| Figure 119 L C N D M E E L C N O Y G T B G X V N D G S S H W A W J Q E V L H O W Y I J W L E X A P V E C L B H D Q E K U W W G R H X J F B D Y P I P K Q D W A R G U W R L G N I Q S L V L E S P H E U T X B O N D H V X D C O U D S J T F J N U Q N Q L A A I L M Z U X I E W O B Y I W E H P D Q |
we may find some fairly good clue, leading us to give the first trial to the correct group-length; and again we are left, clueless, to try out five or six different group-lengths before striking the correct one. Results, then, are variable, and the only certainty, at any rate in a short cryptogram, is that of being able to limit the group-length to a given few. With the group-length determined, or with one selected for trial, we may take our choice of two processes.
Process 1 (Bassières). With group-length 7, as we have seen, our cryptogram includes seven independent series, or “columns,” of letters. By beginning at the 1st letter, and taking the 1st, 8th, 15th, 22d, etc., letters, we may decipher series 1 independently of the others; or, by beginning at the 2d letter, and taking the 2d, 9th, 16th, etc., letters, we may decipher series 2; and so with the other five series. Many persons, before doing this, will rewrite this cryptogram into seven columns, which permits that the decipherment of a series be done straight down its column, and for that reason the word “column” is sometimes used to describe what we have called here a “series.” In order to understand the first of the Bassières processes, we need consider only series 1, it being understood that whatever applies to any one of the seven series applies equally well to the other six.
| Figure 120(a) (b) Interval 8, found 8 times Possible Reason for L C N " 16, " 8 " " 4, " 6 " T H E o r e m/G E T t i.. " 5, " 6 " G E T t i n g T H E b a.. " 7, " 6 " Z L Y . . . . Z L Y . . |
Now, considering Fig. 121: If the unknown first key-letter was A, then the first plaintext letter, found by deciphering with key A, was L, and this became the key for enciphering the eighth letter. If the key which enciphered the eighth letter was L, then the eighth letter, found by deciphering with key L, was A, and this became the key for enciphering the fifteenth letter. Following out this decipherment to the end of series 1, we find that the plaintext letters must have been L A B R Z Z B, etc., as given in full in the figure. A glance at the complete series will show that this decipherment is not a particularly good one. If another decipherment be carried out, on the hypothesis that the original first key-letter was B, we obtain the series K B A S Y A A, etc., which starts out fairly well, but which, when completed, will contain two K’s, one Z, two B’s, and one P. If a third decipherment be carried out, on the hypothesis that the original first key-letter was C, we obtain the series J C Z T X B Z, etc., which is a poor decipherment from the beginning. A trial and error method might consist in making these decipherments one at a time directly on the cryptogram, erasing one when it is obviously poor, and trying to add the next series whenever one proves acceptable.
| Figure 121 Keys: A L A B L C N D M E K L C N O Y G T B G X V N D G S S H W A W J...... Plaintext: L A B R Series 1, (Key A): L A B R Z Z B G Q L F R B G H H C Y Z J. |
The Bassières process, however, consists in setting up the entire 26 possible decipherments as these are shown in Fig. 122. In this figure, the original cryptogram-letters of series 1 are standing in a column at the extreme left. The 26 possible decipherments are also standing in the form of columns, each decipherment headed by the key with which it was initiated. If the group-length 7 is correct, then one of these 26 columns shows the original plaintext letters.
Now let us examine, not the columns, but the rows, of this tableau, and find out just how troublesome it is going to be to prepare tableaux of the same kind for series 2, series 3, and possibly others. The key-letters, across the top, constitute a normal alphabet, and below this each row contains the 26 decipherments for some one letter of series 1. On the odd-numbered rows, the decipherments for the odd-numbered letters are alphabetically arranged, but progressing in a direction contrary to that of their keys, as if these odd letters represented Vigenère encipherment. On the even-numbered rows, the decipherments for the even-numbered letters are also alphabetically arranged, but are progressing parallel to their keys, as if these even-numbered letters might represent variant Beaufort encipherment. Evidently, then, the A-decipherment is the only one which must actually be carried out; afterward, the preparation of the tableau is a matter of extending alphabets. With similar tableaux prepared for the remaining six series, we have seven sheets, and on each one of these there is one column showing the correct decipherment of the series, headed by the correct key-letter. Thus, our solution is to be the mechanical one of the [preceding chapter]. On each one of the tableaux, the apparently “good” decipherments may be checked for attention; the sheets may be creased between columns, and the “good” decipherments of one tableau may be placed directly in contact with those of another.
| Figure 122 SERIES No. 1, Prepared as a Tableau. (Corresponds to SHEET No. 1 of Figure 112). THECIPHER The 26 Decipherments, with KeysLETTERS A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (Keys) L L K J I H G F E D C B A Z Y X W V U T S R Q P O N M L A B C D E F G H I J K L M N O P Q R S T U V W X Y Z B B A Z Y X W V U T S R Q P O N M L K J I H G F E D C S R S T U V W X Y Z A B C D E F G H I J K L M N O P Q Q Z Y X W V U T S R Q P O N M L K J I H G F E D C B A Y Z A B C D E F G H I J K L M N O P Q R S T U V W X Y A B A Z Y X W V U T S R Q P O N M L K J I H G F E D C H G H I J K L M N O P Q R S T U V W X Y Z A B C D E F W Q P O N M L K J I H G F E D C B A Z Y X W V U T S R B L M N O P Q R S T U V W X Y Z A B C D E F G H I J K Q F E D C B A Z Y X W V U T S R Q P O N M L K J I H G W R S T U V W X Y Z A B C D E F G H I J K L M N O P Q S B A Z Y X W V U T S R Q P O N M L K J I H G F E D C H G H I J K L M N O P Q R S T U V W X Y Z A B C D E F N H G F E D C B A Z Y X W V U T S R Q P O N M L K J I O H I J K L M N O P Q R S T U V W X Y Z A B C D E F G J C B A Z Y X W V U T S R Q P O N M L K J I H G F E D A Y Z A B C D E F G H I J K L M N O P Q R S T U V W X X Z Y X W V U T S R Q P O N M L K J I H G F E D C B A I J K L M N O P Q R S T U V W X Y Z A B C D E F G H I |
Process 2 (Bassières). Fig. 123 shows the second of the Bassières processes. With 7 decided upon as the group-length, we make up a trial key having the right number of A’s, and decipher the cryptogram. The new cryptogram, produced in this way, is periodic, and its period, for Vigenère, will be twice the group-length, in the present case 14. In Fig. 124, where this new cryptogram has been repeated, written into its period, it is possible to check its periodicity: It has two repeated sequences, C J B and W G, at suitable intervals, and while these are very few, their evidence is amply supported by the fact of repeated single letters in every column. When the periodicity is not confirmed in this way, it can be assumed that the chosen group-length was not correct.