To explain its use: The decryptor here is dealing with a sheet of trigrams. Each one of these trigrams is to be deciphered as THE, AND, THA, and so on, following the list of normally frequent trigrams, and the resulting key-fragments are to be written down for comparison with one another, in the hope that some two or more will be duplicates, or will contain overlapping letters. The first of these cipher trigrams is HDG. These three cipher-letters, found on the three slides, are placed, in order, below A. Now, on the first of the slides, every possible decipherment for H is standing opposite its key-letter, found in the “decrypting alphabet”; on the second slide, every possible decipherment for D is standing opposite the the proper key-letter; and on the third slide, every possible decipherment for G. To know, then, what key-letters will be deciphered by THE, find T on the first slide and note key-letter O; find H on the second slide and note key-letter W; find E on the third slide and note key-letter C; the complete key-fragment is OWC. This may be written down, Then, without changing the adjustment of the device: For AND, key-fragment HQD, and so on down the list.
Where the cipher is Vigenère, the text-letters may be found in the “decrypting alphabet” and their keys on the slides, without changing results. But with either of the Beauforts, a key is specifically a key and not a text-letter. Thus, when the card is reversed, and the same process applied for one of the Beauforts, the student must be careful as to where he finds his letters T H E in each of the two ciphers. This peculiar relationship of Vigenère-variant-Beaufort is not hard to untangle if all three of the encipherments are considered to be purely mathematical operations of addition and subtraction. If we must add two numbers, as 5 and 10, it makes no difference whether we call it the sum of 5 plus 10 or the sum of 10 plus 5. But where we must perform a subtraction, there are two separate cases.
In straight Vigenère encipherment, the process is addition, in which text-letters may be considered to have the values 1 to 26 (their serial positions in the normal alphabet), while key-letters may be considered to have the values 0 to 25 (the amount of alphabetical shift represented by each one). Thus, the encipherment of J by P (10 plus 15) will not result differently from the encipherment of P by J (16 plus 9); in both cases, we obtain Y, alphabetical value 25.
In variant Beaufort, we have one of the subtractions: Message minus key, with the occasional necessity for “borrowing” 26 in order to make a subtraction possible. Thus, J enciphered by P (10 minus 15) does not give the same result as P enciphered by J (16 minus 9). In the first case (after borrowing 26), we obtain U, or 21, while in the other case we obtain G, or 7.
In the true Beaufort, we have the other subtraction: Key minus message. This time, we value the key-letters 1 to 26, and the text-letters 0 to 25. Thus, J enciphered by P (9 taken from 16) results in G, or 7, while P enciphered by J (16 taken from 9) results in U, or 21. Our results, then, are exactly the reverse of those obtained in the other subtraction.
If these mathematical comparisons be understood, or simply kept in mind, it will always be possible, whenever a decryptment process has been explained in connection with only one of the encipherments, to examine its “mathematical” details and learn from these in just what respects it would have to be modified in order that it may be applied with equal success to the other two encipherments. There is another interesting possibility which may have escaped the student’s notice. If he will turn back to Fig. 98, in which the same message, using the same key, was enciphered in both of the Beauforts, one encipherment coming out as K K Z B B I Z. . . . . and the other as Q Q B Z Z S B. . . . . , he will notice that these two cryptograms are complementary from beginning to end. If we saw any reason for doing so, we might convert either one of the Beaufort cryptograms to the other form, and apply its probable word with its own slide.
Now, having seen the great vulnerability of the famous “indecipherable cipher,” suppose we glance at some of the devices which have been used for doing away with its periodicity. One such device, that of auto-encipherment (autokey, autoclave), has been given its own separate [chapter] (the one immediately following), not because of its value as a cipher, but because of the very interesting decryptment problem it presents. A second device, the details of which may be examined in Fig. 115, consists in the use of a very long nonrepeating key, the popular name for which is “running key.” The value of such a key, for practical purposes, we have already seen; it was a key of this kind which Castle had used on his five or six cryptogram-beginnings. In single examples, however, it gives more trouble. Unless there is a probable word, its message and key must be dug out bit by bit, and if the encipherment is Vigenère, any recovered fragments can belong equally well to the
| Figure 115 Vigenère with a "Running Key" Key-letters: M Y C O U N T R Y T I S ... Plaintext letters: S E N D S U P P L I E S ... Cryptogram: E C P R M H I G J B M K ... |
message or to the key. However, with its key known to be purely plaintext, no fragments need be considered except those which are usable combinations, and since the “running key cipher” makes a fascinating puzzle, a specimen has been included among the practice cryptograms. The original of this, apparently, was the Hermann cipher. This employed a slide which was identical with the Saint-Cyr slide except that the stationary alphabet carried an extra cell (position) marked “index” to be used instead of the Saint-Cyr index A. As the writer saw this, the index-cell was standing just ahead of A, so that the resulting encipherment would have been that of a Saint-Cyr slide on which the letter Z was serving as index-letter.
Of other devices aimed at destroying periodicity, quite a few have been based in some way on key-interruption. A key-word is selected, as INDEPENDENCE, but the encipherer breaks off before completely using his rotation, so that the completed cryptogram will be enciphered very irregularly by such a key as INDEP INDEPEND I IN INDEPENDENC IND INDEPEN. . . . . . Sometimes this is found as a word-spacing device, the key beginning over with each new word, though naturally not with word-separations showing in the cryptograms. But in the average case, the key-interruption takes place at the discretion of the encipherer; sometimes the agreement with his correspondent allows him to break off as he pleases without any sort of signal, leaving the decipherer to discover the interruptions through the fact that he can no longer decipher; again, he may use an indicator, as J. In the latter case, he must encipher any J’s which may happen to occur in his message by using the I-substitute; then, whenever he decides to break the key, he first enciphers a J. Thus, whenever the decipherer brings out the letter J, he knows that his key is to begin over with the encipherment of the next letter. It will be noticed that in all of these cases, the decipherer will have to do his work one letter at a time.