Now let us consider a concrete example of decryptment. The (purely imaginary) history of the cryptogram shown as Fig. 14 is meager. It was taken from the body of an unnamed man, killed in attempting to dynamite a bridge in an American town called Baysport.
To begin with, the cipher appears to be transposition. Its cryptogram shows 37½% of vowels, very close to the number expected of English or German. It is
| Figure 14 I Y W B B O R T A F T I X D G S S E G H N A T O O I T O X T L U T R E L X F A Y S D R C H T O M E D E I O V I K F T V T L A E U. |
too short to provide any reliable distinction between these two languages, but the source of the cryptogram points to English. Again, the encipherer, although he has grouped his message in the usual fives, has neglected to complete his final group with a null, and from this we judge that 64 letters is the actual length of the message. The fact that 64 is a square is promptly noticed. But it is also the sum of several smaller squares, and the unit might be 16. To investigate this possibility, we may mark the cryptogram off into four equal segments of 16 letters each, and count the vowels per segment. The normal number of vowels in a 16-letter segment should be about 6, and segments of this length are long enough to afford reliable information, so that we may promptly discard the possible unit 16 when we find that the first segment shows 5 vowels (31%), the second, 7 vowels (44%), and the remaining two, respectively, 4 and 8. Such a distribution does not prove that the unit 16 is a total impossibility, because many things are not average in single examples, but it is an extremely bad one and would never be accepted. On the other hand, a satisfactory distribution does not prove absolutely that a given unit-length, or block arrangement, is correct. Here, had there been no question of the ever-present square, we might have been led astray by the unit 32, which divides the vowels of the present cryptogram into two equal halves. In this connection, we can only say that the decryptment of any cipher, even the simplest, will at times include a number of wanderings which we shall have to overlook in demonstrating principles.
Assuming, then, that the large unit, 64, is correct, we must get it back into its block — presumably square — in the encipherer’s original arrangement. Fig. 15 shows the same cryptogram written into two different blocks. For an 8-letter unit, the normal number of vowels is about 3 (actually 3.2). In block (a), a count taken on the horizontal lines shows half of the units normal, two of the others with the smallest possible variation, and two greatly outside the 35%-45% limits. When the unit is so short, and when the line containing only one vowel may be the one which was completed with nulls, and most particularly when we have no other units to act as a check, we cannot confidently discard a block of this kind. In practice, we might waste some time giving it a trial, or we might look for something better. Notice that its distribution is “ragged.” We expected to find even distribution, with more than half of the units exactly normal. This block (a) is the simple horizontal arrangement. To find out what the simple vertical arrangement would give us, we have only to examine the columns of this. Here the count is obviously bad.
In block (b), we have one of the diagonal rearrangements from which two sets of vowel counts can also be taken. Here, the horizontal lines have given us exactly what we hoped for: Evenness of distribution, more than half of the units normal, and only one unit outside of limits. This, almost surely, is the encipherer’s original block, in which every line contains one intact unit.
From our meager history of the case, we do not, of course, know that this is specifically the Nihilist cipher. It becomes a case of considering the various ciphers
| Figure 15 (a) Horizontal Rearrangement, (b) Diagonal Rearrangement, With TWO Vowel-Counts With TWO Vowel-Counts I Y W B B O R T 3 I W O F G N O L 3 A F T I X D G S 2 Y B A D H T E R 3 S E G H N A T O 3 B T X G I R D E 2 O I T O X T L U 4 R I E O T S M V 3 T R E L X F A Y 3 T S O U Y O O T 5 S D R C H T O M 1 S T L A T I F L 2 E D E I O V I K 5 A T F H E K T E 3 F T V T L A E U 3 X X C D I V A U 3 4 3 2 3 1 3 4 4 3 1 4 3 4 2 4 3 |
with which we happen to be acquainted, and a columnar transposition of the general kind shown in Fig. 11 is an exceedingly common case. Moreover, a series of juggled columns is suggested here in the fact that intact units are standing on their own lines and still have not resulted in plaintext.
In Fig. 16, we have the successive steps which would be taken in order to investigate this probability. At (a), the diagonal rearrangement of our cryptogram, selected as the most likely of those which were examined, has been repeated with its eight columns set wide apart, and consecutively numbered for identification. These presumed columns are now cut apart, and thus we have eight paper strips which can be moved about and rearranged in various manners in the hope of causing words to form on some of the lines.