| Figure 126 Where the KEY is a Segment of Ordinary PLAINTEXT: Estimated Rank of the Cryptogram Letters and Their Frequencies Per 10,000 Figured by C. Stanley Lamb From Table of Ohaver. VIGENÈRE V A I S ERL WHB XGM FOZ K N T P U J Y C Q D 344 314 304 296 (Intermediate) 150 112 84 84 84 72 72 64 49 -- BEAUFORT & VARIANT A N E W O M Z BQK JRT HVF GUDX P L S I Y C 480 262 246 246 196 196 191 (Intermediate) 121 121 104 104 57 57 PORTA K N L E RMF TWP UYQ XGC AVI BJZ D H O S 329 300 282 275 (Intermediate) 132 113 97 -- |
deal. As these are shown, the alphabet across the top of any table is a list of possible cryptogram-letters, each cryptogram-letter heading its own column; and each column contains only those letters which are themselves members of the high-frequency group E T A O N I R S H, and which, if enciphered by another letter from the same group, would result in the cryptogram-letter standing at the top of the column. The key, in each case, can be found at the left. Hurst says that he always attacks a cryptogram at the second letter, on the theory that this particular letter is likely to have been a frequent one in both the message and the key. He then attempts to follow out series 2, or, if the group-length has not previously been determined, to find this series. To explain, without going into too much detail, the second letter in our foregoing autokeyed Vigenère was C. A glance at the table for Vigenère shows that this letter can result from only one pair of high-frequency co-efficients, O enciphered by O. Hurst will make his first trial on series 2, beginning with initial key-letter O, and come out with the correct decipherment at his very first attempt! With other letters, as V or A, it might be necessary to make as many as six trials, but, as we have seen, it is hardly ever necessary to carry a trial very far in order to see that the decipherment is going to be a poor one. The second letter, of course, will not necessarily give results; but the cryptogram, remember, is filled with these vulnerable letters, and a decipherment may be started with any letter whatever and carried out in both directions.
Another method, originated by C. Stanley Lamb, differs from Hurst’s chiefly in that his observations were made from digrams and not from single letters. Originally, Lamb had been collaborating with Admiral Snow in establishing frequency counts for various kinds of ciphers, so that when the system was unknown, it would be possible to tell one from another. Fig. 126, for instance, gives a rough estimate as to what the rank and frequency should be for each letter in the kind of cipher we have under consideration. Finding a reasonably long cryptogram in which the
| Figure 127 (a) Preparation of the mixed alphabet............ C U L P E • • R A B D F G H I J K M N O Q S T V W X Y Z C A K W U B M X L D N Y P F O Z E G Q H S I T R J V 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 (b) ENCIPHERMENT - Auxiliary Key X, or 8: Plaintext: S E N D S U P P L I E S T O M O R FIRST Substitution: 21 17 11 10 21 5 13 13 9 22 17 21 23 15 7 15 24 AUTOKEY (Addition): 8 21 17 11 10 21 5 13 13 9 22 17 21 23 15 7 15C R Y P T O G R A M... 29-38-28-21-31-26-18-26-22-31-39-38-44-38-22-22-39- ════════ ══════════════ L E Y T O M O P R O W S T O P 9 17 12 23 15 7 15 24 24 15 4 21 23 15 13 24 9 17 12 23 15 7 15 24 24 15 4 21 23 15 33-26-29-35-38-22-22-39-48-39-19-25-44-38-28. ══════════════ ════════ xxxxxxxxxxx xxxxx (c) Detail of DECIPHERENT: Cryptogram Numbers: 29 38 28 21 31 26 18 26 ... AUTOKEY (Subtraction): 8 21 17 11 10 21 5 13 ... PRIMARY CRYPTOGRAM...... 21 17 11 10 21 5 13 13 ... Re-Substitution......... S E N D S U P P ... (d) Vigenère Autokey - What Happens to REPEATED SEQUENCES with a ONE-LETTER KEY: Key... X/ T H E M O N T H E X T Text... T H E M O N T H E X T E A L A L |
letters D and Q have ranked among the last, with letters V, A, I, and S ranking among the first, we have a fairly good reason for suspecting that the encipherment was accomplished with a very long Vigenère plaintext key.
But for short cryptograms, Lamb did not find these characteristic frequency counts half so convincing as the presence in a cryptogram of certain digrams, which appeared to be characteristic for each cipher, since he was always able to find from 7 to 10 of them in each 100 letters. By making use of the high-frequency digrams (th, he, er, in, an, and so on), he then established lists of cipher digrams which were very characteristic indeed for each type of encipherment. Thus, in attacking an autokey, it is possible to make a good beginning with such a digram as VV (er-re) or XK (th-ed), if the cipher is Vigenère, and work in both directions.
“Key-Length 1.” — Many writers are inclined to make a special case of the autokey in which the “priming” is done with a single letter, not that this actually constitutes a different cipher, but because of the decryptment curiosities which can be brought to light in connection with it. For instance: Having a cryptogram fragment . . . . . . .W S Y Q L A H T G B. . . . . known to be Vigenère autokey, initiated with a single letter, can you find instantly the trigrams SAY and HAT? Would you have any reason for trying the word WAS? Of the many interesting observations which have come the writer’s way with reference to the one-letter initial key, only one has seemed to present the germ of an additional decryptment method. This observation was one made by Ohaver in connection with a cipher in which the substitutes were numbers. The cipher itself can be examined in Fig. 127.
The first step, (a), consists in the preparation of a simple substitution key in which the plaintext alphabet is in mixed order and the cipher alphabet is made up of the numbers 1 to 26. The encipherment, shown at (b), involves two steps. First, there must be a simple substitution, using the key of (a), and this results in a primary cryptogram. Afterward, this primary cryptogram, preceded by an
| Figure 128 A TRIAL-Decipherment (M. E. OHAVER) The Cryptogram: 29 38 28 21 31 26 18 26 22 31 39 38 44 38 22 22 39 9 20 18 10 11 20 6 12 14 8 23 16 22 22 16 6 16 20 18 10 11 20 6 12 14 8 23 16 22 22 16 6 16 23 ════════ 33 26 29 35 38 22 22 39 48 39 19 25 44 38 28 23 10 16 13 22 16 6 16 23 25 14 5 20 24 14 1O 16 13 22 16 6 16 23 25 14 5 20 24 14 14 ════════ |
initial key-number, is added to itself. In the discussion to follow, our objective will be that of recovering the primary cryptogram (and not the plaintext, which would have to be found later by simple substitution methods). Decipherment, indicated at (c), consists in reversing the two steps of the encipherment: A series of subtractions restores the primary cryptogram, and is followed by the resubstitution of letters. At (d) we have a Vigenère fragment for comparison. The essential fact to be noticed in (d) is the behavior of repeated sequences when the group-length is 1. Any repeated sequence in the plaintext continues to show a repetition in the cryptogram which is shorter by one letter than the original. Even the repeated digrams will give repeated single letters.