convenient enough for encipherment purposes, it is much less so for decipherment, and ordinarily there will be two separate tables, the second of these making it more convenient to find numbers. This deciphering key can be prepared as a list, running in numerical order; but a much more usual and convenient method is that of preparing it in the form of a chart; that is, the ten digits are written across the top and along one side of a 10 x 10 square, exactly as if making ready to take a number-count, and the letters, or other characters, are then distributed in the 100 cells so that the correct digits will serve as co-ordinates for pointing them out. Such a key is changeable, but not readily communicated and remembered without written documents; and to overcome this very serious defect, many mnemonic devices have been conceived, of which the following is perhaps the most practical: Simply treat the one hundred numbers as if they were a plaintext message, and encipher the series by any one of the irregular transposition processes.
The two commonest of the checkerboard keys are shown in Fig. 81. When digits are used, as in (a), an order must be observed in reading the two co-ordinates. The letter L, for instance, may have any one of the substitutes 13, 18, 63, or 68, but may not also have their reversals, since these, using the same order, row-column, would all be substitutes for G. Using letters, however, it is possible to have two
| Figure 81 (a) (b) 1 2 3 4 5 A C E G I 6 7 8 9 0 B D F H J 1-6 C U L P E K-L C U L P E 2-7 R A B D F M-N R A B D F 3-8 G H I J K O-P G H I J K 4-9 M N O Q S Q-R M N O Q S 5-0 T V W Y Z S-T T V W Y Z |
entirely different series at top and side, as in (b); in this case, no order need be observed, and the letter L may have any one of eight substitutes: KE, KF, LE, LF, EK, FK, EL, or FL. By including the still unused letters U V W X Y Z, it can be arranged to provide yet more substitutes for some of the letters. For either of these cases, the external numbers or letters (preferably in mixed order), could constitute a semi-fixed key — that is, one not changed every day — while the mixed alphabet of the square could be changed as often as desired. Innumerable other keys of this type are found. For the most part, they are based on rectangles of 35, 36, or 40 cells, the extra cells being used for digits, or other desired symbols, and especially for extra appearances of the more frequent letters.
One such key, the Grandpré cipher shown in Fig. 82, uses 100 cells. The filling of the square with ten ten-letter words provides letters in somewhat the normal frequency proportions, and an eleventh ten-letter word, composed of the ten initials, serves as a sort of mnemonic device for stringing the first ten together. The words, of course, must be chosen in such a way as to include all 26 of the letters.
General Sacco, dealing with fractional substitutions ([Chapter XXII]), shows the same idea in a checkerboard which he describes as “frequential.” This square is simply filled with letters, used in proportions roughly approximating their normal frequencies; for ready finding, all repetitions of a letter are placed close together, but filled in on diagonals, which, to some extent, will prevent their being represented by consecutive numbers.
| Figure 82 The GRANDPRÉ Cipher 1 2 3 4 5 6 7 8 9 0 1 E Q U A N I M I T Y 2 X Y L O P H O N E S 3 H A L F O P E N E D 4 U N B L O C K I N G 5 M O V A B I L I T Y 6 A D J U R A T I O N 7 T H E O R I Z I N G 8 I G N O R A N T L Y 9 O W N E R S H I P S 0 N O V I T I A T E S |
In Fig. 83, we have the checkerboard again, with a modification. If the key used is exactly the one of the figure, those letters which are standing on the first three rows may have twelve substitutes each, and those which are standing on the fourth row may have eight. In all of these cases, the substitute for any letter is a pair. But the final row, including here the letters V W X Y Z, is not enciphered with a pair of co-ordinates; each letter may represent itself, or each may represent the one on its left or right, but in any case, the substitute is a single letter. Thus we have cryptograms in which most of the letters are represented by pairs, but a few are not. Such words as ever, you, with, when, by, have, and so on, will occasionally occur; or, if not, then the encipherer may insert a few nulls at strategic points. Thus, the decryptor, taking his count purely on pairs, is expected to take some of them correctly and “straddle” the rest. Such a device is described by Givierge, also the following similar device. The cipher alphabet consists only of two-digit numbers, but includes no number coming from the 40’s. With all of the 40’s omitted, a sequence 44 becomes impossible; and the encipherer, having first prepared his cryptogram, looks it over, and, here and there, inserts a digit 4 beside another digit 4, producing the impossible sequence 44. The decipherer, wherever he sees this, need merely erase one of the 4’s, and since the digits,
| Figure 83 K L M N O F G H I J A-E-S A B C D E b a X t t a l i o n B-P-T F G H I K AG EF Y NR DI SK KU TI CN HQ C-Q-U L M N O P = D-R Q R S T U V W X Y Z |
in Morse, have their own distinctive symbols, there is no great danger of errors in transmission which the decipherer will be unable to straighten out; but the decryptor, as before, is expected to “straddle.” Concerning decryptment, in all of these cases, there is little that we can say here except that, given sufficient material, these ciphers can all be decrypted with comparatively little trouble.* [footnote: For a clear and detailed exposition of the decryptment method ordinarily used in multiple-substitute cases, see Secret and Urgent (Bobbs-Merrill), page 64 et seq. For dictionary cipher and simple codes, see The Solution of Codes and Ciphers, by Louis C. S. Mansfield (Maclehose), page 56 et seq., or Cryptography (Langie-Macbeth; Dutton), page 88 et seq.] The “straddling” devices, perhaps, would represent the most difficult case, presuming that the decryptor has no probable words and none of the information which comes through espionage or from that even more fertile source, the carelessness of the encipherer. In dealing with one of these, the decryptor, who normally expects a certain amount of uniformity in the frequency counts made from different portions of a same cryptogram, is likely to find that his count is showing altogether new substitutes, or the same substitutes with altogether new frequencies. He suspects, then, that he may be “straddling” between two pairs, and tries making his count in sections until he finally discovers what letters (or digit) are causing the trouble.