ACA and YOU : Chapter 3

How to solve a problem in The Cryptogram

An average copy of The Cryptogram contains 13-14 pages of cipher puzzles, or "cons" (for "constructions"). No information s included on how to solve these problems; all you are given is the type of cipher, a hint as to the subject of the con, and often a crib (tip) which services as a probable word. If you are new to decipherment, you will need some help on how to proceed. Here are a few notes; more details can be found in the literature.

Enciphered Tips

In real cryptography one would have an indication of the subject, and probably a wealth of ciphertext. Space limits us, so that we try to accommodate by giving titles and tips. Enciphered tips are those that are optional for solving. They are enciphered so that those who want the greater challenge can ignore them. For those who need the help, the tips are recovered by running down (or up) the alphabet, as tips are always enciphered in a Caesar cipher. The Caesar shift is not normally more than five in either direction.

 
    EXAMPLE 1:                     EXAMPLE 2:
 
Enciphered tip:  Z L Z H I B       Enciphered tip:  U Q E K G V A
                 A M A I J C                        T P D J F U Z
                 B N B J K D       Plain tip:       S O C I E T Y
Plain tip:       C O C K L E
 

Here the Caesar shifts are +3 and -2. Unless the tip is simply giving the period of the cipher, it is always found somewhere in the message. Enciphered tips are always in UPPER CASE, and plain tips are in lower case.

Keyword Recovery

Many ciphers use a keyword to develop their particular jumble of letters. (The origin of the keyword is as an easily remembered key for hypothetical spies to use.) Recovery of the keyword offers an alternative or parallel path to solution alongside direct recovery of the plaintext. As the plaintext is revealed, so is the keyword, and guessing a letter in one will give a letter in the other that might aid solution.

Keywords are dealt with in more detail in Chapter 7.

General Properties of Letters

A large vocabulary is helpful, but even more useful is a knowledge of the habits of letters and their relationships to each other in English (or the language of the message). The Frequency Table for English is:

 
  E  T  AO  NIR  SH  LD  CUPF  MWY  BGV  KQXJZ
  13 9  8    7    6   4    3    2    1     -    total: 100
 
 

The high-frequency letters ETAONIRSH make up 70% of plain text. Vowels AEIOU and Y make up 40% of the text. Consonants LNRST make up 35% of the text. The low frequency letters occupy less than 3% of the text, but are important because of their rarity, and also because adjacent letters (contacts) are more likely to be vowels than consonants.

We will now take a look at the various letters in more detail:

VOWELS

 
1-letter words  :  A, I; O occasionally.
2-letter words  :  begin with A, I, O, U; end with E, O, Y.
Doubles         :  O, E often double; A, U, I, Y rarely double.
Digraphs       A:  follows E, O(EA is most frequent); reverses
                   with I, U, Y.
               E:  precedes A; follows O; reverses with I,U, Y.
               I:  follows U, Y; reverses with A, E, O.
               O:  precedes A, U; reverses with I, Y.
               U:  follows U; precedes I; reverses with A, E.
               Y:  follows U; precedes I; reverses with A, E, O.
 
Common Positions:
               A:  initial and 2nd from end.
               E:  2nd and final, also scattered throughout.
               I:  3rd from end.
               O:  2nd and final.
               U:  initial and 2nd from end.
               Y:  final.

Vowel-Consonant Digraphs

ER-RE is the most frequent reversed digraph.

 
A: follows H;        precedes N,T,S;   reverses with R.
E: follows H;        precedes S,D;     reverses with R,T.
I: follows H,R,D;    precedes N;       reverses with T,S.
O: follows T,S,H;    precedes N;       reverses with R,L.
U: follows S,T,F;    precedes N;       reverses with P,B.
Y: follows L,R,T,N;  precedes S.

High-Frequency Consonants HLNRST

 
     H:  likes 1st, 2nd, last position; precedes vowels; follows
         W,S,C,T.  Note TH and GHT.
     L:  likes 2nd, next-to-last; prefers vowels contacts; follows
         P,C,B; precedes P,D; doubles at 3-4 in 6-letter words;
         before final S,Y in 5-letter words; in last position in
         4-letter words.
     N:  likes last and next-to-last position; follows vowels;
         precedes D,T,G,S,C.
     R:  likes 2nd and next-to-last (thus looks like a vowel, BUT
         it reverses freely with vowels); follows B,P,T; precedes
         T,S; doubles freely; often reverses with T (a common
         consonant reversal); seldom follows S.
     S:  likes last (very strongly), 1st and third position;
         doubles freely at middle and last positions; follows
         vowels and D,T,R,N; precedes vowels and THPCM; reverses
         often with T.
     T:  likes 1st, last and next-to-last(also scatters); doubles
         freely; follows vowels and B,C,F,L,N,P,R,S,X; precedes
         vowels and H,R.
 
 
The following two consonants (with E,S,T,N,R,Y) end most English words:
 
     D:  likes 1st and last position; prefers vowel contacts;
         doubles freely when followed by L; follows L,N,R;
         precedes R,W,L.
     G:  likes last (strongly), sometimes 1st 3rd from last and
         next-to-last; doubles freely when followed by L; follows
         vowels and D,R,N; precedes vowels and H,R,L.
 

Other Consonants

 
(These, with T,O,S,   begin   most English words).
 
     B:  follows vowels; precedes vowels, L,R; doubles when
         followed by L.
     C:  follows vowels, S,N; precedes vowels, H,T,L,R,K; doubles.
     F:  follows vowels; precedes vowels, T,R; doubles within and
         last.
     J:  usually initial only, precedes O,U; never doubles.
     M:  follows vowels, S,R; precedes vowels, P; doubles within.
     P:  follows vowels, R,L,M,S; precedes vowels, R,L,T; doubles
         freely.
     V:  follows vowels, L,R; precedes vowels.
     W:  follows vowels, D,S,T; precedes vowels, H,R.
 
 

Low-Frequency Consonants

 
     K:  likes first position followed by vowel or N; last
         position preceded by N,R,C,L; otherwise contacts vowels.
     Q:  likes 1st, 2nd, 3rd positions; normally followed by U;
         preceded by E,O,N,S,C.
     X:  follows vowels and N; precedes vowels and C,G,P,T.
     Z:  contacts vowels on both sides normally. (NB: UK uses "S"
         for USA "Z" in many instances.)
 

SOLVING ARISTOCRATS

An Aristocrat is a simple substitution cipher maintaining word divisions. No letter stands for itself.

Check the title first, and think of any word that might appear in the text. Look for short common words and pattern words. Make a frequency count to determine likely letter equivalencies. Look for 3 and 4-letter words, especially those containing TH. Look for common endings and beginnings.

Look for these short words:

an, in, is, it, on, to, and, are, has, his, her, not, see, the, was, why, you, from, into, once, have, that, than, this, there, these, those.

Look for these word beginnings:

an, at, be, de, dr, en, in, no, pre, pro, re, se, th, un.

Look for these word endings:

ance, ant, ate, (a)ble, ded, ed, en, er, ere, es, ese, est, ess, ful, ght, is, ine, ing, ion, ist, ive, ll, lly, ment, ous, rst, ses, sts, tion.

Computer solution often involves the use of large dictionaries to provides word-matches, which by trial and error can then lead to a solution.

SOLVING PATRISTOCRATS

A Patristocrat is a simple substitution cipher without words divisions. No letter stands for itself.

Tips will suggest THE, THAT, ING, TION, OR, etc. or patternwords. A frequency count is usually needed to establish the basis for these. Proceed as for Aristocrats, looking for frequent digraphs, reversals, and letter patterns.

Computer solution usually starts with a program to locate the tip accurately in the ciphertext, after which dictionary look-up methods can be used to obtain a solution.

SOLVING CRYPTARITHMS

A Cryptarithm is an arithmetical puzzle in which letters have been substituted for numbers. One letter represents one and only one number. Leading zeros are suppressed.

If a keyword or phrase is used, it will normally contain the same number of letters as the base of the numbering system, i.e. ten letters for a decimal system. The order of the letters in the keyword is indicated by "0-9" or "1-0" (for decimal problems). For higher-base systems, use A=11 decimal, B=12 decimal, and so on. Digits may be reversed so that the keyword looks random, or the key may not make sense at all ("No word").

 
EXAMPLE
 
 
Long Division.  (one word; 1-0).
 
     SORN /DIE = DS;  -NMH = DRDN;  - AHHM = AOD
 
Set up to solve:
 
                   D  S
           ______________
      D I E) S  O  R  N
             N  H  M
            --------------
             D  R  D  N
             A  H  H  M
             --------------
                A  O  D
 
  

Take each section of the calculation in turn dealing with it as a simple addition. Look for left hand digits; if single, they are probably "1". Look for columns containing two identical letters, try to place the zero. If a keyword is expected, be sure and fill in the equivalencies as you go.

More complex arithmetic, such as square roots, etc. should be reduced to a combination of additions to ease the solution.

The arithmetic manipulation lends itself to computer solution, although the challenge, as ever, is to find the short cuts used by the human brain.

THE CIPHER EXCHANGE

This department of The Cryptogram contains a selection of ciphers which do not use simple substitution. Some 60 ciphers are in current use by the ACA, and these are detailed in Chapter 8. Methods of solution are found in the literature and are continually being improved, particularly with the application of computers.

SOLVING XENOCRYPTS

A Xenocrypt may be any of the regular cipher types, but using a foreign language. It is usually not necessary to know the language to solve the ciphers, especially when the tips are given. However, such things as small dictionaries, beginner's books, and the familiarity gained by previous attempts can be very useful.

Xenocrypts are attacked in the same way as problems in English, but using, of course, frequency tables and other data for the language in question. Additional data can be found in the literature; frequency tables for some languages are given below, together with references to The Cryptogram and Elcy.

 
Frequency Tables
 
                                                    Refs:
  English:      ETAONIRSHLDCUPFMWYBGVKQXJZ
  Dutch:        ENIARDTOGLSHVRMUWJBZCPFXYQ          DN87
  Esperanto:    AIEONSLTRJUKMPDGCVBFZHQWXY          SO86
  French:       EANRSITUOLDCMPVBFGHQJZXY            MA86, Elcy
  German:       ENIRSADTUGHOLBMCWFKVZPJQXY          Elcy
  Interlingua:  EAILNOSTRUDCMPVGBFHXQJWYZK          MJ75
  Italian:      EAIOLNRTSCDMPUVGZFBHQ               MJ86, Elcy
  Latin:        IEUTAMSNRODLVCPQBFGXHJKWYZ          ND50
  Portuguese:   EAOSIDRTNCPUMLVFGQHJXZBKWY          Elcy
  Spanish:      EAOSRNIDLCTUMPGWBQVHFZ              JF86, Elcy
  Swedish:      AENRTSIOMGKLDVFBCHPUYJXQWZ          JA81
  

THE ANALYST'S CORNER

These ciphers are considered somewhat harder, and may break the "rules" for the cipher in some way, such as by the omission of a tip. The ciphers in this department are usually longer than those in the Cipher Exchange , to improve statistical analysis. A generous title or short narrative to "set the stage" is sometimes included.

ORNAMENTALS

Ornamentals are pictorial ciphers, often found as front cover designs for The Cryptogram. The ciphers are usually Aristocrats, but the challenge is to determine how the artist has hidden the message in the pattern, and then to solve it. Look for a typical "cell" that could represent a letter. Checking the dimensions of the figure may give a clue, for there are likely to be 75-100 characters hidden in it.

SPECIALS AND CHALLENGES

These are ciphers that the Editors consider more difficult than normal (such as a Patristocrat without plaintext "e"s), or examples of new types introduced in articles. Because of the nature of these ciphers, they are not included in the requirements for a complete ("*") solution in the Solvers List, although they do count in the total solved.