more different progressions of 6, and the new columns, throughout some portion of their length, will differ from one another by exactly 6, the original key-length.
We have seen, then, the general case in which the “enemy” decryptor, having several cryptograms of the same length, enciphered with the same key, is able to use a purely mechanical method in order to restore the plaintext, and afterward, by observing traces of a known cipher, to extract their key. For the solution of single cryptograms enciphered in complicated systems, the writer knows of no other method than straight anagramming, in which the single letters, accompanied by their serial numbers, are written on individual cardboard squares (or imagined to be so), and the attempt made to match them up. Attention has already been called to some possibilities which may lie in the serial numbers whenever the sequences or probable words are thought to be correctly matched. But with absolutely nothing known or suspected as to source or subject matter, and with nothing discoverable from serial numbers or possible routes (and taking it for granted that any accumulation of letters represented in about the normal frequency-proportions can be made to yield dozens of different solutions), it would hardly seem that the decryptor, even should he find the correct solution, would have a means of distinguishing it from any other.
For the student who may care to struggle with a case of single anagramming, we have appended a problem in Fig. 57, together with a means for finding out the solution
| Figure 57 A Single Cryptogram in Double Columnar Transposition: L H D L A O D D H L H E E U I X D F P I U T A E R O I T Q A E T E R L N I E N A U D K L I E E H Y N M S J L C N H P B O A D G R N. The Solution, Enciphered by a Method Mentioned in [Chapter III]: M T Q P I N A I E N E I T H R G E K D U U D L L I R I H F R T E C L O L N J L A S H A A U Y D O E E L N E N D H P D H D E A B O. |
and perhaps even the key-word. It has come from the Philadelphia headquarters of a band of revolutionists, and our stool-pigeon tells us that the leaders of this movement are to be called together for consultation during the coming summer.
The finding of a key-word, after recovery of the numerical key, is not, of course, necessary to the decipherment of further cryptograms. However, this recovery will afford us the same convenience which it gave to the encipherer; that is, a simple mnemonic device for reproducing the numbers at will. And to recover the actual original key-word may, at times, provide some insight into the habits or mental make-up of the person who selected it, and who may select others like it, or might, conceivably, make use of this same key-word in some other kind of encipherment. If the key is short, it is practically always possible to recover more than one word; but with long keys, we seldom, if ever, recover more than the one word on which the numbers were actually based. In this connection, however, it must be remembered that key-words are not necessarily taken from any one language; thus, their recovery becomes largely a matter of combined information, intuition, guesses, trials, and determination, so that an exact method for accomplishing it is hard to give. But, presuming that key-numbers have been derived in the usual way, those which are small are, in general, likely to have derived from the earlier portion of the alphabet, which contains A, E, I. So long as they increase toward the right, they may continue to represent a same letter, and when they do, this letter is usually a vowel, When an increase occurs on the left, the new number has certainly derived from a new letter, coming later in the alphabet. Whatever the language, then, it is very easy to determine the two extreme alphabetical limits outside of which no one of the letters can possibly be found.
This can be seen at (a) of Fig. 58. The numbers 1, 2, 3, might all have derived from A, but the number 4 cannot have derived from a letter coming earlier in the alphabet than B. Similarly, the numbers 4, 5, might, by possibility alone, have derived from B; the numbers 6, 7, 8, might all have derived from C, the numbers 9, 10, from D, and, finally, the number 11, from no letter earlier than E. When these earliest possible limits have been established for every key-number, and it is seen that the range is five letters, then the last five letters of the alphabet, V, W, X, Y, Z, may be used to establish the limits at the other end of the alphabet. It is seen now, that the key-number 6, must have derived from some letter between C and X, inclusive, and similarly with the others. But when we come to the particular case, it becomes necessary to make assumptions; for instance, were these numbers derived from a common English word or from a Russian proper name? The person who selected it, so far as we know, is accustomed to speaking English, and in all of his past cryptograms we have been able to recover common English words rather than proper names. Assuming, then, as at (b) of the same figure, that we are to
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Figure 58 (a) Limits: (b) Assumption of English word: 6 9 1 4 11 7 10 2 3 8 5 6 9 1 4 11 7 10 2 3 8 5 C D A B E C D A A C B A A B L E X Y V W Z X Y V V X W (FL (MY A C (NZ (FL (MY A B L E D E (New limits) |
recover his usual common English word, we set down A as a possible letter for the key-numbers 1 and 2. But when we arrive at the number 3, we see that we cannot assign here a third A, since common English words of this length do not contain a doubled A. The earliest letter possible, then, is B, and, upon noting the consecutive letters AB at this particular point, we think at once of the common English terminal sequence -ABLE.
To find whether this is possible, we make sure that the new letters, L E, alphabetically considered, do not run contrary to their supposed numbers, 8 5. Then, having accepted these four letters as entirely possible and likely, we work back to the missing number, 4, and find, now, that it has new limits; it must have derived from E, D, or C, and from nothing else, and of these, we are inclined to discard E, which would give a sequence AE. We then work back to other missing numbers, 6 and 7, and find that these, too, have acquired new limits; they must be found somewhere between F and L, inclusive. All numbers which follow 8 have attained a new limit in the earlier portion of the alphabet, but not in the latter portion. These are all shown in (b). At this point, any knowledge at all of English prefixes will suggest what the first two letters are and will narrow the limits still further. The student, perhaps, has already guessed the word.