1 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
2 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
3 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
4 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
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
6 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
7 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

The clues add up.  The Keywords are PLOWING and COUNTRY.

The RST sequence is obvious.  The message reads: The city
thought awhile and replied I don't rightly know but I call him
JACK.

QUAGMIRE II

This polyalphabetic substitution uses a Normal plain and a
keyword mixed cipher alphabet.  Lets tackle a problem with the
tip of 20 letters TAPHORICORTABOONATUR and also the tip
"usage."   Sometimes we have hunches.  Assume the period is 10,
and write out the tip on this basis.  Nice pattern with a
digraphic hit TT, OO, RR

TAPHORICOR
TABOONATURe    I have added the e
possibility.

and the cipher is:

12345678910 12345678910 12345678910 12345678910 12345678910
GJGQHJLELW  SZGGETGMQS  YVAHUOLFYN  NIRJHVKJDS  XMZVUEPETG

12345678910 12345678910 1
HIAHWZOTFN  HIHVWQUQDN  UENAEQMFQA  YXIOVUIVYG  NYLUJMOCVL
TAPHORICOR  TABOONATUR  e

RXSOTVSSMT  CIIFHVEFYA  VJLEUVDQFX  OZJHNNUHQY  EOGQDYGHEG

RXVVVOBVYY  SR

Now we develop the deciphering tableaux.

Plain  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
-----------------------------------------------------
Cipher 1         U                             H
2 I
3   H                           A
4               H              N
5                              W
6                            Q      Z
7 U               O
8     T                                 Q
9                              F          D
10                                   N

QUAGMIRE II ATTACK

We know that the plain sequence is normal. it is in the right
order and we can base our interval analysis on the plain.  We
introduce Mr. Friedman's principle of symmetry to discover the
relationships in the cipher alphabets.

We know that the cipher text reads from left to right just as
we see it.  The skeleton sequence is:

H------V------A, Q---Z----T, U-------O, and  F-----D,

We can fill in a few letters.  The Q---Z is either QVW-Z or Q-
VWZ. In No 1 Q cipher is either Y or Z and Z cipher is either C
or D.   [MASTERTON jumps in with a NIO combination and VW but I
didn't see this until after the solution.]   Alpha 4 puts V +6
from H, transposing that to alpha 1, puts a V under the A
plain, and suggests Q V W X Z sequence with Y in the Keyword.
X is pretty unpopular in keywords so we will go with this
assumption.

INTERMEDIATE DECIPHERING TABLEUX

Plain  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
-----------------------------------------------------
Cipher 1 V W X Z U ? ? A T       O              H           Q
2 I
3   H           Q V W X Z U ? ? A T       O
4               H           Q V W X Z U     A T
5             H           Q V W X Z U     A T        O
6 O              H           Q V W X Z U     A T
7 U       T        O              H            Q V W X Z
8   A T       O              H           Q V W X Z U
9                              F          D
10                                   N

So we build up alpha's 1, 3, 5, 6, 8.   We can place the H's
back in them from the Q by -6. in alpha 8 and 5.   We see that
U +8 = O in alpha 7.  The sequence ---A starts the keyword from
alpha three.   Look at the T behind the Q by -17 offset in
alpha 8.  Remember my assumed 'e' = U in alpha 1. We place this
hunch and let it play through.

We have U - - AT ........Y.  I see the prefix UN and digram SA.
The word "unsatisfactory" comes to mind but I haven't got
enough hard evidence yet.  We have a U +8 to O in the 7th
alpha.  Fill in the alphas.

FINAL DECIPHERING TABLEUX

Plain  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
-----------------------------------------------------
Cipher 1 V W X Z U n s A T i f c O r Y b d e g H j k l m p Q
2 I
3   H           Q V W X Z U ? ? A T       O
4               H           Q V W X Z U     A T
5             H           Q V W X Z U     A T        O
6 O              H           Q V W X Z U     A T
7 U       T        O              H            Q V W X Z
8   A T       O              H           Q V W X Z U
9                              F          D
10                                   N

I know that Y is in the keyword and could be the last letter of
it.  Look at the F-----D sequence.  F is in the keyword and the
O-------H is the only area than can fit the F and the Y.

Plug in my UNSATifcOrY guess.  The lower letters require
checking.  Alphabet 1 fits the key as UNSATISFACTORY adjusted
for duplicate letters.

The message reads in part: Slang is language or phrases of a
vigorous colorful metaphoric or taboo nature invented to ...

QUAGMIRE III

The QUAGMIRE III is a very important class of ciphers because
they introduce the one of the most important tools invented by
Mr. Friedman, as explained in his Riverbank papers, called
"Direct and Indirect Symmetry."

The title of this problem is "Inertia in the British Labor
Market"  and has the tip "ANDTHREECALLINGFORAMANTOSTANDON."

IBWVU  PLTPJ  TKPPM  YCTDV  XYGNY  QYNTW  NFSUI  XNACX  CFTGV

AIKPS  RTCOJ  JWPRR  VOLAA  ZRURJ  NUIXM  XPQBV  UIBWO  GPCDP

LNNRD  FPSLI  BUGOC  DOTWK  CPIRQ  RVQGY  GCXLV  MNOBE  QFVOL

GBWGP  ATNJL  YWRMW  EKLAA  VICVE  AQBKU  VFJUR  DVIOZ  MPTZO

VSLIH  QBQXF  LLLWH  PUSGV  XP.

QUAGMIRE III ATTACK

Note the repeat of the first three letters IBW at interval 81.
If the message starts with THE and the period turns out to be 9
we have found a wedge.  Next place the tip in columnar line for
a cycle of nine.

A N D T H R E E C              A I K P S R T C O
A L L I N G F O R              J J W P R R V O L
A M A N T O S T A              A A A R U R J N U
N D O N t w o f e e t  ?       I X M X P Q B V U
t h e -------  ?       I B W O G P C D P

(also first three IBW)

The three A's in the first column followed by the two N's
prove the period of 9.  This is not accidental.  My guesses
of additional plain text are partially right - 'the' as you
will see later.  Note the triple R's, two U's and Two I's in
the ciphertext lined up by columns in a period of 9.

Break the ciphertext into groups of nine.

123456789  123456789  123456789  123456789  123456789
IBWVUPLTP  JTKPPMYCT  DVXYGNYQY  NTWNFSUIX  NACXCFTGV

AIKPSRTCO  JJWPRRVOL  AAARURJNU  IXMXPQBVU  IBWOGPCDP
ANDT  HREECALLI  NGFORAMAN  TOSTANDON  THE

LNNRDFPSL  IBUGOCDOT  WKCPIRQRV  QGYGCXLVM  NOBEQFVOL

GBWGPATNJ  LYWRMWEKL  AAVICVEAQ  BKUVFJURD  VIOZMPTZO

VSLIHQBQX  FLLLWHPUS  GVXP.

Place the extended tip.  In a QUAGMIRE III, or in any case
where the cipher component is the same as the plain component,
if one cipher -plain  matches E for E, all pairs must match,
for the sequence is set A to A, B to B, etc.  When this
happens, we get a column of our write-out as "free plain text,"
which is of considerable help.

I can not overemphasize the next step.  Because of the K3
nature of the keying, the Plain component and the Cipher 1
alphabet represents pairs that are the same distance removed -
H to J, N to A, T to I, in this case.  Similarly G to A, H to
B, O to X, and R to J are equally separated - though not at the
same interval as the first pairs obtained from line 1.
(Obviously, if H to J is "x" distance, H to B cannot be the
same distance.)   Check this observation of Symmetry on the
decipher tableaux.

INITIAL DECIPHERING TABLEUX

Plain 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
-----------------------------------------------------
Cipher1               J           A           I
2             A B             X     J
3         W A                         M
4         P                   R         X
5 P   R                             U
6 R                         Q
7       B               V J T
8 N     C               O     V
9                 L         U           O

Let us write down all the pairs we get by going from plain to
cipher in each of the alphabets in turn.  We can also write
down the from the sidewise relationships.  For instance, A to C
on the plain sequence is the same distance P to R on Row 5.  In
addition, Row 7 to Row 8 tells us that BC is the same distance
apart as VO.

This is a most powerful tool in solution of a sequence against
itself.  You can imagine a little "square" and go up, or down,
or across, to find relationships within and between both plain
and cipher components.

Plain sequence to Row 1  HJ NA TI
2  GA HB OX RJ
3  EW FA SM
4  EP OR TX
5  AP CRU      (CR-RU)
6  AR NQ
7  DB LV MJ NT
8  AN DC LOV    (LO-OV)
9  IL NU TO
>From Plain A to C        AC PR
>From Row 7 to 8          BC VO

There are a lot of relationships. I have not listed the
sidewise ones like Plain to Row 1 - H to N and J to A.

MASTERTON points out that Row 1 is the reverse of Row 8.
[MAST] I didn't see this "little" jump.

But I did make sense of the three letter chains; if L-O is the
same as O-V we have a three letter segment.  Do you see that
the pairs in the listing above are separated by one letter in a
sequence obtained from the next set, as evidenced by LV in 7
and LOV in 8?  We can add the two together:

DCB   LOV   M-J   AN-T

Look at the fragments, and realize that we have found some good
information about the sequence.  First of all the sequences are
reversed alphabets.  The sequence has BCD, VOL, JKM since we
have used L and T-NA in it?  [We can also look at a process
called decimination to bring the sequence to bear.  We will do
that in the Friedman section.]  Remember the very important
part of the tool of symmetry - that because the plain and all
the cipher alphabets are the same, we can associated pairs in
the straight, sideways, down etc as we find them, using the
plain or all nine cipher alphabets.  In a QUAGMIRE IV, we
cannot use the plain sequence in this way because of a
different key.

We continue our recovery  with A to N plain as the same
distance as R to Q in alpha 6. We add QR to our line.

VOL   TINA      BCD     HJKM   QR

Notice the H to B and G to A in the plain to alphabet 2
relationship.  This tells us to put G ahead of H, then A goes
behind B as we expect.  Since O is in VOL and N is in TINA

VOL/TINABCD/GHIJM/QR

the only missing element is P which we place as follows:

ku  VOL/?/TINABCD (f)GHJMPQR swxyz

missing elements at this stage are e, k, u, w , x , y , z which
likely the E and U are in the Keyword.

INTERMEDIATE DECIPHERING TABLEUX - PARTIALS

Plain 0   V O L         T I N A B C D F G H J M P Q R S
-----------------------------------------------------
Cipher1 V O L         T I N A B C D F G H J M P Q R S w
2     X                     T I N A B C D F G H J M P Q
3                             T I N A B C D F G H J M P
4   Q R S W? X
5
6
7
8     V O L            T I N A B C F G H J M P Q R S
9

The line ups are not correct.  We can find where alphabets 1,
2 and three start by putting the low frequency X in the right
spot.  I leave this part of the work to the you all. [ Hint:
compress the V O L -----T I N A space and what keyword will fit
into  - V O L u? T I (O)N. and place the E in the beginning.]

The answer is with Keywords EVOLUTION and BLUEPRINT:

FINAL DECIPHERING TABLEUX

Plain 0 E V O L U T I N A B C D F G H J K M P Q R S W X Y Z
-----------------------------------------------------
Cipher1 V O L U T I N A B C D F G H J K M P Q R S W X Y Z E
2 S W X Y Z E V O L U T I N A B C D F G H J K M P Q R
3 W X Y Z E V O L U T I N A B C D F G H J K M P Q R S
4 P Q R S W X Y Z E V O L U T I N A B C D F G H J K M
5 C D F G H J K M P Q R S W X Y Z E V O L U T I N A B
6 F G H J K M P Q R S W X Y Z E V O L U T I N A B C D
7 Y Z E V O L U T I N A B C D F G H J K M P Q R S W X
8 Z E V O L U T I N A B C D F G H J K M P Q R S W X Y
9 X Y Z E V O L U T I N A B C D F G H J K M P Q R S W

The message reads: The British created a civil service job in
eighteen hundred and three calling for a man to stand on the
cliffs of Dover with a spyglass.....

QUAGMIRE IV

The QUAGMIRE IV is probably the most difficult of the QUAGMIRES
because we need to recovery two keyworded alphabets and direct
symmetry will not work with the plain.

We are given:

MWQYD  KMCAO  KHSEE  YULIH  WYTEW  YRLHG  LMEJC  ZHAKE  NYWUP
thegr  reat

QSQSO  ESYEP  BIZEW  QYPKZ  FHAAM  GWPTR  XNYWR  LKSQE  XHGRA

QCWAV  JNCPM  HDHZT  BCBHR  AMXUE  OLTWR  RIKNQ  AKKDZ  VJOYW
bet?

WHQJR  FGYVP  GILWV  WGPTF  MLYKX  TAKOZ  ATFGL  AUT.
weenl  atese  ptemb  erand  decem  berof  thaty  ear

QUAGMIRE IV ATTACK

The Title is "Lost Horsepower", the tips are starts with THE
GREAT and has WEENLATESEPTEMBERANDDECEMBEROFTHATYEAR in the
text. The letters bet?WEEN might be inferred.

Finding the cycle is our first challenge.

The WQY is +58, a discouraging number for factors.  The cribs
are pretty generous, so looking at them we might find
something.  Obviously, a plain hit at the correct interval of
the cycle would result in a cipher coincidence at the same
interval.  Two occurrences of a plain letter at some interval
other than the period or multiple of the cycle, the ciphers
cannot be the same.  MASTERTON describes a graphical technique
for knocking out intervals. [MAST]

OYWWHQJRFGYVPGILWVWGPTFMLYKXTAKOZATFGLAUT
betweenlateseptemberanddecemberofthatyear
* --9--  *

Thus the Y over E and H and Q over E "knock out" the intervals
3, 4 which are too short anyway, and also 11 because of the Y
over P.  Note the +9 hit for Y over E.  So we write out the
cipher in a period of nine:

123456789  123456789  123456789  123456789  123456789
MWQYDKMCA  OKHSEEYUL  IHWYTEWYR  LHGLMEJCZ  HAKENYWUP
thegreatE              E GH EE                    E A

QSQSOESYE  PBIZEWQYP  KZFHAAMGW  PTRXNYWRL  KSQEXHGRA
E  ?HE   E T    EA  R      RT  ER    E    R E     E

QCWAVJNCP  MHDHZTBCB  HRAMXUEOL  TWRRIKNQA  KKDZVJOYW
T    A  TE                    NH  E   E  R     bet

WHQJRFGYV  PGILWVWGP  TFMLYKXTA  KOZATFGLA  UT.
weenlates  eptembera  nddecembe  rofthatye  ar

Even with all the help and correct hits, the message is not a
give a way.

INITIAL DECIPHERING TABLEUX

Plain 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
-----------------------------------------------------
Cipher1 U       P                 T       K   M     W
2       F H     W             O G   T
3       M Q Z                           I
4         L   Y             J           A
5     Y         T       R W         D
6 F V     K
7 M O     W               X             G
8   T     Y                         G   C
9 P       A   C                       V W

Since the alphabets are different we can not chain from the
plain to cipher.  However, WITHIN the cipher, the same rules
apply as before - except their isn't nearly as much
information.  In Cipher 1 row we see that U to P is the same
distance as F to K , M to W and P to A. Ok.  Remember that we
are dealing with unknown decimations, so the relationships
between UPA, PK and PT is unknown.

By decimation I mean the process of selection of elements from
a sequence according to some fixed interval.   For example, the
sequence A E I M is derived, by decimation , from a normal
alphabet by selecting every fourth letter.  It is the key to
Symmetry solutions because the latent relationships in a cipher
alphabet can be made patent by decimation.  Lecture 11 will
give two methods of decimation in detail.
Table of Relationships in foregoing example:

UPA FK  MW         Plain A to E and Rows 1 to 9
PT  LJ              "    E to N
PK  HT  YG          "    E to R and Rows 1 to 6  adding UF
PM  QI  LAWG  YC    "    E to T and Rows 9 to 7 and 4 to 9
UMG  PW             "    A to T and Rows 1 to 7
TM  JA              "    N TO T
FH  MQ              "    D to E
WTD                 "    H to R and Rows 2 to 5
FV  MO              "    A to B
VK  OW  TY          "    B to E
OG  TC              "    B to T
PH  KT             Rows  1 to 2
PQ  MI             Rows  1 to 3
PL  TJ  MA         Rows  1 to 4
PY  KG  MC         Rows  1 to 8
FM  HQ  KW  VO     Rows  2 to 0
HY  TG             Rows  2 to 9
QL  IA             Rows  3 to 4
QW  IG             Rows  3 to 7
QY  IC             Rows  3 to 8
QA  IW             Rows  3 to 9
LW  AG             Rows  4 to 7
LY  AC             Rows  4 to 8   and Plain A to G adding
Cipher C under Plain G on Row
FP  KA             Rows  6 to 9   9
OT  WY  GC         Rows  7 to 8
YA  CW             Rows  8 to 9

Row 2 to 3 and 6 to 7 are combined.  S and T in plain are most
likely adjacent from VW in Cipher 9.  Partials FH and MQ look
good without an intervening letter.

LAWG is our best bet for the wedge.  It ties together E and T
in the same decimation.   So:

Plain         E T
Cipher        P M
H
Q I
L A W G

K
L A W G
Y C
L A W G

If FH and MQ are the right order, P is in the keyword, since
the reverse bits of above (MP, IQ, GWAL) would not be
consistent with MPQ.  Unfortunately, we have run out of gas and
must guess more plain.  The plain E-gh-EE most likely is
Eighteen and since they are talking about years, why not
Seventy, since so many E's are fitting? The plain T of seventy
is confirmed.  The plain V may not produce much but the cipher
G might be a bonanza.  These new values add KE and JR to the
chain.

123456789  123456789  123456789  123456789  123456789
MWQYDKMCA  OKHSEEYUL  IHWYTEWYR  LHGLMEJCZ  HAKENYWUP
thegreatE       T      EIGHTEEN  SEVENTY          E A

QSQSOESYE  PBIZEWQYP  KZFHAAMGW  PTRXNYWRL  KSQEXHGRA
E  THE   E T    EA  R      RT  ER    E    R E     E

QCWAVJNCP  MHDHZTBCB  HRAMXUEOL  TWRRIKNQA  KKDZVJOYW
T    A  TE                    NH  E   E  R     bet

WHQJRFGYV  PGILWVWGP  TFMLYKXTA  KOZATFGLA  UT.
weenlates  eptembera  nddecembe  rofthatye  ar

FINAL DECIPHERING TABLEUX

Plain 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
-----------------------------------------------------
Cipher1 U       P                 T       K L M     W
2       F H     W             O G   T
3       M Q Z     W                     I   G
4         L   Y             J           A
5     Y         T       R W M       D
6 F V     K                         J   E
7 M O     W               X             G
8   T     Y                         G   C
9 P       A   C                       V W

We look at VW and LM and KLM under the plain RST.  We must
conclude that G-C is correct.  Rows 7 and 8 have a G and C
under plain T, and WY under E and OT under B. This suggests
that WXY and O-T are part of the final chain. So push the
following chains:

KLM, G-C, VWXY, EA, O-T

The cipher sequence appears to go:

JKLMQVWXYZ

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

The cipher keyword has this form  O U T - P R  - A I N G
with S, E, D  candidates.   The keyword is SPREADING.
The plain keyword can be derived as PANDEMIC and the cipher
setting key is HORSETAIL.  The groundwork is left to the
student.  Notice how resistant the QUAGMIRE IV was even with

LECTURE 10 HOMEWORK PROBLEMS

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

KKQHPQR  KTYOHTA  TLGAWBM  XORKTAT  BSOOIYI  CGICEJV  UCYZRJP

ALNSFRZ  UCQDXIS  TDRBFYS  YTFDZBD  USQWKMT  CPPDOAI  CAAKEHK

UAYFHQA  TLNIFSI  SIGJHAS  V.

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

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.

QQ-3  QUAGMIRE IV  Economics Lesson.     EDNASANDE

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.

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Military Cryptanalytics Part IV,  Aegean Park Press,
Laguna Hills, CA, 1995.

[FR5]  Friedman, William F. Military Cryptanalysis - Part I,
Aegean Park Press, Laguna Hills, CA, 1980.

[FR6]  Friedman, William F. Military Cryptanalysis - Part II,
Aegean Park Press, Laguna Hills, CA, 1980.

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

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

[FRE]  Friedman, William F. , "Elements of Cryptanalysis,"
Aegean Park Press, Laguna Hills, CA, 1976.

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

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

[FRAA] Friedman, William F. , "American Army Field Codes in The
American Expeditionary Forces During the First World
War, USA 1939.

[FRAB] Friedman, W. F., Field Codes used by the German Army
During World War. 1919.

[FR22] Friedman, William F., The Index of Coincidence and Its
Applications In Cryptography, Publication 22, The
Riverbank Publications,  Aegean Park Press, Laguna
Hills, CA, 1979.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[GODD] Goddard, Eldridge and Thelma, "Cryptodyct," Marion,
Iowa, 1976

[GORD] Gordon, Cyrus H., " Forgotten Scripts:  Their Ongoing
Discovery and Decipherment,"  Basic Books, New York,
1982.

[GRA1] Grandpre: "Grandpre, A. de--Cryptologist. Part 1
'Cryptographie Pratique - The Origin of the Grandpre',
ISHCABIBEL, The Cryptogram, SO60, American Cryptogram
Association, 1960.

[GRA2] Grandpre: "Grandpre Ciphers", ROGUE, The Cryptogram,
SO63, American Cryptogram Association, 1963.

[GRA3] Grandpre: "Grandpre", Novice Notes, LEDGE, The
Cryptogram, MJ75, American Cryptogram Association,1975

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

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

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

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

[HA]   Hahn, Karl, " Frequency of Letters", English Letter
Usage Statistics using as a sample, "A Tale of Two
Cities" by Charles Dickens, Usenet SCI.Crypt, 4 Aug
1994.

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

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

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

[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
senshi."  unpublished manuscript, NIDS.

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

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

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

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

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

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

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

[HIS1] Barker, Wayne G., "History of Codes and Ciphers in the
U.S. Prior to World War I," Aegean Park Press, Laguna
Hills, CA, 1978.

[HITT] Hitt, Parker, Col. " Manual for the Solution of Military
Ciphers,"  Aegean Park Press, Laguna Hills, CA, 1976.

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

[HOFF] Hoffman, Lance J., editor,  "Building In Big Brother:
The Cryptographic Policy Debate," Springer-Verlag,
N.Y.C., 1995. ( A useful and well balanced book of
cryptographic resource materials. )

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

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

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

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

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

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

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

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

[HUNG] Rip Van Winkel, "Hungarian," The Cryptogram, March -
April,  American Cryptogram Association, 1956.

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

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

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

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

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

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

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

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

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

[KAHN] Kahn, David, "The Codebreakers", Macmillian Publishing
Co. , 1967.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[LISI] Lisicki, Tadeusz, 'Dzialania Enigmy', Orzet Biaty,
London July-August, 1975; 'Enigma i Lacida',
Przeglad lacznosci, London 1974- 4; 'Pogromcy
Enigmy we Francji', Orzet Biaty, London, Sept.
1975.'

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

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

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

1972.

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

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

[MANS] Mansfield, Louis C. S., "The Solution of Codes and
Ciphers", Alexander Maclehose & Co., London, 1936.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[MM]   Meyer, C. H., and Matyas, S. M., " CRYPTOGRAPHY - A New
Dimension in Computer Data Security, " Wiley
Interscience, New York, 1982.

[MODE] Modelski, Tadeusz, 'The Polish Contribution to the
Ultimate Allied Victory in the Second World War',
Worthing (Sussex) 1986.

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

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

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

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

[NIBL] Niblack, A. P., "Proposed Day, Night and Fog Signals for
the Navy with Brief Description of the Ardois Hight
System," In Proceedings of the United States Naval
Institute, Annapolis: U. S. Naval Institute, 1891.

[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
Languages," ACA-L, August 18, 1995.

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

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

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

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

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

[NIC7] Nichols, Randall K., "Arabic Contributions to
Cryptography,", in The Cryptogram, ND95, ACA, 1995.

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

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

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

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

[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
History, 1992, pp 201 ff.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[RAJ1] "Pattern and Non Pattern Words of 2 to 6 Letters," G &
C.  Merriam Co., Norman, OK. 1977.

[RAJ2] "Pattern and Non Pattern Words of 7 to 8 Letters," G &
C.  Merriam Co., Norman, OK. 1980.

[RAJ3] "Pattern and Non Pattern Words of 9 to 10 Letters," G &
C.  Merriam Co., Norman, OK. 1981.

[RAJ4] "Non Pattern Words of 3 to 14 Letters," RAJA Books,
Norman, OK. 1982.

[RAJ5] "Pattern and Non Pattern Words of 10 Letters," G & C.
Merriam Co., Norman, OK. 1982.

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

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

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

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

[RELY] Relyea, Harold C., "Evolution and Organization of
Intelligence Activities in the United States,"
Aegean Park Press, 1976.

[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'", Bulletin
Trimestriel de l'association des Amis de L'Ecole
superieure de guerre no 78, 1978.

[RHEE] Rhee, Man Young, "Cryptography and Secure Commun-
ications,"  McGraw Hill Co, 1994

[RIVE] Rivest, Ron, "Ciphertext: The RSA Newsletter 1, 1993.

[RIV1] Rivest, Ron, Shamir, A and L. Adleman, "A Method for
Obtaining Digital Signatures and Public Key
Cryptosystems," Communications of the ACM 21, 1978.

[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,
1980.

[ROH2] Rohwer Jurgen, et. al. , "Chronology of the War at Sea,
Vol I, 1939-1942, London, Ian Allan, 1972.

[ROH3] Rohwer Jurgen, "U-Boote, Eine Chronik in Bildern,
Oldenburs, Stalling, 1962. Skizzen der 8 Phasen.

[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
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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",
3rd ed., Rome, 1947.

[SALE] Salewski, Michael, "Die Deutscher Seekriegsleitung,
1938- 1945, Frankfurt/Main: Bernard and Graefe, 1970-
1974.  3 volumes.

[SANB] Sanbohonbu, ed., "Sanbohonbu kotokan shokuinhyo." NIDS
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[SAPR] Sapir, E., "Conceptual Categories in Primitive
Language," Science: 74: 578-584., 1931.

[SASS] Sassoons, George, "Radio Hackers Code Book", Duckworth,
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[SCHN] Schneier, Bruce, "Applied Cryptography: Protocols,
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[SCH2] Schneier, Bruce, "Applied Cryptography: Protocols,
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[SCHU] Schuh, fred, "Master Book of Mathematical Recreation,"
Dover, 1968.

[SCHW] Schwab, Charles, "The Equalizer," Charles Schwab, San
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[SEBE] Seberry, Jennifer and Joseph Pieprzyk, "Cryptography: An
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[CAREFUL!  Lots of Errors - Basic research efforts may
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[SHAN] Shannon, C. E., "The Communication Theory of Secrecy
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[SHIN] Shinsaku Tamura, "Myohin kosaku," San'ei Shuppansha,
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[SIC1] S.I. Course in Cryptanalysis, Volume I, June 1942,
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[SIC2] S.I. Course in Cryptanalysis, Volume II, June 1942,
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[SIG1] "International Code Of Signals For Visual, Sound, and
Hydrographic/Topographic Center, United States Ed.
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[SIG2] "International Code Of Signals For Visual, Sound, and
Radio Communications,"  U. S. Naval Oceanographic
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[SIMM] Simmons, G. J., "How To Insure that Data Acquired to
Verify Treaty Compliance are Trustworthy, " in
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[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
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[SISI] Pierce, C.C., "Cryptoprivacy," Author/Publisher, Ventura
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[SMIH] Smith, David E., "John Wallis as Cryptographer",
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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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[SPAN] Barker, Wayne G. "Cryptograms in Spanish," Aegean Park
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[SPEE] "Speech and Facsimile Scrambling and Decoding - A Basic
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[STEV] Stevenson, William, 'A Man Called INTREPID',
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[STIN] Stinson, D. R., "Cryptography, Theory and Practice,"
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[STIX] Stix, F., Zur Geschicte und Organisation  der Wiener
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[SUVO] Suvorov, Viktor "Inside Soviet Military Intelligence,"
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[TERR] Terrett, D., "The Signal Corps: The Emergency (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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[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio
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[TRAI] Lange, Andre and Soudart, E. A., "Treatise On
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[TRIB] Anonymous, New York Tribune, Extra No. 44, "The Cipher
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[TRIT] Trithemius:Paul Chacornac, "Grandeur et Adversite de
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[TUCK] Harris, Frances A., "Solving Simple Substitution
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[TUKK] Tuckerman, B.,  "A Study of The Vigenere-Vernam Single
and Multiple Loop Enciphering Systems," IBM Report
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[TURN] Turn, Rein, "Advances in Computer Security," Artec
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[UBAL] Ubaldino Mori Ubaldini, "I Sommergibili begli Oceani: La
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[USAA] U. S. Army, Office of Chief Signal Officer,
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[USSF] "U.S. Special Forces Operational Techniques," FM 31-20,
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[USOT] "U.S. Special Forces Recon Manual," Elite Unit Tactical
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[VAIL] Vaille, Euggene, Le Cabinet Noir, Paris Presses
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[VALE] Valerio, "De La Cryptographie," Journal des Scienses
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[VAND] Van de Rhoer, E., "Deadly Magic: A personal Account of
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[VERN] Vernam, A. S.,  "Cipher Printing Telegraph Systems For
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[VIA1] de Viaris, "L'art de chiffre et dechiffre les depeches
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[VOGE] Vogel, Donald S., "Inside a KGB Cipher," Cryptologia,
Vol XIV, Number 1, January 1990.

[VN]  "Essential Matters - History of the Cryptographic Branch
of the Peoples Army of Viet-Nam, 1945 - 1975," U.S.
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[WALL] Wallis, John, "A Collection of Letters and other Papers
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[WAL1] Wallace, Robert W. Pattern Words: Ten Letters and Eleven
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[WAL2] Wallace, Robert W. Pattern Words: Twelve Letters and
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[WATS] Watson, R. W. Seton-, ed, "The Abbot Trithemius," in
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[WAY]  Way, Peter, "Codes and Ciphers," Crecent Books, 1976.

[WEBE] Weber, Ralph Edward, "United States Diplomatic Codes and
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[WEL]  Welsh, Dominic, "Codes and Cryptography," Oxford Science
Publications, New York, 1993.

[WELC] Welchman, Gordon, 'The Hut Six Story', McGraw-Hill,
New York 1982.

[WHOR] Whorf, B. L., "A Linguistic Consideration of Thinking In
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[WINT] Winton, J., " Ultra at Sea: How Breaking the Nazi Code
Affected Allied Naval Strategy During WWII," New Uork,
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[WINK] Winkle, Rip Van, "Hungarian: The Cryptogram,", March -
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[WINT] Winterbotham, F.W., 'The Ultra Secret', Weidenfeld
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[WOLE] Wolfe, Ramond W., "Secret Writing," McGraw Hill Books,
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[WOLF] Wolfe, Jack M., " A First Course in Cryptanalysis,"
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[WRIX] Wrixon, Fred B. "Codes, Ciphers and Secret Languages,"
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[XEN1] PHOENIX, "Xenocrypt Handbook," American Cryptogram
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[YARD] Yardley, Herbert, O., "The American Black Chamber,"
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[YAR1] Yardley, H. O., "The Chinese Black Chamber," Houghton
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[YOKO] Yukio Yokoyama, "Tokushu joho kaisoka," unpublished
handwritten manuscript.

[YOUS] Youshkevitch, A. P., Geschichte der Mathematik im
Mittelatter, Liepzig, Germany: Teubner, 1964.

[YUKI] Yukio Nishihara, "Kantogan tai-So Sakusenshi," Vol 17.,
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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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