CHAPTER XXII

Highlights of Fractional Substitution

Fractional substitution requires a cipher alphabet of the “multifid” type; that is, one in which the symbols are composed of two or more units, as in the Bacon and Trithemius alphabets (Chapter II: Figs. 3 and 4), the various “checkerboards” (Chapter XI), and so on. Polygram “alphabets” are also of this type, and seriation is a forrn of fractional substitution.

Among the older fractionals, we find a system called the “Pollux,” in which the basis was the Morse telegraphic alphabet. There were three units, the dot, the dash, and a separator (made necessary by the irregular lengths of the substitutes). There was a first substitution in which the letters of the text were replaced with their Morse symbols, including the space. The resulting cryptogram, composed entirely of the units dot, dash, space (. — x), was then subjected to a second substitution, using a small cipher alphabet (either digits or letters) in which each one of the three units might have any one of several different substitutes, chosen at will. For instance, a dot might be replaced with any one of digits 1, 8, 5, 6, a space with any one of digits 3, 9, 0, and a dash with any one of digits 2, 4, 7.

Figure 172

Delastelle's "BIFID" Substitution -(Keyword Feature Added by M. E. OHAVER)

Preparation of Alphabet: Checkerboard Key: Substitutes:

G E N • R A L 1 2 3 4 5 S = 43 B C D F H I K E = 15 M O P Q S T U 1 G B M V E N = 24 V W X Y Z 2 C O W N D D = 25 3 P X F Q Y 4 R H S Z A 5 I T L K U Preliminary Substitution:

S E N D S U P P L I E S T O M O R L E Y S R I G H T A W A Y. 4 1 2 2 4 5 3 3 5 5 1 4 5 2 1 2 4 5 1 3 4 4 5 1 4 5 4 2 4 3 3 5 4 5 3 5 1 1 3 1 5 3 2 2 3 2 1 3 5 5 3 1 1 1 2 2 5 3 5 5

Re-Substitution:

41 22 45 33 54 53 51 35 51 45 21 31 53 22 12 45 13 43 21 35 53 R O A F K L I Y I A C P L O B A M S C Y L

45 14 54 21 11 22 53 43 55 Transmitted: A V K C G O L S U. R O A F K L I Y I A C P L O B, etc.

We find also a number of systems called “Collon” in which the basis is some one of the “checkerboards.” The text is subjected to a simple substitution in the agreed alphabet, and the resulting cryptogram is then subjected to a transposition, usually seriation, this being the final operation.

A similar system called the “Mirabeau” uses an alphabet of the same type as that of the _Polybius square_, in which only the digits 1-2-3-4-5 are significant. The remaining digits are all null, and numbers like 67 or 88 may be inserted at will. Numbers are written vertically (tens below units); then, in the taking off of the cryptograms, the whole series of units is taken first, and the second half of the cryptogram includes all of the tens-digits. In all of these forms, the undesirable features are self-evident. The later devices have added another operation: the regrouping of the scattered units, and their reconversion into letters.

Classic examples are those described by Delastelle as “bifid” and “trifid” (terms, incidentally, which some of our own writers find objectionable, as they do also the term “multifid”). Delastelle’s “bifid” cipher was of the kind shown in Fig. 172. A two-unit alphabet must be used, and all possible two-unit combinations must be convertible into letters. Any desired seriation-length may be agreed upon, though it should not be divisible by 2. In the figure, the key-word GENERAL, 7 letters, governs the seriation-length as well as the mixing of the key-square, a feature suggested by Ohaver. The substitution is identical with that of the Polybius square, except that the two units of the substitute are written vertically below the original. Digits are then grouped horizontally in pairs, treating one seven-letter group at a time (if the seriation index is 7), and these pairs are replaced with letters from the same key-square. It will be noticed that we have here a form of polygram substitution, in which one seven-letter group has been replaced with another. Also, that possible errors have been confined by the seriation feature to their own seven-letter group.

Figure 173

A Fractional Substitution Based on Morse Symbols - M.E.OHAVER

The Alphabet, Arranged by Group-Lengths:

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

S E N D S U P ... . -. -.. ... ..- .--. Reverse digits, and re-group: 3 1 2 3 3 3 4 4 3 3 3 2 1 3 .... -.- ... ... .- . --. H K S S A E G

Delastelle’s “trifid” cipher was of the same kind, except that a three-unit alphabet was required, resulting in three rows of units. It would have been the same as that of Fig. 4, Chapter II, but with the French accented _E_ replacing the character _&_. All combinations of three units must be re-convertible into letters.

Fig. 173 shows a form of “mutilation” cipher once published by Ohaver. Beyond stating that its only key is the group-length (7 in the example), we leave the student to figure it out for himself.

As an example of recent use (1918), we are told on excellent authority that the Germans, for quite a long time during the World War, used a field cipher of the following description: There was a preliminary substitution using a key-square of the Nihilist type, except that the external co-ordinates were letters, and not digits, and were chosen in such a way that the five or six letters used were letters having very distinctive Morse symbols; this was for the avoidance of telegraphic errors. In some cases a 5 x 5 square was used, containing only a 25-letter mixed alphabet, and in others a 6 x 6 square containing a 26-letter mixed alphabet and all of the digits. The preliminary cryptogram obtained from this first encipherment was then written into a transposition block and taken off by columns, using key-word columnar transposition. The cryptograms were not afterward shortened by resubstitution, but were always twice as long as their messages, and never contained any other letters than the five (or six) originally used as co-ordinates. This German Field Cipher proved very effective until finally broken by the great French analytical genius, Georges Painvin.

We shall make no attempt, here, to go into the decryptment of these ciphers. The Delastelle “bifid” is, perhaps, a practical cipher, and the student may try his own hand at analyzing the example. The other examples should give no trouble.

154. By PICCOLA. (Delastelle's "Bifid." - Repeated words: AMERICA(N), ATTEMPT, REPORT, THAT, THE, OF, TO. Other short words: FROM, WITH, BEEN, HAVE. Likely words: REPORT, AGENT, CONFIRM, CABLE, etc).

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

The mixed alphabet here was placed in the square by straight horizontals. History: Message intercepted following a report that on the tenth of August an attenpt had been made to enter the American embassy in a country where Royalists are opposed to a group of radicals.

155. By PICCOLA. (Fractional. - Not so hard).

3 3 3 2 3 1 1 1 2 3 2 2 1 3 1 1 1 1 3 1 3 3 1 1 3 2 2 1 2 2 1 1 2 3 1 2 3 3 2 1 2 3 3 1 1 3 2 1 1 2 1 2 2 2 3 1 2 2 2 3 1 1 2 2 1 2 3 2 3 2 2 1 2 3 1 3 3 2 3 1 1 2 2 1 3 2 1 2 2 3 2 1 3 1 2 2 2 2 3 2 3 2 2 2 2 3 1 1 1 3 1 2 3 2 1 1 2 2 2 3 2 3 1 3 2 2 2 2 1 2 3 1 2 2 1 2 1 2 2 1 1 2 2 3 2 3 2 2 3 2 2 2 3 2 2 3 3 1 2 2 3 1 2 1 3 1 1 1 1 2 1 3 3 3 3 1 2 3 3 3 2 1 3 3 1 1 1 1 2 2 3 1 1 3 1 1 1 1 1 1 1 1 3 2 2 1 2 3 2 2 2 1 2 1 2 1 2 2 2 3 3 2 2 1 3.

156. By PICCOLA. (Fractional. - Nor is this very hard).

E D C Y B A Z C B Z A V W X C X B A E Y D C B V A E D W B X A E Y Z D A E Z V W D C A E D X C B Y D Y Z V C B W B A Z V E W X B X A E Y D C B V A E W D C X A E Y Z D C E Z V D W C B E D X C B Y A Z D C B V W A A E D C B A E E W D C B X Y D C Y Z B V A B A Z V E W X A E W D C X Y E D Y Z C B V E D C W B A X E D Z V C B A C B V W A X Y X B Y A E D Z E Y Z D V W C W E D X C B A D Y Z V C B A D C W B A X E E D C B A V E D C X Y B Z A E D C B A E W D Y Z C B V A B A Z V E W X E D V W C X Y X D C Y B A Z C Z B A V E W B A E W D X Y E D X Y C Z V V E D W C B A.