| Figure 154 Forms of Key-Progression Keys: A B C D E F G... A C E G I K M... A Z Y X W V U... S E N D... S E N D... S E N D... S F P G... S G R J... S D L A... This type of key-progression can be decrypted by "running down the alphabet," and watching the diagonals for plaintext. |
logically, would be applied with a cipher disk. The initial key, as A of the examples, would indicate the starting position of the revolving disk, the first letter being enciphered with the disk in this initial position, after which the disk is made to revolve, so many angles at a time, without further reference to key-letters. For this kind of cryptogram, the solution is purely mechanical. A series of alphabets may be extended, with each cryptogram letter as a beginning, and the message can be found following a diagonal path in the resulting set-up.
A much commoner scheme, when using a cipher disk, is that of following a series of irregular shifts in accordance with a numerical key. If, for instance, the initial
| Figure 155 Progressing Key: C U L P E P E R D V M Q F Q F S E W N R ... Plaintext: T H E R E I S O T H E R C A U S E F O R ... Partial Encipherment: V B P G . . . . W C Q H . . . . . . . I ... |
position has been established and the first letter enciphered in that position, and if the numerical key is 3-5-2-1-6, the disk will now be revolved 3 positions for encipherment of the second letter, 5 positions for encipherment of the third letter, 2 positions for encipherment of the fourth letter, and so on, so that the disk must move 17 positions during encipherment of five letters. This can produce a very long period indeed, especially when the collective shifts result in an odd number.
Substantially the same encipherment as the foregoing can be had with a slide and a key-word, as indicated in Fig. 155. The progression index, in this figure, is 1. The preliminary key-word, CULPEPER, enciphers the first eight letters, then moves forward in the alphabet and becomes D V M Q F Q F S for the encipherment of the next eight, E W N R G R G T for the encipherment of the third eight, and so on. In its practical application, one column could be taken at a time. Notice, however, in Fig. 156, that when a key-letter progresses in the alphabet, the possible substitutes for any one letter will also progress, and to exactly the same extent. If the encipherment is Vigenère or Beaufort proper, this progression is in the same alphabetical direction as that of key-letters, while the variant encipherment causes the substitutes to progress in the contrary direction. Probably, then, the
| Figure 156 Vigenère and Beaufort Progression Variant Progression Progressing Key: A B C D E..... Progressing Key: A B C D E..... Plaintext letter: H H H H H..... Plaintext Letter: H H H H H..... Cipher letter (V) H I J K L.....(B) T U V W X..... Cipher letter: H G F E D..... |
most convenient method of application, and the one least likely to result in errors, would be that of Fig. 157. The cryptogram is first enciphered as an ordinary periodic, and the progression is added later, using group-by-group encipherment. Thus, as we receive the cryptogram, our repeated ther has been enciphered once as V B P G, again as W C Q H, and possibly, later on, as A G U L, and the only period we shall be able to find, using the regular methods, will be 26 x 8, or, if the progression index is an even number, 13 x 8. But notice, in the same figure, comparisons (a) and (b).
Vigenère, it will be remembered, has been compared to the mathematical process of addition. If the key-digram CU be added to the plaintext digram TH, their sum is the cipher-digram VB. The alphabetical distance from C to U is 18, the alphabetical distance TH is 14, and the alphabetical distance VB is 6 or could be 26 plus 6, 52 plus 6, and so on. It is a fact that when we “add” the two digrams CU and TH, we actually do add their separating intervals, 18 and 14, since we obtain a sum 32 in that of the cipher digram VB. It is also an easily verified fact that the same reasoning applies to the subtractions of the two Beauforts. The student who cares to investigate may make use of the tableau shown as Fig. 158; to find quickly the distance from one letter to another, find the first of these at the left, the second at the top, and the alphabetical interval between the two is shown in the cell of intersection. If it is desired to know the reverse interval, find the first letter at the top and the second at the side. Now notice, carefully, that when any digram progresses in the alphabet, as CU would become DV, EW, FX, and so on, in a series of periods, it does not change its alphabetical interval; in all of these digrams, the distance apart of the two component letters is still 18. Thus, while our period vanishes, the alphabetical intervals which represent it are still present in the cryptogram; we have only to find these intervals, subject them to a Kasiski examination, and convert the cryptogram to an ordinary Vigenère.
Fig. 159 shows the preparation of the cryptogram: The alphabetical interval