| Figure 116 Vigenère Autokey: C O M E T/S E N D S U P P L I E S T O M O R L E Y S Plaintext: S E N D S U P P L I E S T O M O R L E Y S S T A T I CRYPTOGRAM: U S Z H L M T C O A Y H I Z U S J E S K G J E E R A |
referred to as “period,” includes five individual series of letters, any one of which can be enciphered and deciphered independently of the rest. That is, beginning with C, or O, or M, or E, or T, and taking each fifth letter, it is possible to proceed straight through to the end, enciphering or deciphering only this one series, or “column.” It will be noticed from the foregoing that the decipherer gets the short end of the bargain. The encipherer knows in advance what the key is, and, to some extent, can apply one cipher alphabet at a time; the decipherer knows only the key to the first group; the rest he must ferret out for himself.
There is, however, a second form of autokey encipherment in which the respective difficulties of encipherer and decipherer would be reversed. This form of auto-encipherment, which can be seen in Fig. 117, makes use of a preliminary key, as in the regular form, but follows this with the enciphered text instead of with the plaintext. Such an encipherment results, occasionally, from the mechanical construction of a cipher machine, and in this case, where the 26 cipher alphabets are in mixed order, and unknown to the decryptor, may present an interesting decryptment problem. But where the cipher is Vigenère (or any other in which the decryptor possesses the full set of cipher alphabets), it can hardly be argued that there is any great problem about a cryptogram which carries its key in full view. We will confine ourselves, then, to the usual form of autokey, as first explained, beginning our studies with a brief glance at the two common practical cases, that of accumulated cryptograms, and that of probable words. Procedure, in the former case, is self-evident. Possessing several cryptograms all initiated with the same preliminary key, we may write their beginnings one below another to form columns, and the first few of these columns will constitute an ordinary case of Vigenère in which every message is known to be the beginning of a sentence. With beginnings discovered, a little industry accomplishes the rest.
The case of probable words, on the other hand, presents some interesting possibilities inherent in the auto-encipherment itself. When the probable word is short (or if a search is to be made for normally frequent trigrams), the task of bringing out and testing the possible key-fragments is made much less onerous by the fact of the purely plaintext key. Being sure of an abundance of excellent sequences, we need consider none but the very best of the deciphered fragments; and for any one considered, the trials need be made only within a very short range of the spot at which it was found. All of this work may be done directly on the cryptogram. A correct sequence, correctly applied, can be followed out in both directions, and will yield, in full, several of the “columns,” and several consecutive letters of the initial key. But if it so happens that the probable word is longer than the initial key, its first few letters must become the keys for enciphering its last few. Consider, for instance, the word SIMPLICITY, which has a length of ten letters. If the preliminary key contains only five letters, then, beginning at -ICITY, the keys SIMPL- will begin to encipher, causing a certain long cryptogram-sequence which, for Vigenère, will always be A K U I J. If the preliminary key has
| Figure 117 Key: C O M E T/ U S Z H L O H O S T ..... S E N D S U P P L I E S T O M ..... U S Z H L O H O S T ..... Note that the cryptogram itself is the key, except that the first five letters are missing. To decrypt, With any alphabet, need merely find where to begin using it! |
six letters, the same word causes a sequence U Q F N when the cipher is Vigenère; if it has seven letters, the cryptogram-sequence will be A B K; and even an eight-letter key brings out one certain digram, L G. Thus, knowing what the cipher is, and having at our disposal any comparatively long probable words, we may write out these sequences in advance and be ready to look for them in the cryptograms. In addition to whatever words we consider probable, it is obvious that any other long word may encipher itself in the same way, and, if it is one important to the subject matter, is likely to be repeated, causing the cryptogram to show a long repeated sequence. Thus, if we find a long repeated sequence in a cryptogram, we are able to try this as a common suffix, TION, MENT, ENCE, ABLE, etc., in the expectation of bringing out some common prefix, CON, PRE, etc.
More fascinating, by far, than its practical aspects, however, are the possibilities presented by the autokeyed cryptogram for analytical attack. The devices immediately to follow are described by General Givierge in his Cours de cryptographie, and are credited by him to Commandant Bassières.
First, it is possible to discover the length of the short preliminary key, or, at any rate, to confine this to certain definite probabilities. This key, as we have seen, governs a definite group-length, or “period.” If this group-length, say, is 5, then, barring the first and final groups, every plaintext letter will be enciphered by the letter standing five positions to its left, and will, in its own turn, serve to encipher the one standing five positions to its right. Since all plaintexts are filled with repeated letters, roughly half of them separated by even intervals, it stands to reason that there will be many occasions on which the letter standing five positions to the left and the one standing five positions to the right will be the same letter. That is, we must often find the encipherment pattern of Fig. 118. Some one letter, as S, is repeated at an interval of exactly twice the group-length, with some other letter, as R, standing at exactly the group-length interval from both of the S’s. The first S enciphers R, and R enciphers the second S. Or, if the repeated letter is T and the intermediate one is L, then T enciphers L, and L afterward enciphers T. Where the cipher is Vigenère, the result, in the cryptogram, is a repeated letter standing at exactly the group-length interval. If the cipher is one of the Beauforts, the same pattern produces a pair of complementary letters separated by exactly the group-length interval.
| Figure 118 S . . . . R T . . . . L S . . . R . . . . S T . . . . L . . . . T J . . . . J E . . . . E |
Now, in order to consider the value of this observation, let us examine the cryptogram of Fig. 119, an autokeyed Vigenère, which, for convenience, is presented in groups of the correct length, 7. According to Bassières, should we inspect this cryptogram for repeated single letters, noting, in each case, the interval of separation, the correct group-length, 7, will be present among those intervals which are noted oftenest, and, in many cases, will be the one which predominates. For making such an examination, perhaps the simplest plan would be that of listing the possible group-lengths at the tops of a series of columns, beginning with group-length 1 and carrying them as far as desired. The counts could then be made by placing a tally mark in the proper column for each time that a given interval is noted. The results of this examination, as compared with the Kasiski examination for a period, may be studied in Fig. 120. At (a), where the leading intervals of our cryptogram have been listed with their frequencies, it is noticeable that the correct group-length, 7, is not represented by the predominating interval or even by the one which is second in frequency; it is merely present among the five leaders. But we find other cryptograms, not necessarily of great length, in which some one letter, as V, will be repeated five or six times in succession at exactly the group-length interval, and its evidence amply confirmed in other repetitions. Then, as at (b),