The other drawback is the danger which lies in the fact of so very many cryptograms. These, originating at many different sources, and all enciphered with the same key, will invariably include many of identically the same length. The nature of transposition cipher makes it inevitable that when any two texts of exactly the same length are enciphered with the same key, they will follow exactly the same route. The first letter in both messages will be transferred to exactly the same serial position in both cryptograms; the second letter in both will be transferred to another same serial position, and so on. If we are able to match correctly any two or three letters in one of the cryptograms, the two or three corresponding letters of the other cryptogram will also be correctly matched and will serve as a check. This being the case, any two or more cryptograms which are found to have the same length can be written one below another so as to place corresponding letters in the form of columns, and the problem is reduced to one of geometric columnar transposition.
With ciphers of the complete-unit type, the same thing can be done having several of the major units. We have, say, a single cryptogram accomplished with a Fleissner grille, and taken off by spirals. It may be that nulls were added in the final group, or at the beginning, or the final unit may have been left incomplete (by blanking out the unwanted portion of the final grille-block). In spite of these possibilities, the unit-length, known to be a square based on an even number, can be determined — or assumed — and the placing of the several units one below another provides columns made up of corresponding letters. It is even possible, at times, to apply this process, with suitable modifications, to several cryptograms whose length is only approximately the same. It has been done, for instance, with cryptograms from Sacco’s indefinite grille, mentioned in [Chapter III] (General Sacco himself has explained the modifications). Such a process is ordinarily referred to as multiple anagramming, and we have already seen, in the case of the grille, how it may be modified so as to take full advantage of any inherent weaknesses when the cipher is known.
For discussion of the general case, suppose that we have intercepted a number of cryptograms (seen, by their letter-frequencies, to be transpositions), and that among these we have been able to find five in which the length is 25 letters. Since all of these have been coming from the same two stations, and within a comparatively short period of time, it seems reasonable to suppose that at least a portion of them have been enciphered with the same key, and, upon this assumption, we have written the five cryptograms one below another so as to set up the 25 columns shown in Fig. 50. We wish now to rearrange the 25 columns in such a way as to bring out plaintext on every row, or, failing that, on some of the rows. Once the set-up has been prepared, we may arrive at our goal by any road that suits our fancy. The majority of solvers will simply cut the columns apart and start matching strips at random; and this, probably, is a good enough method, especially when columns are so short. The writer, personally, prefers to leave the set-up intact, at any rate until solution is well started, trying out in pencil the various possible column-combinations, and circling out accepted columns from the set-up in the same way in which segments were circled out of cryptograms in the [preceding chapter].
| Figure 50 A series of five cryptograms prepared as columns: 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 C D D N C A A R T H L O I K A O E R T L S N A N O D A I T E L O C W A I U X D N T Y M I N M O E Y O B T O A T T U T O C F L I Y K X N E I O S B F Y Y T A R O T O R E I L N A O H R I O N M D S R J Y S W E K L N C H T S T S I E G E I H O O P D T N A O |
For those who like this method, we repeat a suggestion which has already been made: Many columns are usually present in such a set-up which contain more than one of the “clue-letters,” as here, for instance, column 14 is practically made up of them. Such a column makes a good point of beginning, since we may search the set-up, not for some single letter, but for a pattern made up of several. For column 14, specifically, we might examine the top row of letters, pausing whenever we come to one of those letters frequently preceding K, and examining the rest of its column to find out what letter would have to precede H on the fourth row. We may fail with the first such column, but not with all.
Another particularly good method, and one which might work in the present case in spite of the very brief columns, is that of finding the particular column which contains the first letters of all the messages. Well over half of the initials used in the language will be found in the group T A O S W C I H B D, and with a frequency in somewhat that order. Any column made up entirely of these particular letters may be the one which begins the messages; and when this can be found, it pays to remember that a vowel is practically always present among the first three letters of each message.
As to finding the end-segment, it seems that this would be of little value except in those cases where final groups are not completed. However, the letter E has a great fondness for final positions, with terminals restricted largely to the group E S T D N R Y O; and it is also true that many encipherers make a habit of completing their final groups with such letters as X and Q.
Aside from the general case, each individual case carries clues of its own, and the finding of these must depend upon the detective ability (or experience) of the decryptor. Here, for instance, we find that the letter K has appeared three times in only 125 letters of text. This letter, normally, has one of the lowest frequencies in the language, and often is not found at all in 125 letters of text. Finding it three times, then, rather suggests the presence of some one word, a word so important to the subject-matter that it has been used in three different messages.
When considering the letter K, the first combination which comes to mind is a digram CK preceded by a vowel; and the letter C, also, is not a letter which we expect to find in confusing numbers. When an examination of the set-up shows that, for each of the K’s, there is a C present on the same row, we are inclined to accept the hypothesis of a repeated word. In practice, we should pick out the three columns containing K, place beside each one a column which will set the digram CK together, and build on all three combinations simultaneously to the point at which the supposed word appears or is proved non-existent. Following out only one of these, let us consider column 14, where K is on the top row. On this row we find that C has appeared twice. Both of the C’s are tried with K, as shown in Fig. 51; we find that both combinations will provide acceptable digrams, but there is little doubt as to which we would select. Combination 1-14 is merely acceptable, while combination 5-14 provides a very accurate description of the column which would fit best on its left. There should be a vowel on the top row, to precede CK, and another on the bottom row, to precede NG. After that, perhaps another vowel should be found on the fourth row, to precede TH, or perhaps, in this case, an S, since the list of frequent trigrams includes a sequence STH; and, finally, something suitable to precede TY, which appears to be a syllable, but may belong to two different words. The five columns which will meet these requirements have been
| Figure 51 1-14 5-14 C K C K D D E D B Y T Y T H T H W G N G |