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
| 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. |
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.
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,