Lesson 5: Xenocrypt Morphology
CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI
December 27, 1995
Revision 0
LECTURE 5
XENOCRYPT MORPHOLOGY
SUMMARY
In Lecture 5, we begin our attack on substitution ciphers
created in languages other than English. First, we develop an
understanding of cryptography in its role as a cultural
universal. Next, we tour the elements of language and the
common cryptographic threads that make cryptographic analysis
possible. We then look at GERMAN Xenocrypts, applied traffic
analysis and the ADFGVX cipher of 1918 WWI vintage.
XENOCRYPTS
Xenocrypts are foreign language substitutions. Solving a
Xenocrypt (aka XENO) gives double pleasure; not only do you
have the fun of solving, but also the satisfaction of knowing
that you are acquiring a bowing acquaintance with other
languages.
PHOENIX has compiled and edited a Xenocrypt handbook [XEN1]
which brings together material published in The Cryptogram
since 1940. The book will be available to the KREWE in 1996.
It is an excellent tool. Lectures 5-7 will augment his
efforts. Quoted from PHOENIX's Preface in reference [XEN1]:
" Don't be afraid of Xenocrypts. The languages used
should not offer particular difficulties. Comparing an
English printers table (ETAINORSH...) with any of these
languages will show a lot of resemblance. That's because
English contains elements of most of the languages. Spellings
and endings will differ, but there often will be solid 'root'
that strongly resembles an English word. Most short English
words are of Saxon origin, akin to Danish, Swedish, Dutch, and
more remotely German. Longer words come to us from Latin or
Norman - French in many instances, and all have cognates in
common with English, generally differing slightly from the
English version, but often not at all, especially in French. "
In New Orleans, I keynoted the 1994 ACA Convention with the
possibility that any language could be learned from its
cryptographic building blocks. Xenocrypts represent a cultural
universal expressed at its common denominator - mathematics.
[NICX]
I suggested that languages be taught in schools first via
cryptography and then via sound and structure. This is how I
taught myself the rudiments of Russian, Japanese and Korean.
Cryptography enhanced my passable understanding of French and
reasonable efforts with German.
The real enjoyment came when I could understand Goethe in
German, and translated parts of Budo Shoshinshu by the 17
Century author Daidoji Yuzan [SADL]. Solving Xeno's can open
our eyes to other cultures.
THE STRUCTURE OF LANGUAGE
Linguistic anthropologists have used cryptography to
reconstruct ancient languages by comparing contemporary
descendants and in so doing make discoveries about history.
Others make inferences about universal features of language,
linking them to uniformities in the brain. Still others study
linguistic differences to discover varied world views and
patterns of thought in a multitude of cultures. [KOTT]
The Rossetta Stone found by the Egyptian Dhautpol and the
French officer Pierre-Francois Bouchard near the town of
Rosetta in the Nile Delta, gave us a look at Syriac, Greek and
Egyptian Hieroglyphs all of the same text. The fascinating
story of its decipherment is covered in Kahn. [KAHN] Of
special interest was the final decipherment of the Egyptian
writing containing homophones - different signs standing for
the same sound. [ROSE]
Until the late 1950's linguists thought that the study of
language should proceed through a sequence of stages of
analysis. The first stage was phonology, the study of sounds
used in speech. Phones are speech sounds present and
significant in each language. They were recorded using the
International Phonetic Alphabet, a series of symbols devised to
describe dozens of sounds that occur in different languages.
The next stage was morphology, the study of forms in which
sound combine, to form morphemes - words and their meaningful
constituents. The word cats has two morphemes /cat/ and /s/
indicating the animal and plurality. A lexicon is a dictionary
of all morphemes. A morpheme is the smallest meaningful unit
of speech. [MAYA] Isolating or analytic languages are those
in which words are morphologically unanalyzable, like Chinese
or Vietnamese. Agglutinative languages string together
successive morphemes. Turkish is a good example of this.
Inflection languages change the form of a word to mark all
kinds of grammar distinctions, such as tense or gender. Indo-
European languages tend to be highly inflectional.
The next step was to study syntax, the arrangement and order of
words in phrases and sentences.
PHONEMES and PHONES
No language contains all the sounds in the International
Phonetic Alphabet. Nor is the number of phonemes -significant
sound contrasts in a given language - infinite. Phonemes lack
meaning in themselves but through sound contrasts distinguish
meaning. We find them in minimal pairs, words that resemble
each in al but one sound. An example is the minimal pair
pit/bit. The /p/ and /b/ are phonemes in English. Another
example is bit and beat which separates the phonemes /I/ and
/i/ in English. [KOTT] Friedman describes a similar phenomena
called homologs and uses them to solve a variety of
cryptograms. [FR2] A phoneme is the smallest unit of
distinctive sound. [MAYA]
Standard (American) English (SE), the region free dialect of TV
network newscasters, has about thirty-five phonemes of at least
eleven vowels and twenty four consonants. The number of
phonemes varies from language to language - from fifteen to
sixty, averaging between thirty and forty. The number of
phonemes varies between dialects. In American English, vowel
phonemes vary noticeably from dialect to dialect. Readers
should pronounce the words in Figure 5-1, paying attention to
whether they distinguish each of the vowel sounds. We
Americans do not generally pronounce them at all. [BOLI]
Figure 5-1
Vowel Phonemes
Standard American English
According to Height of Tongue and Tongue Position
in Front, Center and Back of Mouth
Tongue High
i u
I U
ea ua o
e ou Mid
ae a
Tongue Low
Tongue Central Tongue
Front Back
Phonetic symbols are identified by English words that include
them; note that most are minimal pairs.
high front (spread) [i] as in beat
lower high front (spread) [I] as in bit
mid front (spread) [ea] as in bait
lower mid front (spread) [e] as in bet
low front [ae] as in bat
central [ua] as in butt
low back [a] as in pot
lower mid back (rounded) [ou] as in bought
mid back (rounded) [o] as in boat
lower high back (rounded) [U] as in put
high back (rounded) [u] as in boot
Phonetics studies sounds in general, what people actually say
in various languages.
Phonemics is concerned with sound contrasts of a particular
language. In English /b/ and /v/ are phonemes, occurring in
minimal pairs such as bat and vat. In Spanish, the contract
between [b] and [v] doesn't distinguish meaning, and are not
phonemes. The [b] sound is used in Spanish to pronounce words
spelled with either b or v. (Non phonemic phones are enclosed
in brackets).
In any language a given phoneme extends over a phonetic range.
In English the phoneme /p/ ignores the phonetic contrast
between the [pH] in pin and the [p] in spin. How many of you
noticed the difference? [pH] is aspirated, so that a puff of
air follows the [p]. not true with [p] in spin. To see the
difference, light a match and watch the flame as you say the
two words. In Chinese the contrast between [p] and [pH] is
distinguished only by the contrast between an aspirated and
unaspirated [p]. [BOLI]
TRANSFORMATIONAL-GENERATIVE GRAMMAR
Norm Chomsky's influential book Syntactic Structures (1957)
advocated a new method of linguistic analysis - Transform-
ational-generative grammar. [CHOM] Chomsky felt that a
language is more than the surface phenomena just discussed
(sounds, words, word order). He felt that all languages shared
a limed set of organizing principles. Chomsky observed that
every normal child who grows up in society develops language
easily and automatically. This occurs because the brain
contains a genetically transmitted blueprint, or basic
linguistic plan for building language. Chomsky called this
universal grammar. As children learn their native language,
they experiment with their blueprint, reject some sections
applying to other languages and gradually focus in and accept
the principles of their own language. They do this at about
the same age. His study also showed that we learn languages at
similar rates. There are universal improper generalizations
(foot, foots; hit, hitted) which eventually are corrected.
We master a specific grammar as we learn to speak. These rules
let us convert what we want to say into what we do say. People
who hear us and speak our language understand our meaning.
This works at a cryptographic level also. Chomsky
distinguishes between competence (what the speaker must and
does know about his language in order to speak and understand)
and performance (what a speaker actually says in social
situations or writes to someone ). Competence develops during
childhood and becomes an unconscious structure. The linguist
or cryptographer must discover the structure by looking at
deep structures (the mental level) and the surface structure
(actual speech) to find the transformational rules that link
them. Figure 5-2. shows the Chomsky Model.
Figure 5-2
Chomsky Model
For Message From Speaker to Hearer
or Writer on Both Sides
... Sounds (phonological component)...
. .
. .
. .
Surface-structure sentence Surface-structure sentence
. .
. .
Transformational rule Transformational rule
. .
. .
Deep structure sentence Deep structure sentence
. .
. .
. .
Thought Thought
(meaning, semantic component (meaning, semantic component
^
SPEAKER HEARER
The Chomsky model tells us why Xenos are so valuable.
The human brain contains a limited set of rules for organizing
language. The fact that people can learn foreign languages and
that words and ideas can be translated from one language into
another supports the Chomsky model that all humans have similar
linguistic abilities and thought processes.
THE SAPIR-WHORF HYPOTHESIS
Other linguists take the view that rather than universal
structures as clues to relationships between languages, they
belief that different languages produce different thinking
and writing. Edward Sapir and Benjamin Whorf argue that
speakers think about things in particular ways. For example,
the third person singular pronouns of English (he, she, him,
her, his, hers) distinguish gender, whereas those of the
Palaung of Burma do not. [BURL] [SAPR] [WHOR]
Gender exists in English, although a fully developed noun-
gender and adjative-agreement system as in French and other
Romance Languages (la belle fille, la beau fils), does not.
The Sapir-Whorf hypothesis suggests that English speakers
pay more attention to differences between males and females
than the Palaung but less than the French and Spanish speakers.
English divides time into past, present, and future. Hopi,
a language of the Pueblo region of the Native American
Southwest does not. Hopi does distinguish between events that
exist or have existed and those don't or don't yet, along with
imaginary and hypothetical events. Differing perceptions of
time and reality cause difference in spoken and written
thought.
FOCAL VOCABULARY
A lexicon or vocabulary is a language's dictionary, its set of
names for things, events and ideas. APEX DX can probably
confirm that Eskimos have several distinct words for snow. In
English all forms of snow are the same (unless you are a dope
dealer). The Nuer of the Sudan have an elaborate vocabulary to
describe cattle. Specialized distinctions between groups is
called focal vocabulary. Cattle vocabulary of Texas ranchers
is more extensive than New Yorkers; Aspen ski bums
differentiate types of snow that are missing from the lexicons
of Florida retirees. Ten years ago who would have 'faxed'
anything. Simplification of often used words are called
monolexemes and compound expressions are simplified such as
tropical storm to rain. A television becomes TV, an automobile
a car, and a videocassette recorder becomes a VCR.
Semantics refers to a language meaning system. Language,
culture and thought are interrelated. There is considerable
difference between female and male Americans in regard to color
terms. Distinctions implied by such terms as salmon, rust,
peach, beige, teal, mauve, cranberry, and dusk orange aren't in
the vocabularies of most American men. Ask a fashionable woman
and she will know them all. [LAKE]
HISTORICAL LINGUISTICS
Knowledge of linguistic relationships is often valuable to
determine the events of the past 5000 years. By studying
contemporary daughter languages, past language features can be
reconstructed. Daughter languages descend from the same parent
language that has been changing for thousands of years. The
original language from which they diverge is called a
protolanguage. French and Spanish are daughter languages of
Latin. Language evolves over time into subgroups (closely
related from a taxonomy point of view) but with distinct
cultural differences. Figure 5-3. shows the main languages
and subgroups of the Indo European language stock.
All these daughter languages have developed out of the
protolanguage (Proto-Indo-European) spoken in Northern Europe
about 5,000 years ago. Note subgroupings. English, a member
of the Germanic branch, is more closely related to German and
Dutch than it is to Italic or Romance languages such as French
and Spanish. However, English shares many linguistic features
with French through borrowing and diffusion. [FROM]
The doctrine of linguistic relativity is central to
cryptographic treatment of language ciphers. It states that
all known languages and dialects are effective means of
communication. [KOTT] Nichols Theorem states that if they
are linguistically related, they can be codified, enciphered,
deciphered and treated as cryptographic units for analysis and
statistical treatment. [NICX]
Figure 5 -3
Main Languages of Indo-European Stock
INDO-EUROPEAN
.
............................................................
. . . .
. . . .
CELTIC ITALIC GERMANIC .
. . . . . . . . .
. . . . .
o Welsh . . . .
o Irish . West North .
o Scots Gaelic . . . .
o Breton . . . .
. . . .
ROMANCE o Dutch o Danish .
. o English o Icelandic .
Latin o Flemish o Norwegian .
. o Frisian o Swedish .
. o German .
o Catalan o Yiddish .
o French .
o Italian .
o Portuguese .
o Provencal .
o Rumanian .
o Spanish .
.
.
.............................................................
. . .
. . . .
HELLENIC Albanian . .
. . .
. Armenian .
Ancient Greek .
. .
. .
Greek .
.
.
...............................................
. . .
. . .
INDO-IRANIAN BALTIC SLAVIC
. . .
. . .
. o Latvian o Bulgarian
. o Lithuanian o Czech
. o Macedonian
. o Polish
o Old Persian o Russian
o Persian o Serbo-Croatian
o SANSKRIT o Slovak
. o Slovenian
. o Ukrainian
.
o Bengali
o Hindi
o Punjabi
o Urdu
DEAD LANGUAGES
Figure 5-3 pertains to live languages. Professor Cyrus H.
Gordon in his fascinating book "Forgotten Scripts" shows how
cryptography is used to recover ancient writings. He tells the
story of the unraveling of each of these ancient languages:
Egyptian, Old Persion, Sumer-Akkadian, Hittite, Ugaritic,
Eteocretan, Minoan and Eblaite. He specializes in cuniform and
hieroglyphic inscriptions and gives us a glimpse into the
ancient societies that gave birth to the Western world. [GORD]
See also references [BARB], [POPE] and [STUR].
CRYPTOGRAPHIC THREAD
There is a common cryptographic thread for most languages.
All known writing systems are partly or wholly phonetic, and
express the sounds of a particular language. Writing is speech
put in visible form, in such a way that any reader instructed
in its conventions can reconstruct the vocal message. Writing
as "visible speech" was invented about five thousand years ago
by Sumerians and almost simultaneously by ancient Egyptians.
The ancient Mayan knew that it was 12 cycles, 18 katuns, 16
tuns, 0 uinals, and 16 kins since the beginning of the Great
Cycle. The day was 12 Cib 14 Uo and was ruled by the seventh
Lord of the Night. The moon was nine days old. Precisely
5,101 of our years and 235 days had passed. So said the
ancient Mayan scribes. We remember the day as 14 May 1989.
WRITING SYSTEMS
Three kinds of writing systems have been identified: Rebus
which is a combination of logograms and phonetic signs;
Syllabic such as CV - consonant vowel such as Cherokee or
Inuit; and Alphabetic, which is phonemic, the individual
consonants and vowels make up the sounds of the language.
Table 5-2 differentiates writing systems by the number of signs
used. [MAYA]
TABLE 5-3
Writing System No. of Signs
Logographic
Sumerian 600+
Egyptian 2,500
Hittite Hieroglyphic 497
Chinese 5,000+
"Pure" Syllabic
Persian 40
Linear B 87
Cypriote 56
Cherokee 85
Alphabetic or Consonantal
English 26
Anglo-Saxon 31
Sanskrit 35
Etruscan 20
Russian 36
Hebrew 22
Arabic 28
Michael D. Coe classifies the entire Proto- Mayan languages.
In fourteen daughter divisions of Proto-Mayan, there are thirty
one sub languages from Huastec to Tzuthil. Extraordinary
story of applied cryptanalysis and applied linguistics.
[MAYA]
XENOCRYPTS
I used to think that Xenocrypts - non English cryptograms, were
very difficult to solve. The 'aha' light came on several years
ago, when I realized that most languages share the common
framework of mathematics and statistics. To be able to solve
Xenocrypts, it is only necessary to learn the basic (group)
mathematical structure of the language, to use a bidirectional
translation dictionary and to recognize the underlying cipher
construct. [NICX]
Many challenge ciphers start with the problem of recognizing
the language and then the distribution of characters within the
particular language. The legendary W. F. Friedman once
remarked: "treating the frequency distribution as a statistical
curve, when such treatment is possible, is one of the most
useful and trustworthy methods in cryptography." [FR1], [FRE]
Table 1 gives the frequency distributions of ten of my favorite
languages (sans Russian, Chinese and Japanese which require
character sets that will not transfer via my e-mail). The
frequencies in Table 5-1 have been developed from various
sources. Table 5-1 frequencies may differ from other published
data, based on text derived solely from literature or military
sources, because I have included the practical text from my
solved Xeno's over the years. Letters used in cryptograms tend
to shift the frequency distribution. Frequencies of letters,
and their order, are not fixed quantities in any language.
Group frequencies, however, are fairly constant in every
language. This is the common thread - the linguistic
relativity of all languages. [NICX], [NIC1]
TABLE 5-1
Partial Frequency Distribution For Cracking Xenocrypts
16 8 7 6 5 4 2 <1
NORWEGIAN: E RNS T AI LDO GKM UVFHPA' JBO' YAECWXZQ
10 9 7 6 4 3 <2
LATIN: I E UTA SRN OM CPL (bal)
18 8 7 6 5 4 3 2 <1
FRENCH: E AN RSIT UO L D CMP VB F-Y
14 13 12 8 6 5 4 3 2 <1
PORTUGUESE: A E O RS IN DMT UCL P QV (bal)
18 11 8 7 5 4 3 2 <1
GERMAN: E N I RS ADTU GHO LBM CW (bal)
15 12 8 7 5 4 3 1 <1
CATALAN: E A S ILRNT OC DU MP BVQGF (bal)
16 13 8 6 5 4 3 <2
HUNGARIAN: E A T OS LNZ KIM RGU (bal)
13 12 11 9 7 6 5 3 2 <1
ITALIAN: E A I O L NRT SC DMO'U VG (bal)
20 10 7 6 5 4 3 2 <1
DUTCH: E N IAT O DL S GKH UVWBJMPZ (bal)
13 9 8 7 5 4 3 1 <1
SPANISH: EA O S RNI DL CTU MP GYB (bal)
ENGLISH REVISITED
English has its characteristic frequencies and sequence data
(based on 10,000 letters):
% 12 10 8 8 7 7 7 6 5 4-3 2 1 < 1
ENGLISH: E / T A / O N I S R H / LDCU / PFMW / YBGV / KQXJZ
GROUP PERCENTAGES:
A E I O U 38.58%
L N R S T 33.43%
J K Q X Z 1.11%
E T A O N 45.08%
E T A O N I S R H 70.02%
ORDER
Digram Order: TH / HE / AN / IN / ER / RE / ES / ON / EA / TI
/ AT / ST / EN / ND / OR
Trigram Order: THE / AND / THA / ENT / ION / TIO / FOR / NDE
Reversals: ER RE / ES SE / AN NA /TI IT /ON NO / IN NI
Initials: T A O S H I W C B P F D M R
Finals: E S T D N R O Y
Vowel % 40% (y included)
The ACA Xenocrypt Handbook compiled by PHOENIX, develops
similar mathematical data on fifteen languages presented in The
Cryptogram on a regular basis. [XEN1]
Review Lecture 2 Kullback's tests and Friedman's I.C. test.
Kullback gives the following tables for Monoalphabetic and
Digraphic texts for eight languages:
Note that the English plain text value is slightly less than
Friedman's. [KULL] [SINK]
Monoalphabetic Digraphic
Text Text
English 0.0661N(N-1) 0.0069N(N-1)
French 0.0778N(N-1) 0.0093N(N-1)
German 0.0762N(N-1) 0.0112N(N-1)
Italian 0.0738N(N-1) 0.0081N(N-1)
Japanese 0.0819N(N-1) 0.0116N(N-1)
Portuguese 0.0791N(N-1)
Russian 0.0529N(N-1) 0.0058N(N-1)
Spanish 0.0775N(N-1) 0.0093N(N-1)
Random Text
Monographic Digraphic Trigraphic
.038N(N-1) .0015N(N-1) .000057N(N-1)
XENO's - foreign language substitutions, as given in the
Xenocrypt Department of The Cryptogram, are usually quotations,
or simple normal wording. Thus the Frequency Table of a
Xenocrypt will follow closely to the normal Frequency Table of
its language. Arranging these two tables in order of
frequency, rather than alphabetically, may be used for testing
probable equivalents. When words are found, if the meaning is
not known, a dictionary helps.
The Contact and Position Tables are used just as in solving
English cryptograms.
Lets start off with German Xenocrypts.
GERMAN DATA [ Based on 60,046 letters of text in FRE2]
Absolute Frequencies
A 3,601 G 1,921 L 1,988 Q 6 V 523
B 1,023 H 2,477 M 1,360 R 4,339 W 899
C 1,620 I 4,879 N 6,336 S 4,127 X 12
D 3,248 J 192 O 1,635 T 3,447 Y 24
E 10,778 K 747 P 499 U 2,753 Z 654
F 958 ======
60,046
Monographic Kappa Plain, German Language = 0.0787, I.C. = 2.05
Relative Frequencies reduced to 1000 letters
E 180 T 57 G 32 F 16 P 8
N 106 D 54 O 27 W 15 J 3
I 81 U 46 C 27 K 13 Y -
R 72 H 41 M 23 Z 11 X -
S 69 L 33 B 17 V 9 Q -
A 60 =======
1,000
Groups
Vowels: A, E, I, O, U, Y = 39.4%
High-Frequency Consonants: D, N, R, S, T = 35.8%
Medium-Frequency Consonants: B, C, F, G, H, L, M, W = 20.4%
Low-Frequency Consonants: J, K, P, Q, V, X, Z = 4.4 %
8 most frequent letters (E, N, I, R, S, A, T, and D) = 67.9%
(descending order)
Initials ( based on 9,568 letters of text)
D 1,716 U 550 Z 343 K 263 O 135
A 762 W 544 M 339 P 181 T 106
S 698 G 461 N 306 R 167 C 22
E 686 B 460 F 280 L 158 Q 2
I 581 V 408 H 265 J 135 ======
9,568
Digraphs [Based on 60,046 letters reduced to 5,000 digraphs]
A B C D E F G H I J K L M
A 4 14 10 4 33 7 9 7 1 1 2 33 13
B 6 48 1 1 5 3
C 130 5
D 29 2 8 127 1 2 2 60 1 3 2
E 13 22 10 31 13 12 32 24 90 2 6 28 25
F 7 1 3 15 7 2 2 2 1
G 10 1 8 78 1 2 2 8 2 7 1
H 29 1 8 64 1 2 1 14 2 8 3
I 3 1 39 7 91 2 18 7 2 7 12 11
J 4 8
K 12 1 1 11 1 1 1 5
L 26 3 1 6 27 1 2 37 3 20 1
M 16 3 4 26 2 22 1 14 1 2 1 11
N 39 12 118 58 9 57 8 35 4 10 6 10 18
O 1 3 5 3 11 3 3 3 1 18 6
P 10 5 4 1 2 1
Q
R 34 11 5 35 60 9 12 9 37 2 11 6 8
S 14 6 55 13 46 3 7 3 30 1 5 4 7
T 25 3 17 88 2 4 6 40 1 3 7 3
U 1 2 8 2 37 15 5 1 2 2 11
V 1 19 3
W 16 24 20 3
X
Y
Z 1 1 8 5 1
Digraphs [Based on 60,046 letters reduced to 5,000 digraphs]
N O P Q R S T U V W X Y Z
A 48 2 22 27 23 36 1 1 1
B 3 11 2 1 3 1 1
C
D 2 4 1 5 6 2 9 2 2 2
E 235 3 6 195 68 28 24 9 15 7
F 1 3 10 2 10 12
G 3 1 11 8 5 8 2 1 1
H 6 6 1 20 4 23 7 2 3 1
I 84 13 1 7 53 44 1 2 1 1
J 3
K 9 10 1 5 4
L 2 4 10 12 6 1 1
M 1 8 5 1 3 3 9 1 1 1
N 18 8 5 4 36 27 20 10 17 14
O 33 1 5 18 12 4 1 1 5 1
P 7 2 7 1 1
Q 1
R 12 19 3 6 22 18 26 6 8 5
S 3 16 6 2 40 57 9 5 5 1 5
T 4 4 14 20 7 16 2 10 13
U 76 2 18 28 14 1 1 2 1
V 21
W 6 6
X
Y
Z 2 4 27 4
Digraphic Kappa plain = 0.0111, I.C. = 7.50
95 Digraphs comprising 75% of German plain text based on 5,000
digraphs arranged according to relative frequencies.
EN- 235 RE- 60 NA- 39 ED- 31 TA- 25 HR- 20 TU- 16
ER- 195 DI- 60 LI- 37 SI- 30 EM- 25 LL- 20 WA- 16
CH- 130 NE- 58 UE- 37 HA- 29 EH- 24 VE- 19 UF- 15
DE- 127 NG- 57 RI- 37 DA- 29 EU- 24 RO- 19 FE- 15
ND- 118 ST- 57 AU- 36 EL- 28 WE- 24 OR- 18 EW- 14
IE- 91 SC- 55 NS- 36 US- 28 HT- 23 UR- 18 AB- 14
EI- 90 IS- 53 NI- 35 ET- 28 AT- 23 NN- 18 HI- 14
TE- 88 BE- 48 RD- 35 AS- 27 AR- 22 RT- 18 TR- 14
IN- 84 AN- 48 RA- 34 LE- 27 RS- 22 OL- 18 SA- 14
GE- 78 SE- 46 AE- 33 NT- 27 EB- 22 IG- 17 MI- 14
----- IT- 44 ------ ZU- 27 VO- 21 NW- 17 NZ- 14
a) 1,236 SS- 40 2,508 b)LA- 26 NU- 20 TD- 16 UD- 14
TI- 40 ME- 26 WI- 20 MA- 16 SD- 13
UN- 76 IC- 39 ON- 33 RU- 26 TS- 20 SO- 16 ------
ES- 68 AL- 33 3,750
HE- 64 EG- 32
a) 10 digraphs before this line represent 25% of German Plain
b) 37 digraphs before this line represent 50% of German Plain
Frequent Digraph Reversals (based on table of 5,000 digraphs)
EN- 235 NE- 58 IE- 91 EI- 90 ES- 68 SE- 46 AN- 48
ER- 195 RE- 60 IN- 84 NI- 35 IS- 53 SI- 30 IT- 44
DE- 127 ED- 31 GE- 78 EG- 32 NA- 39 TI- 40
Rare Digraph Reversals (based on previous 5,000 digraphs)
CH- 130 HC- 0 ND-113 DN- 2 NG- 57 GN-3 SC- 55 CS-0
Doublets (based on previous 5,000 digraphs)
SS- 40 EE- 13 FF- 7 RR- 6 GG- 2 PP- 2 OO - 1
LL- 20 MM- 11 TT- 7 AA- 4 II- 2 HH- 1 UU - 1
NN- 18 DD- 8
Initial Digraphs (based on 9,568 words)
DE- 805 EI- 300 DA- 244 WE- 192 ER- 153 ZU- 124 ST- 112
DI- 567 GE- 299 VO- 214 VE- 172 HA- 140 MI- 117 IN- 111
UN- 428 BE- 252 SI- 197 WI- 155 AL- 134 SN- 112 SE- 111
AU- 318
Trigraphs (top 102 based on 60,046 letters of German text)
SCH- 666 ERE- 313 NEN- 198 AUS- 162 IST- 142 HRE- 124
DER- 602 ENS- 270 SSE- 191 TIS- 159 STA- 141 HER- 122
CHE- 599 CHT- 264 REI- 190 BER- 157 DES- 140 ACH- 119
DIE- 564 NGE- 263 TER- 188 ENI- 157 FUE- 139 GES- 118
NDE- 541 NDI- 259 REN- 185 ENG- 155 NTE- 139 ABE- 117
EIN- 519 IND- 254 EIT- 184 ION- 154 UER- 138 ERA- 117
END- 481 ERD- 248 EBE- 178 SEN- 152 ERU- 137 BEN- 116
DEN- 457 INE- 247 ENE- 175 ITI- 151 TUN- 136 MEN- 115
ICH- 453 AND- 246 LIC- 175 AUF- 149 SEI- 133 RIE- 112
TEN- 425 RDE- 239 EGE- 173 IES- 149 ESE- 132 VER- 110
UNG- 377 ENA- 214 DAS- 172 ASS- 148 ERT- 128 LAN- 109
HEN- 332 ERS- 212 ENU- 171 ENW- 148 NDA- 127 ENB- 108
UND- 331 EDE- 209 NUN- 169 ENT- 146 IED- 126 ESS- 108
GEN- 321 STE- 205 NER- 166 ERI- 143 ERN- 125 LLE- 108
ISC- 317 VER- 204 RUN- 163 EST- 142 NAU- 108 TSC- 107
ENN- 106 ERG- 106 RIT- 106 EHR- 105 CHA- 104 VON- 104
SIC- 103 IGE- 102 ITE- 101 ENZ- 100 ERB- 100 EUT- 100
Initial Trigraphs (based on 9,568 word beginnings)
EIN- 242 DAS- 79 SCH- 73 AUF- 64 DEU- 61 UNT- 57
VER- 170 BRI- 79 AUS- 69 NER- 63 GES- 60 GRO- 56
FUE- 89 DIE- 76 SEI- 68 IND- 62 GEG- 59 AUC- 55
SIC- 86 NIC- 73 STA- 65 ALL- 61 UEB- 53 POL- 52
WIR- 51
Tetragraphs (50 top based on 60,046 letters)
SCHE-398 NUND-106 NICH- 80 ATIO- 65 RSCH- 60 ENZU- 54
ISCH-317 ITIS-104 UNGD- 80 GEND- 65 EDEN- 59 ITEN- 54
CHEN-296 SICH-103 EITE- 79 TEND- 65 ERGE- 59 KRIE- 54
NDER-243 RUNG-101 DEUT- 78 EBER- 67 ESSE- 59 RIEG- 54
EINE-218 ANDE-100 FUER- 78 GEGE- 65 UNTE- 59 SDIE- 54
ENDE-216 UNGE-100 CHTE- 77 POLI- 64 EICH- 58 URCH- 53
NDIE-176 EREI- 94 EGEN- 76 SIND- 64 TLIC- 58 ALLE- 52
LICH-168 TION- 93 NEIN- 76 TUNG- 64 INER- 57 DERS- 52
ICHT-151 SEIN- 92 IESE- 75 ENSI- 64 EBEN- 56 ENWE- 52
TISC-146 IEDE- 91 ERST- 74 FUTS- 64 ENDA- 56 HABE- 52
ERDE-144 LAND- 91 RDIE- 74 LITI- 62 ENST- 56 ONEN- 52
ENDI-141 SSEN- 90 ERDI- 72 UEBE- 62 IGEN- 56 SCHI- 52
NDEN-136 BRIT- 89 STEN- 72 UTSC- 62 ONDE- 56 DEND 51
RDEN-133 DASS- 86 CHER- 71 AUCH- 62 TENS- 56 DISC- 51
ENUN-120 NTER- 86 INDI- 71 DENS- 62 EDIE- 55 ENEN- 51
ICHE-120 EDER- 83 REIN- 71 EIND- 61 ERTE- 55 NACH- 51
INDE-111 EREN- 83 DERE- 70 OLIT- 61 HREN- 55 NDAS- 51
NGEN-110 ENGE- 81 NGDE- 70 SCHA- 61 TDIE- 55 UNGS- 51
ERUN-109 ENAU- 80 ENBE- 68 SCHL- 61 ATEN- 55 ABEN- 50
DIES-108 ENIN- 80 RITI- 66 WERD- 61 DIEB- 54 NBER- 50
TSCH-107
One-letter words: O (very rare)
Two-letter words: ZU SO ER ES DU DA IN AN IM AM UM WO OB JA
Three-letter words: DER DIE UND IST DAS EIN ICH SIE MAN MIT DEN
DEM VON WAR WAS NUR MIR ALS AUF AUS BEI BIS
Four-letter words: SICH ABER WIRD SIND ODER AUCH NACH NOCH MICH
ALSO DOCH DREI FAST SEHR WELT ZWEI WERT OHNE
Common Pattern words: TUT NUN SEE ALLE EINE NEIN DASS DENN DANN
KANN MUSS WENN WILL SOLL KOMM HERR NEUE GING ALLES IMMER EINES
EINEN LEBEN KEINE JETZT
Common prefixes: BE- GE- AUF- ER- VER- HER- UN- HIN- ZU- VOR-
Common suffixes: -LICH -HEIT -KEIT -ISCH -SCHAFT --EN -ER -IG
Pecularities: C generally followed by H or K; SC invariably by
H giving SCH
Common articles:
masc fem neut plu masc fem neut
the der die das die a, one ein eine ein
of the des der des der of a eines einer eines
in the dem der dem den in a einem einer einen
by the den die das die by a einen eine ein
True Diphthongs: AI AU EI EU
Consonant Rules
B. May appear in any position.
C. Combines with other consonants. CH, CK, SCH.
D. Forms gerund ending, -ende, -ende; similar to ing in
English. Doubles occasionally.
F. Doubles freely.
G. Occasionally doubles.
H. Does not form SH.
J. Initial letter only. Rare.
K. Doubles with CK if separated by - as in bakken
L. Not followed by CK or TZ.
M, N, P, R, T. Doubles freely.
Q. Same as English.
S. Freely doubled, forms SP ST SK not SC nor SH. SCH acts as a
single consonant.
V. Initial.
W. Does not form Wh.
X. Very infrequent. Sound of X is CHS
Y. Not a final.
Z. Never doubles. Follows vowels, changes to TZ. Rare as a
final.
SOLUTION OF GERMAN ARISTOCRAT
Ger-1 K1. [BRASSPOUNDER]
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
*Z. *D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
OGFJDNR.
A frequency analysis of Ger-1 yields:
G - 20 16.1% Try G=e.
K - 13 10.5% Try K=n.
J - 10 8.1% Try J=i.
S - 9 7.3%
D,E - 9 7.3%
F - 7 5.6%
N,R,H - 6 4.8%
V,O,U - 5 4.0%
I - 3
P,Q,M - 2
X,Z,A,T,L - 1
B,C,W,Y - 0
1 2 3 4 5 6
e i ein e i ni en e e e
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
7 8 9 10 11
n n ne i i e e i e en
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
12 13 14 15 16 17 18 19
en e n e en gi e en i n
Z. D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
20
e
OGFJDNR.
So the first three letters follow the German frequency table.
Note we have ein. Word 19 is und? and word 1 might be es.
The frequencies match. Try these substitutions.
1 2 3 4 5 6
es i ein e i nis en deu s e eu
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
7 8 9 10 11
und n ne i i e es i e s en
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
12 13 14 15 16 17 18 19
u s en u e n s e en eide en i s und
*Z. *D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
20
deu s
OGFJDNR.
A common trigram is sch. Word 20 might be deutsch. Word 1
could be es followed by gibt. Word 17 might be beide.
1 2 3 4 5 6
es gibt ein e i nischen deutscher teur
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
7 8 9 10 11
rund n net i ittel estlic e st ten
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
12 13 14 15 16 17 18 19
u s en un e n sprechen beide englisch und
*Z. *D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
20
deutsch
OGFJDNR.
Word 18 becomes english and word 16 could be speaks in german =
sprechen. (insert above)
I note that I have missed a high frequency letter pair E=a.
Inserting brings three additional words.
1 2 3 4 5 6
es gibt a ein americanischen-deutscher amateur
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
7 8 9 10 11
rund n net im mittelwestliche staaten am
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
12 13 14 15 16 17 18 19
u s allen un e n sprechen beide englisch und
*Z. *D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
20
deutsch
OGFJDNR.
The flow of the german now is clear. A little worterbuch gives
us the balance of letter relationships.
1 2 3 4 5 6
es gibt ja ein americanischen-deutscher amateur
GD QSMJ TE GSK EVGHSIEKSDNRGK-OGFJDNRGH EVEJGFH
7 8 9 10 11
rundfunk netz im mittelwestliche staaten am
HFKOPFKI KGJL SV VSJJGUAGDJUSNRG DJEEJGK EV
12 13 14 15 16 17 18 19
u s allen funkern sprechen beide englisch und
*Z. *D. EUUGK PFKIGHK DXHGNRGK MGSOG GKQUSDNR FKO
20
deutsch
OGFJDNR.
The keyword = sauerkraut.
Note the simularities to English Aristocrat solving and to
English endings and words. Note the group statistics of the
two languages and my comments on common threads. Do you see
how this commonality flows from Figure 5-1?
SOLUTION OF GERMAN PATRISTOCRAT
Lets remove the word divisions and try a German Patristocrat.
Ger-2. Traurige Wahrheit. (zwei ewige) Eng K4 GEMINATOR
1 2 3 4 5 6 7
JGKMH FDZJM JZMKJ IMRKJ ICGXR MYJWG XQXRI
8 9 10 11 12 13 14
IMJQJ RGELP MELJI XQQLJ MFCHJ WQMFI JQXRM
15 16 17 18 19 20 21
YJWGX QMGFI CGRME LFKCR DGMEL JWCPH JWFJM
22 23
RGFJM R.
The hint tells us that the words [zwei ewige] is in the
cryptogram plain text. We also know that K4 password scheme
has been used. Nichols rule says ignore the descriptive part
in the title as a red hering.
Start with the frequency analysis:
J - 17 15.3% K - 5 4.5% O - 0
M - 15 13.5% C - 5 4.5% A - 0
R - 9 8.1% W - 5 4.5% B - 0
G - 9 8.1% E - 4 3.6% N - 0
I - 7 6.3% H - 3 2.7% T - 0
Q - 7 6.3% Z - 2 1.8% S - 0
X - 6 5.4% Y - 2 1.8% V - 0
F - 6 5.4% P - 2 1.8% U - 0
L - 5 4.5% D - 2 1.8%
Let J=e and note the patterns at groups 2 and 3 for the
hint zwei ewige. So Z=w, D=z, M=i K=g.
1 2 3 4 5 6 7
e gi zwei ewige i ge i e
JGKMH FDZJM JZMKJ IMRKJ ICGXR MYJWG XQXRI
8 9 10 11 12 13 14
ie e i e e i e i e i
IMJQJ RGELP MELJI XQQLJ MFCHJ WQMFI JQXRM
15 16 17 18 19 20 21
e i i g z i e e ei
YJWGX QMGFI CGRME LFKCR DGMEL JWCPH JWFJM
22 23
ei
RGFJM R.
The G is a high frequency letter and could be S, A, or N.
Try 'es gibt' in groups 1 and 2. s works, b works, t might.
1 2 3 4 5 6 7
esgib tzwei ewige i ge s i e s
JGKMH FDZJM JZMKJ IMRKJ ICGXR MYJWG XQXRI
8 9 10 11 12 13 14
ie e s i e e it be it e i
IMJQJ RGELP MELJI XQQLJ MFCHJ WQMFI JQXRM
15 16 17 18 19 20 21
e s i t s i tg z i e b e tei
YJWGX QMGFI CGRME LFKCR DGMEL JWCPH JWFJM
22 23
stei
RGFJM R.
Now we must find the n, r and the a. R might be our n.
(see last group). And QQ = mm, A long leap for C=a by
frequency only - later to confirm by digrams. A short leap
lets us assume W=r. Placing these guesses in temporarily,
we find the following:
1 2 3 4 5 6 7
esgib tzwei ewige dinge dasun ivers umund
JGKMH FDZJM JZMKJ IMRKJ ICGXR MYJWG XQXRI
8 9 10 11 12 13 14
dieme nschl iched ummhe itabe rmitd emuni
IMJQJ RGELP MELJI XQQLJ MFCHJ WQMFI JQXRM
15 16 17 18 19 20 21
versu mistd asnic htgan zsich eralb ertei
YJWGX QMGFI CGRME LFKCR DGMEL JWCPH JWFJM
22 23
nstei n
RGFJM R.
Our digram table helps us with cipher text L and X. X is a good
candidate for u and L = h is a reasonable guess, because EL =
ch brings us two words. Note group 12 now gives us the W=r
and I = d! A little help from the dictionary yields Y=v and
P=l.
Putting the word divisions back in we have a quote by
Dr. Einstein.
Es gibt zwei ewige dinge das universum und die
menschliche dummheit aber mit dem universum ist
das nicht ganz sicher. == Albert Einstein.
The kewords are (facts; SAD). The plain text x is over the
cipher text S for the initial position of the keying alphabets.
GERMAN REDUCTION CIPHERS - TRAFFIC ANALYSIS
A small sister to cryptanalysis is the applications of traffic
analysis. Traffic analysis was the forerunner to differential
cryptanalysis and a primary reason for the cracking of the
German Codes in WWII. {Unfortunately, the same principles
worked on the British and American Codes as well.} The German
Army (maybe even the German Soul) was dedicated to unquestioned
organization. Paperwork and radio messages must flow to the
various military units in a prescribed manner. Traffic
Analysis is the branch of signal intelligence analysis which
deals with the study of external characteristic of signal
communications.
The information is used: 1) to effect interception, 2) to aid
cryptanalysis, 3) to rate the level and value of intelligence
in the absence of the specific message contents and 4) to
improve the security in the communication nets. [AFM]
COMPONENTS
Allowing for differences in language and procedure signs and
signals, there are six standard elements for military radio
communications systems. These are: 1) call-up, 2) order of
traffic, 3) transmission of traffic, 4) receipting for traffic,
5) corrections and services, and 6) signing off. [TM32]
In order to insure proper handling of messages in the field and
message center, some information was sent in the clear or using
simple coding. This information about routing and accounting
was usually in the preamble or message postamble. This
included: 1) Serial numbers, message center number, 2) Group
Count, 3) File Date and Time [like a PGP signature] 4) Routing
System - origin, destination and relay, (distinction is made as
to action or FYI locations) 5) Priority (important stuff was
originally signal flashed - hence the term FLASH message for
urgent message) 6) transmission and delivery procedure, 7)
addresses and signatures, 8) special instructions. As a
general rule, German high-echelon traffic contained most of
these items and German low-echelon traffic cut them to a
minimum.
The German penchant for organization could be seen in the way
they handled serial numbers. Any radio message flowing from
division level to soldier in the field would have a reference
serial number attached in clear or matrix cipher, by the
writer, the HQ message center, the signal center or code room,
the "in desk" , the transmitter, linkage, and/or operator. The
routing system usually consisted of a code and syllabary that
represented the location or unit. [HIN1]
An example taken from WWII U. S. Army procedure:
A45 BR6 B STX-O-P P-A45 BR6-T-N-A45 A-79K 011046Z
A-45-W-F2P SLW BR6
GR 28
BT TEXT
BT 011046Z K
where:
A45 BR6 - multiple callup; receiving calls
STX-O-P - transmitting call with precedence designation, OP=
operational priority
P-A45 - message priority to A45 only; to others routine
BR6-T-N-A45 - BR6 to relay to all except A45
A-79K - originator of message
011046 - Date and Time Zulu used pre and postamble
A-45 - action destination
W-F2P SLW BR6 - Information destinations
GR 28 Group Count.. note how small for such external
information envelope
You can see where modern E-Mail and word processing systems
have made some of this information easier to handle by the
portable desk idea but traffic analysis would still apply.
American "cryptees' were adept in determining the German Order
of Battle from their cryptonets (ex. from intercepts re limited
distribution from corp to a theater). Traffic analysis not
only gave the locations but the communication relationships
between units or groups of units in the field. Some German
commands were allowed latitude in their compositions of codes
and ciphers. This proved to be an exploitable fault in the
German security.
ANALYSIS OF ROUTING
American success in reconstructing German communication
networks was partly do to the appropriate (and sometimes lucky)
analysis of the routing system. The radio station could be
tied into the code group. Crib techniques included focusing on
the relay point, recognizing a book message crib to several
locations, correlating the address and signature cribs, tagging
the operational chatter, separating the addresses, using solved
messages to give outright routing assignments, syllabary
solutions and changes in the system itself.
The textual features of the message gave valuable information.
Tabulations of messages, text type, and volumes helped
discriminate the practice and dummy traffic. Recognition of
the communications net as order of battle often gave away the
crypto-entity.
APPLICATIONS TO CRYPTANALYSIS
Traffic analysis yields information via Crib messages, Isologs
and Chatter. Crib messages assume a partial knowledge of the
underlying plain text through recognition of the external
characteristics. Command sitrep reports, up and down German
channels, were especially easy for American crypees. The
origin, serial number range, the cryptonet id, report type, the
file date and time, message length and error messages in the
clear, gave a clear picture of the German command process.
German order of battle, troop dispositions and movements were
deduced by traffic analysis. [TM32]
An Isolog exists when the underlying plain text is encrypted in
two different systems. They exist because of relay repetition
requirements, book messages to multiple receivers (spamming
would have been a definite no-no), or error by the code clerk.
American crypees were particularly effective in obtaining
intelligence from this method.
Traffic analysis boils down to finding the contact
relationships among units, tracking their movements, building
up the cryptonet authorities, capitalizing on lack of
randomness in their structures, and exploiting book and relay
cribs. I submit that American intelligence was quite
successful in this endeavor against the Germans in WWII.
ADFGVX
"Weh dem der leugt und Klartext funkt" - Lieutenant Jaeger
German 5th Army. ["Woe to him who lies and radios in the
clear"]
Jaeger was a German code expert sent to stiffen the German Code
discipline in France in 1918. Ironically, the double "e" in
Jaeger's name gave US Army traffic analysis experts a fix on
code changes in 1918.
ADFGVX, is one of the best known field ciphers in the history
of cryptology. Originally a 5 x 5 matrix of just 5 letters,
ADFGX, the system was expanded on June 1, 1918 to a 6th letter
V. The letters were chosen for their clarity in Morse: A .-, D
-.., F ..-., G --., V ...-, and X -..-.
W. F. Friedman describes one of the first traffic analysis
charts regarding battle activity from May to August, 1918
at Marne, and Rheims, France. It was based solely on the ebb
and flow of traffic in the ADFGVX cipher. This cipher was
restricted to German High Command communications between and
among the headquarters of divisions and army corps.
The ADFGVX cipher was considered secure because it combined
both a good substitution (bipartite fractionation) and an
excellent transposition in one system. During the eight month
history of this cipher, only 10 keys were recovered by the
Allies (in 10 days of heavy traffic) and fifty percent of the
messages on these days were read. These intercepts effected
the reverse of the German advances (15 divisions) under
Ludendorff at Montdidier and Compiegne, about 50 miles North of
Paris. Solution by the famed French Captain Georges Painvin
was based on just two specialized cases. No general solution
for the cipher was found by the Allies. In 1933, William
Friedman and the SIS found a general solution. French General
Givierge, of the Deuxieme Bureau also published a solution to
the general case.
The June 3 message that Painvin cracked which changed the
course of WWI:
From German High Command in Remaugies: Munition-ierung
beschleunigen Punkt Soweit nicut eingesehen auch bei Tag
"Rush Munitions Stop Even by day if not seen."
CT starts: CHI-126: FGAXA XAXFF FAFFA AVDFA GAXFX FAAAG
This told the Allies where and when the bombardment preceding
the next major German push was planned.
ENCIPHERING ADFGVX
26 letters and 10 digits of the ADFGVX were placed into a 6 x 6
Bipartite Square:
A D F G V X
A F L 1 A O 2
D J D W 3 G U
F C I Y B 4 P
G R 5 Q 8 V E
V 6 K 7 Z M X
X S N H 0 T 9
PT: a l l q u i e t o n t h i s
CT: AG AD AD GF DX FD GX XV AV XD XV XF FD XA
PT: f r o n t t o d a y
CT: AA GA AV XD XV XV AV DD AG FF
The bilateral cipher which results is transposed with a keyed
matrix, written in by row and removed by column.
G E R M A N
3 2 6 4 1 5
A G A D A D
G F D X F D
G X X V A V
X D X V X F
F D X A A A
G A A V X D
X V X V A V
D D A G F F
and the final CT is:
AFAXA XAFGF XDDAV DAGGX FGXDD XVVAV VGDDV FADVF ADXXX
AXA
Known decipherment was accomplished with the Key and possession
of the original matrix. Fine and dandy but cryptanalysis in
1918, was another thing.
ADFGVX CRYPTANALYSIS
According to William Friedman, there were only three viable
ways to attack this cipher. The first method required 2 or
messages with identical plain text beginnings to uncover the
transposition. Under the second method, 2 or more messages
with plain text endings were required to break the flat
distribution shield of the substitution part of the cipher.
The German addiction to stereotyped phraseology was so
prevalent in all German military communications that in each
days traffic, messages with similar endings and beginnings were
found (sometimes both). The third method required messages
with the exact same number of letters. Painvin used the first
two methods when he cracked the 5 letter ADFGX version in
April, 1918. [FRAA], [FRAB]
Lest we underestimate the difficulty of this cipher, I think we
might step behind Painvin shoulders as he worked. At 4:30 am
on March 21, 6000 guns opened fire on the Allied line at Somme.
Five hours later, 62 German Divisions pushed forward on a 40
mile front. Radio traffic increased dramatically, Painvin had
just a few intercepts in the ADFGX cipher and the longer ones
had been split in three parts to prevent anagraming.
Five letters, therefore, a checkerboard? Simple mono cipher -
too flat a distribution.
The German oddity of first parts of messages with identical
bits and pieces of text larded in the same order in the
cryptograms begin to show. Painvin feels the oddity could most
likely have resulted from transposed beginnings according to
the same key; the identical tops of the columns of the
transposition tableau. Painvin sections the cryptograms by
timeframe:
chi-110: (1) ADXDA (2) XGFXG (3) DAXXGX (4) GDADFF
chi-114: (1) ADXDD (2) XGFFD (3) DAXAGD (4) GDGXD
He does this with 20 blocks to reconstruct the transposition
key. Using the principle - long columns to the left, he finds
segments 3,6,14, 18 to left. Balance clustered to right.
Using other messages with common endings (repeated) He segments
the columns to the left. Correctly? No. He uses 18 additional
intercepts to juxtaposition 60 letters AA's, AD's, etc. Using
frequency count, he finds a monoalphabetic substitution.
He finds column 5-8 and 8-5 are inverted.
Painvin sets up a skeleton checkerboard - he assumes correctly
the order to be side-top:
A D F G X
A
D e
F
G
X
Since the message was 20 letters, the order might be side-top,
repeated, meaning side coordinates would fall on 1st, 3rd,
5th.. positions during encipherment, so he separates them by
frequency characteristics. In 48 hours of incredible labor,
Painvin pairs the correct letters and builds the checkerboard,
solving the toughest field cipher the world had yet seen. A
cipher that defends itself by fractionation - the breaking up
of PT letters equivalents into pieces, with the consequent
dissipation of its ordinary characteristics. The transposition
further scatters these characteristics in a particularly
effective fashion, while dulling the clues that normally help
to reconstruct a transposition.
HOMEWORK PROBLEMS
Solve these:
Ger-3. Kalenderblatt August. K2 (Sonne) BRASSPOUNDER
QV FHOHIC ICMPC KQM IXWWM QW KML WFMPM KMI
*IQLQHI, KMI *PHWKICMLWI, KFPML KQM "*PHWKIC-
FOMI," KQM AMKML VMWIJP WXJP CQMLM VXMOMW.
Ger-4. Ungerechtes Schicksal. Eng. K4 GEMINATOR
IRFJA DRGAI RAMRT VFAKF DLUFS UXABR ADSEQ
DBHMR XBAIC KVELR JAVKV AFDJI HMBHP IEQII
HMQEL JEIIA QGAUB SSAVJ AVIAQ GATVC KAIIC
VJBAI AQGAD KVELA D. hints: (zum zw-; zimm-)
Fre-1. French digraphic. Christmas Greeting. MON NOM
DBAAB AADBB BBBAB CABAA BBCDC ACCAA BABAC
AABBD ACBAA AAACA CABAC BCCCB BAAAB IJGFG
GKJGJ FFGJH JGFIK JFGFH GGFKG FGHKG FFGJJ
GGJIK GJFJG JGFJH FGIIG KIKJF.
hints: (noel, plus). Look out for disruption area in cipher
square.
REFERENCES / RESOURCES
[ACA] ACA and You, "Handbook For Members of the American
Cryptogram Association," ACA publications, 1995.
[ACA1] Anonymous, "The ACA and You - Handbook For Secure
Communications", American Cryptogram Association,
1994.
[AFM] AFM - 100-80, Traffic Analysis, Department of the Air
Force, 1946.
[ALAN] Turing, Alan, "The Enigma", by A. Hodges. Simon and
Shuster, 1983.
[ANDR] Andrew, Christopher, 'Secret Service', Heinemann,
London 1985.
[ANNA] Anonymous., "The History of the International Code.",
Proceedings of the United States Naval Institute, 1934.
[AS] Anonymous, Enigma and Other Machines, Air Scientific
Institute Report, 1976.
[BARB] Barber, F. J. W., "Archaeological Decipherment: A
Handbook," Princeton University Press, 1974.
[B201] Barker, Wayne G., "Cryptanalysis of The Simple
Substitution Cipher with Word Divisions," Course #201,
Aegean Park Press, Laguna Hills, CA. 1982.
[BALL] Ball, W. W. R., Mathematical Recreations and Essays,
London, 1928.
[BAR1] Barker, Wayne G., "Course No 201, Cryptanalysis of The
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[BAR2] Barker, W., ed., History of Codes and Ciphers in the
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[BAR3] Barker, Wayne G., "Cryptanalysis of the Hagelin
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[BARK] Barker, Wayne G., "Cryptanalysis of The Simple
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[BARR] Barron, John, '"KGB: The Secret Work Of Soviet Agents,"
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[BAUD] Baudouin, Captain Roger, "Elements de Cryptographie,"
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[BLK] Blackstock, Paul W. and Frank L Schaf, Jr.,
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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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[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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[COVT] Anonymous, "Covert Intelligence Techniques Of the Soviet
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[DAN] Daniel, Robert E., "Elementary Cryptanalysis:
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[DAVI] Da Vinci, "Solving Russian Cryptograms", The Cryptogram,
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[DEAU] Bacon, Sir Francis, "De Augmentis Scientiarum," tr. by
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[DEVO] Devours, Cipher A. and Louis Kruh, Machine Cryptography
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[ELCY] Gaines, Helen Fouche, Cryptanalysis, Dover, New York,
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[ENIG] Tyner, Clarence E. Jr., and Randall K. Nichols,
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[FREB] Friedman, William F., "Cryptology," The Encyclopedia
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[FR1] Friedman, William F. and Callimahos, Lambros D.,
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[FR2] Friedman, William F. and Callimahos, Lambros D.,
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[FR3] Friedman, William F. and Callimahos, Lambros D.,
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[FR4] Friedman, William F. and Callimahos, Lambros D.,
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[FR6] Friedman, William F. Military Cryptanalysis - Part II,
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[FRE] Friedman, William F. , "Elements of Cryptanalysis,"
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[FREA] Friedman, William F. , "Advanced Military Cryptography,"
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[FR22] Friedman, William F., The Index of Coincidence and Its
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[FROM] Fromkin, V and Rodman, R., "Introduction to Language,"
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[FRS] Friedman, William F. and Elizabeth S., "The
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[GARL] Garlinski, Jozef, 'The Swiss Corridor', Dent,
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[GAR1] Garlinski, Jozef, 'Hitler's Last Weapons',
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[GERM] "German Dictionary," Hippocrene Books, Inc., New York,
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[GIVI] Givierge, General Marcel, " Course In Cryptography,"
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[GRA1] Grandpre: "Grandpre, A. de--Cryptologist. Part 1
'Cryptographie Pratique - The Origin of the Grandpre',
ISHCABIBEL, The Cryptogram, SO60, American Cryptogram
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[GRA2] Grandpre: "Grandpre Ciphers", ROGUE, The Cryptogram,
SO63, American Cryptogram Association, 1963.
[GRA3] Grandpre: "Grandpre", Novice Notes, LEDGE, The
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[GODD] Goddard, Eldridge and Thelma, "Cryptodyct," Marion,
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[GORD] Gordon, Cyrus H., " Forgotten Scripts: Their Ongoing
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[HIN2] Hinsley, F. H. and Alan Strip in "Codebreakers -Story
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[HIS1] Barker, Wayne G., "History of Codes and Ciphers in the
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[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. )
[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
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[HOM3] Homophonic: Computer Column:"Homophonic Solving,"
PHOENIX, The Cryptogram, MA84, American Cryptogram
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[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
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[IBM1] IBM Research Reports, Vol 7., No 4, IBM Research,
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[INDE] PHOENIX, Index to the Cryptogram: 1932-1993, ACA, 1994.
[JAPA] Martin, S.E., "Basic Japanese Coversation Dictionary,"
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[JOHN] Johnson, Brian, 'The Secret War', Arrow Books,
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[KAHN] Kahn, David, "The Codebreakers", Macmillian Publishing
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[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", Houghton Mifflin, New
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Cryptography, 2nd Ed, Springer-Verlag, New York, 1994.
[KONH] Konheim, Alan G., "Cryptography -A Primer" , John Wiley,
1981, pp 212 ff.
[KOTT] Kottack, Phillip Conrad, "Anthropology: The Exploration
Of Human Diversity," 6th ed., Mcgraw-Hill, Inc., New
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Machine Cipher was Broken and How it Was Read by the
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[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.
[LAKE] Lakoff, R., "Language and the Womans Place," Harper &
Row, New York, 1975.
[LANG] Langie, Andre, "Cryptography," translated from French
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[LEDG] LEDGE, "NOVICE NOTES," American Cryptogram Association,
1994. [ One of the best introductory texts on ciphers
written by an expert in the field. Not only well
written, clear to understand but as authoritative as
they come! ]
[LEWI] Lewin, Ronald, 'Ultra goes to War', Hutchinson,
London 1978.
[LEWY] Lewy, Guenter, "America In Vietnam", Oxford University
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[LEVI] Levine, J., U.S. Cryptographic Patents 1861-1981,
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[LISI] Lisicki, Tadeusz, 'Dzialania Enigmy', Orzet Biaty,
London July-August, 1975; 'Enigma i Lacida',
Przeglad lacznosci, London 1974- 4; 'Pogromcy
Enigmy we Francji', Orzet Biaty, London, Sept.
1975.'
[LYNC] Lynch, Frederick D., "Pattern Word List, Vol 1.,"
Aegean Park Press, Laguna Hills, CA, 1977.
[LYSI] Lysing, Henry, aka John Leonard Nanovic, "Secret
Writing," David Kemp Co., NY 1936.
[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,
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[MAYA] Coe, M. D., "Breaking The Maya Code," Thames and Hudson,
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USGPO, 1879.
[MM] Meyer, C. H., and Matyas, S. M., " CRYPTOGRAPHY - A New
Dimension in Computer Data Security, " Wiley
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[MODE] Modelski, Tadeusz, 'The Polish Contribution to the
Ultimate Allied Victory in the Second World War',
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[NIBL] Niblack, A. P., "Proposed Day, Night and Fog Signals for
the Navy with Brief Description of the Ardois Hight
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[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
Languages," ACA-L, August 18, 1995.
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[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
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[NIC7] Nichols, Randall K., "Arabic Contributions to
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[NICX] Nichols, R. K., Keynote Speech to A.C.A. Convention,
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[NORM] Norman, Bruce, 'Secret Warfare', David & Charles,
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[NORW] Marm, Ingvald and Sommerfelt, Alf, "Norwegian," Teach
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[RAJ2] "Pattern and Non Pattern Words of 7 to 8 Letters," G &
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[RAJ3] "Pattern and Non Pattern Words of 9 to 10 Letters," G &
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[RAJ4] "Non Pattern Words of 3 to 14 Letters," RAJA Books,
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[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma
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[RHEE] Rhee, Man Young, "Cryptography and Secure Commun-
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[ROBO] NYPHO, The Cryptogram, Dec 1940, Feb, 1941.
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[RUNY] Runyan, T. J. and Jan M. Copes "To Die Gallently",
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[RYSK] Norbert Ryska and Siegfried Herda, "Kryptographische
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[SADL] Sadler, A. L., "The Code of the Samurai," Rutland and
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[SACC] Sacco, Generale Luigi, " Manuale di Crittografia",
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[SAPR] Sapir, E., "Conceptual Categories in Primitive
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[SASS] Sassoons, George, "Radio Hackers Code Book", Duckworth,
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[SCHN] Schneier, Bruce, "Applied Cryptography: Protocols,
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[SIG1] "International Code Of Signals For Visual, Sound, and
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[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
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[SISI] Pierce, C.C., "Cryptoprivacy," Author/Publisher, Ventura
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[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret
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[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I-
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[STIN] Stinson, D. R., "Cryptography, Theory and Practice,"
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[TERR] Terrett, D., "The Signal Corps: The Emergency (to
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[TILD] Glover, D. Beaird, Secret Ciphers of The 1876
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[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio
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[TRAD] U. S. Army Military History Institute, "Traditions of
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[TRIB] Anonymous, New York Tribune, Extra No. 44, "The Cipher
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[TRIT] Trithemius:Paul Chacornac, "Grandeur et Adversite de
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[TUCK] Harris, Frances A., "Solving Simple Substitution
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[TUCM] Tuckerman, B., "A Study of The Vigenere-Vernam Single
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[VERN] Vernam, A. S., "Cipher Printing Telegraph Systems For
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[VOGE] Vogel, Donald S., "Inside a KGB Cipher," Cryptologia,
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[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
92654, 1993.
[WATS] Watson, R. W. Seton-, ed, "The Abbot Trithemius," in
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[WEL] Welsh, Dominic, "Codes and Cryptography," Oxford Science
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[WELC] Welchman, Gordon, 'The Hut Six Story', McGraw-Hill,
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[WHOR] Whorf, B. L., "A Linguistic Consideration of Thinking In
Primitive Communities," In Language, Thought, and
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B. Carroll, Cambridge, MA: MIT Press, pp. 65-86., 1956.
[WINT] Winterbotham, F.W., 'The Ultra Secret', Weidenfeld
and Nicolson, London 1974.
[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
Association, 1 Pidgeon Dr., Wilbraham, MA., 01095-2603,
for publication March, 1996.
[YARD] Yardley, Herbert, O., "The American Black Chamber,"
Bobbs-Merrill, NY, 1931.
[ZIM] Zim, Herbert S., "Codes and Secret Writing." William
Morrow Co., New York, 1948.
[ZEND] Callimahos, L. D., Traffic Analysis and the Zendian
Problem, Agean Park Press, 1984. (also available
through NSA Center for Cryptologic History)
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