Links to Lanakis Classical Cryptography Course, Lectures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

 

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

 

 

CLASSICAL CRYPTOGRAPHY COURSE

 
BY LANAKI

 
March 5, 1996


 
Revision 0
COPYRIGHT 1996
ALL RIGHTS RESERVED
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 about the Viggy family. [KAHN]

 

 

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 to help you do the setup work.

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, but 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 perform 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 ...
in which we suspect 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 discards non readable text.

 

 

DECIPHERMENT BY PROBABLE TRIGRAM SEQUENCE

 

For the case where we have no probable word or the sequence is very short, we may use Ohaver's Trigram Method. We start with 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.

Proceeding with Column 2, we have no results. Column shows 2 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.

 

ANSWERS TO LECTURE 10 PROBLEMS

 

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

      (BUSINESSACTIVITYDURINGAPERIOD)

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

 

REFERENCES / RESOURCES

 

 

[updated 5 May 1996]

 

 

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[BAZE] Bazeries, M. le Capitaine, " Cryptograph a 20 rondelles-
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[BECK] Becket, Henry, S. A., "The Dictionary of Espionage:
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[BEES] Beesley, P., "Very Special Intelligence", Doubleday, New
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[BENN] Bennett, William, R. Jr., "Introduction to Computer
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[BLK]  Blackstock, Paul W.  and Frank L Schaf, Jr.,
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[BLOC] Bloch, Gilbert and Ralph Erskine, "Exploit the Double
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[BLUE] Bearden, Bill, "The Bluejacket's Manual, 20th ed.,
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[BODY] Brown, Anthony - Cave, "Bodyguard of Lies", Harper and
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[BOLI] Bolinger, D. and Sears, D., "Aspects of Language,"
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[BOSW] Bosworth, Bruce, "Codes, Ciphers and Computers: An
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[BOW2] Bowers, William Maxwell, "The Digraphic Substitution,"
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[BOW3] Bowers, William Maxwell, "Cryptographic ABC'S:
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[BOWN] Bowen, Russell J., "Scholar's Guide to Intelligence
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[BP82] Beker, H., and Piper, F., " Cipher Systems, The
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[BRAS] Brasspounder, "Language Data - German," MA89, The
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[BROW] Brownell, George, A. "The Origin and Development of
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[BRIG] Brigman,Clarence S., "Edgar Allan Poe's Contribution
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[BRIT] Anonymous, "British Army Manual of Cryptography",
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[BROG] Broglie, Duc de, Le Secret du roi: Correspondance
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[BUGS] Anonymous, "Bugs and Electronic Surveillance," Desert
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[BUON] Buonafalce, Augusto, "Giovan Battista Bellaso E Le Sue
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[BURL] Burling, R., "Man's Many Voices: Language in Its
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[BWO]  "Manual of Cryptography," British War Office, Aegean
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[CAND] Candela, Rosario, "Isomorphism and its Application in
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[CAR1] Carlisle, Sheila. Pattern Words: Three to Eight Letters
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[CAR2] Carlisle, Sheila. Pattern Words: Nine Letters in Length,
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[CASE] Casey, William, 'The Secret War Against Hitler',
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[CCF]  Foster, C. C., "Cryptanalysis for Microcomputers",
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[CHOI] Interview with Grand Master Sin Il Choi.,9th DAN, June
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[CHOM] Chomsky, Norm, "Syntactic Structures," The Hague:
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[CHUN] Chungkuo Ti-erh Lishih Tangankuan, ed "K'ang-Jih
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[CI]   FM 34-60, Counterintelligence, Department of the Army,
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[COUR] Courville, Joseph B., "Manual For Cryptanalysis Of The
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[CLAR] Clark, Ronald W., 'The Man who broke Purple',
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[COLF] Collins Gem Dictionary, "French," Collins Clear Type
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[COLG] Collins Gem Dictionary, "German," Collins Clear Type
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[COLI] Collins Gem Dictionary, "Italian," Collins Clear Type
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[COLL] Collins Gem Dictionary, "Latin," Collins Clear Type
       Press, 1980.

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

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

[COLS] Collins Gem Dictionary, "Spanish," Collins Clear Type
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[COPP] Coppersmith, Don.,"IBM Journal of Research and
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[COVT] Anonymous, "Covert Intelligence Techniques Of the Soviet
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[CREM] Cremer, Peter E.," U-Boat Commander: A Periscope View of
       The Battle of The Atlantic," New York, Berkley, 1986.

[CRYP] "Selected Cryptograms From PennyPress," Penny Press,
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[CULL] Cullen, Charles G., "Matrices and Linear
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[DAGA] D'agapeyeff, Alexander, "Codes and Ciphers," Oxford
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[DALT] Dalton, Leroy, "Topics for Math Clubs," National Council
       of Teachers and Mu Alpha Theta, 1973.

[DAN]  Daniel, Robert E., "Elementary Cryptanalysis:
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[DAVI] Da Vinci, "Solving Russian Cryptograms", The Cryptogram,
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[DEAC] Deacon, R., "The Chinese Secret Service," Taplinger, New
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[DEAU] Bacon, Sir Francis, "De Augmentis Scientiarum," tr. by
       Gilbert Watts, (1640) or tr. by Ellis, Spedding, and
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[DELA] Delastelle, F., Cryptographie nouvelle, Maire of Saint-
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[DENN] Denning, Dorothy E. R.," Cryptography and Data
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[DEVO] Deavours, Cipher A. and Louis Kruh, Machine Cryptography
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[DEV1] Deavours, C. A., "Breakthrough '32: The Polish Solution
       of the ENIGMA,"  Aegean Park Press, Laguna Hills, CA,
       1988.

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

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

[DEV4] Deavours, C. A., "Cryptographic Programs for the IBM
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[DIFF] Diffie, Whitfield," The First Ten Years of Public Key
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[DIFE] Diffie, Whitfield and M.E. Hellman,"New Directions in
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[DONI] Donitz, Karl, Memoirs: Ten Years and Twenety Days,
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[DOW]  Dow, Don. L., "Crypto-Mania, Version 3.0", Box 1111,
       Nashua, NH. 03061-1111, (603) 880-6472, Cost $15 for
       registered version and available as shareware under
       CRYPTM.zip on CIS or zipnet.


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

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

[ENIG] Tyner, Clarence E. Jr., and Randall K. Nichols,
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       publication, November, 1995.

[EPST] Epstein, Sam and Beryl, "The First Book of Codes and
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[ERSK] Erskine, Ralph, "Naval Enigma: The Breaking of Heimisch
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[EVES] Eves, Howard, "An Introduction to the History of
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[EYRA] Eyraud, Charles, "Precis de Cryptographie Moderne'"
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[FL]   Anonymous, The Friedman Legacy: A Tribute to William and
       Elizabeth Friedman, National Security Agency, Central
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[FLI1] Flicke, W. F., "War Secrets in the Ether - Volume I,"
       Aegean Park Press, Laguna Hills, CA, 1977.

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

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

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

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

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

[FR1]  Friedman, William F. and Callimahos, Lambros D.,
       Military Cryptanalytics Part I - Volume 1, Aegean Park
       Press, Laguna Hills, CA, 1985.

[FR2]  Friedman, William F. and Callimahos, Lambros D.,
       Military Cryptanalytics Part I - Volume 2, Aegean Park
       Press, Laguna Hills, CA, 1985.

[FR3]  Friedman, William F. and Callimahos, Lambros D.,
       Military Cryptanalytics Part III, Aegean Park Press,
       Laguna Hills, CA, 1995.

[FR4]  Friedman, William F. and Callimahos, Lambros D.,
       Military Cryptanalytics Part IV,  Aegean Park Press,
       Laguna Hills, CA, 1995.

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

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

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



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

[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,
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[FRAA] Friedman, William F. , "American Army Field Codes in The
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[FRAB] Friedman, W. F., Field Codes used by the German Army
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[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.

[FRAN] Franks, Peter, "Calculator Ciphers," Information
       Associates, Champaign, Il. 1980.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[GRAH] Graham, L. A., "Ingenious Mathematical Problems and
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[GRAN] Grant, E. A., "Kids Book of Secret Codes, Signals and
       Ciphers, Running Press, 1989.

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

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

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

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

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

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

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


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

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

[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
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       III, 1984 and 1988.

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

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

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

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

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

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

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



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

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

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

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

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

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

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

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

[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.

[KADI] al-Kadi, Ibrahim A., Cryptography and Data Security:
       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
       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.

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

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

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

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

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

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

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

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

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

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

[LAI]  Lai, Xuejia, "On the Design and Security of Block
       Ciphers," ETH Series in Information Processing 1, 1992.
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[LAIM] Lai, Xuejia, and James L. Massey, "A Proposal for a New
       Block Encryption Standard," Advances in Cryptology -
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[LAKE] Lakoff, R., "Language and the Women's Place," Harper &
       Row, New York, 1975.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

[MADA] Madachy, J. S., "Mathematics on Vacation," Scribners,
       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

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

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

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

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

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

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

[OTA]  "Defending Secrets, Sharing Data: New Locks and Keys for
       Electronic Information," Office of Technology
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[PEAR] "Pearl Harbor Revisited," U.S. Navy Communications
       Intelligence, 1924-1941, U.S. Cryptological History
       Series, Series IV, World War II, Volume 6, NSA CSS ,
       CH-E32-94-01, 1994.

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

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

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

[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.

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

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

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

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

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

[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
       Academy, 1988, pp 77-109.

[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",
       New York, Farrar, Straus, 1963.

[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
       City, CA, 1994



[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.

[SADL] Sadler, A. L., "The Code of the Samurai," Rutland and
       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
       Archives.

[SAPR] Sapir, E., "Conceptual Categories in Primitive
       Language," Science: 74: 578-584., 1931.

[SASS] Sassoons, George, "Radio Hackers Code Book", Duckworth,
       London, 1986.

[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
       Sons, 1995.

[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
       1949).

[SHIN] Shinsaku Tamura, "Myohin kosaku," San'ei Shuppansha,
       Toyko, 1953.

[SHUL] Shulman, David, "An Annotated Bibliography of
       Cryptography," Garland Publishing, New York, 1976.

[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,
       Aegean Park Press, Laguna Hills , CA.  1989.

[SIG1] "International Code Of Signals For Visual, Sound, and
       Radio Communications,"  Defense Mapping Agency,
       Hydrographic/Topographic Center, United States Ed.
       Revised 1981

[SIG2] "International Code Of Signals For Visual, Sound, and
       Radio Communications,"  U. S. Naval Oceanographic
       Office, United States Ed., Pub. 102,  1969.

[SIMM] Simmons, G. J., "How To Insure that Data Acquired to
       Verify Treaty Compliance are Trustworthy, " in
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       problem uniquely solvable by asymmetric encryption
       techniques.", IEEE EASCON 79, Washington, 1979, pp. 661-
       62.

[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
       Mathematical Association of America, NYU, 1966.

[SMIH] Smith, David E., "John Wallis as Cryptographer",
       Bulletin of American Mathematical Society, XXIV, 1917.

[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret
       Writing," Dover, NY, 1943.


[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I-
       III, " Harper and Row, New York, N.Y., 1975.

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

[STAL] Stallings, William, "Protect Your Privacy: A Guide for
       PGP Users," Prentice Hall PTR, 1995.

[STEV] Stevenson, William, 'A Man Called INTREPID',
       Macmillan, London 1976.

[STIN] Stinson, D. R., "Cryptography, Theory and Practice,"
       CRC Press, London, 1995.

[STIX] Stix, F., Zur Geschicte und Organisation  der Wiener
       Geheimen Ziffernkanzlei, Mitteilungen des
       Osterreichischen Instituts fir Geschichtsforschung,
       LI 1937.

[STUR] Sturtevant, E. H. and Bechtel, G., "A Hittite
       Chrestomathy," Linguistic Society of American and
       University of Pennsylvania, Philadelphia, 1935.






[SURV] Austin, Richard B.,Chairman,  "Standards Relating To
       Electronic Surveillance," American Bar Association
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       Berkley Press, New York, 1985.

[TERR] Terrett, D., "The Signal Corps: The Emergency (to
       December 1941); G. R. Thompson, et. al, The Test(
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       Office of the Chief of Military History, USGPO,
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[THEO] Theodore White and Annalee Jacoby, "Thunder Out Of
       China," William Sloane Assoc., New York, 1946.

[THOM] Thompson, Ken, "Reflections on Trusting Trust,"
       Communications of the ACM 27, 1984.

[TILD] Glover, D. Beaird, Secret Ciphers of The 1876
       Presidential Election, Aegean Park Press, Laguna Hills,
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[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio
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[TORR] Torrieri, Don J., "Principles of Military Communication
       Systems," Artech, 1981.

[TRAD] U. S. Army Military History Institute, "Traditions of
       The Signal Corps., Washington, D.C., USGPO, 1959.

[TRIB] Anonymous, New York Tribune, Extra No. 44, "The Cipher
       Dispatches, New York, 1879.

[TRIT] Trithemius:Paul Chacornac, "Grandeur et Adversite de
       Jean Tritheme ,Paris: Editions Traditionelles, 1963.

[TUCK] Harris, Frances A., "Solving Simple Substitution
       Ciphers," ACA, 1959.

[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
       House, New York, 1982.  [Original papers on Public Key
       Cryptography, RSA, DES]

[UBAL] Ubaldino Mori Ubaldini, "I Sommergibili begli Oceani: La
       Marina Italian nella Seconda Guerra Mondiale," vol XII,
       Roma, Ufficio Storico della Marina Militare, 1963.



[USAA] U. S. Army, Office of Chief Signal Officer,
       "Instructions for Using the Cipher Device Type M-94,
       February, 1922," USGPO, Washington, 1922.

[USAH] Gilbert, James L. and John P. Finnegan, Eds. "U. S.
       Army Signals Intelligence in World War II: A Documentary
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[USSF] "U.S. Special Forces Operational Techniques," FM 31-20,
       Headquarters Department Of The Army, December 1965.

[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
       Communications Intilligence in WWII in the Pacific, New
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[VERN] Vernam, A. S.,  "Cipher Printing Telegraph Systems For
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[VIAR] de Viaris in Genie Civil: "Cryptographie", Publications
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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.
       Cryptological History Series, Series V, NSA CSS,
       CH-E32-94-02, 1994.


[WALL] Wallis, John, "A Collection of Letters and other Papers
       in Cipher" , Oxford University, Bodleian Library, 1653.

[WAL1] Wallace, Robert W. Pattern Words: Ten Letters and Eleven
       Letters in Length, Aegean Park Press, Laguna Hills, CA
       92654, 1993.

[WAL2] Wallace, Robert W. Pattern Words: Twelve Letters and
       Greater in Length, Aegean Park Press, Laguna Hills, CA
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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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[WELS] Welsh, Dominic, "Codes and Cryptography," Oxford Science
       Publications, New York, 1993.


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

[WELS] Welsh, Dominic, "Codes and Cryptography," Oxford Science
       Publications, New York, 1993.

[WHOR] Whorf, B. L., "A Linguistic Consideration of Thinking In
       Primitive Communities,"  In Language, Thought, and
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[WILL] Williams, Eugenia, "An Invitation to Cryptograms," Simon
       and Schuster, 1959.

[WILD] Wildman, Ted, "The Expendables," Clearwater Pub., 1983

[WINJ] Winton, J., " Ultra at Sea: How Breaking the Nazi Code
       Affected Allied Naval Strategy During WWII," New Uork,
       William Morror, 1988.

[WINK] Winkle, Rip Van, "Hungarian: The Cryptogram,", March -
       April 1956.

[WINF] Winterbotham, F.W., 'The Ultra Secret', Weidenfeld
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[WINR] Winter, Jack, "Solving Cryptarithms," ACA, 1984.

[WOLE] Wolfe, Ramond W., "Secret Writing," McGraw Hill Books,
       NY, 1970.

[WOLF] Wolfe, Jack M., " A First Course in Cryptanalysis,"
       Brooklin College Press, NY, 1943.

[WRIX] Wrixon, Fred B. "Codes, Ciphers and Secret Languages,"
       Crown Publishers, New York, 1990.

[XEN1] PHOENIX, "Xenocrypt Handbook," American Cryptogram
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[YARD] Yardley, Herbert, O., "The American Black Chamber,"
       Bobbs-Merrill, NY, 1931.

[YAR1] Yardley, H. O., "The Chinese Black Chamber," Houghton
       Mifflin, Boston, 1983.

[YAR2] Yardley, H. O., "Yardleygrams", Bobbs Merrill, 1932.

[YAR3] Yardley, H. O., "The Education of a Poker Player, Simon
       and Schuster, 1957.

[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.,
       unpublished manuscript, National Institute for Defense
       Studies Military Archives, Tokyo.,(hereafter NIDS
       Archives)

[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)

 

Links to Lanakis Classical Cryptography Course, Lectures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

 

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