This form of transposition is among the most fascinating of decryptment problems, and we shall look at it from several angles. The simplest case is that in which the decryptor correctly assumes the presence in his cryptogram of some word or phrase whose length is greater than that of the key; if this probable word is long enough, he is able to learn, not only the key-length, but the order in which to write his columns. Our present cryptogram, for instance, has key-length 8, and contains
| Figure 30 The Cryptogram Prepared for Examination 5 10 15 20 25 30 E N T H V C C O T X R E M U S O E U Y E I S G A U A M A H Y 35 40 45 50 55 60 T A E I D E X T N B H B N S E I R A S T D A N V N X G G E O 65 70 75 I C R L B X C S U T L T E S R |
two nine-letter words, ADVISABLE and INCREASED. These two words, repeated in Fig. 31, will show what happens when a word is long enough to overlap the block. With the word ADVISABLE, the final E falls below the initial A, and when this column is taken off, the letters A E will stand in sequence in the cryptogram. Similarly, the word INCREASED will provide, in the cryptogram, a digram ID. Should the decryptor suspect the presence of either of these words, he would look at once for sequences of this kind in his cryptogram, and the presence of AE (or ID) would tell him that the key-length is probably 8, which is the distance apart of the two letters in his probable word.
| Figure 31 6 1 7 2 3 5 8 4 . . . . . . . . . . . . . . . A D V I S A B L E . . . . . . . I N C R E A S E D V O L U M E . . |
The ideal case is that in which the probable word is long enough to furnish more than one of these overlapping letters, as shown in Fig. 32 in connection with the “word” INCREASED VOLUME. Suppose that we have suspected the presence of this expression in our cryptogram, and have ascertained that the necessary letters are present for forming it. We consider its letters one by one, in the order I, N, C, R . . . . and go through the cryptogram, underscoring (or otherwise noting) all cases in which the given letter is followed immediately by another of the letters found in the same probable “word.” But, in considering any one letter, say the letter N, we ignore such sequences as NT, NB, NX, whose second letters, T, B, X, do not occur in the expression INCREASED VOLUME. Fig. 33 shows exactly what digrams of this kind can be found in connection with letters I, N, C, R, E, and also the distance (or distances) apart of the two given letters as found in the probable word. Notice that in connection with every letter there is one digram in which this distance is 8, the correct key-length of our present cryptogram. And when these digrams are selected from the tabulation, and set up vertically with top letters in the order I N C R E, the lower five letters prove up in the order D V O L U. In actual work, the tabulation must sometimes be made, though ordinarily it will suffice to start directly with the “proving up.”
| Figure 32 I N C R E A S E D V O L U M E I N C R E A S E D V O L U M E I N C R E A S E D V O L U M E |
Now let us go ahead and solve the cryptogram, as shown in Fig. 34. We will assume, to begin with, that our cryptogram has been prepared at the top of a sheet, and that our various trials are being made on the blank space beneath it. We will assume also that, having discovered key-length 8, we have divided this cryptogram roughly into eight segments, three of which contain ten letters and the rest nine.
First, we are in possession of a series of embryo columns, shown at (a), and these can be set up without looking at the cryptogram at all. Having done this, we turn to the cryptogram, find each one of the sequences again, and lengthen the columns of our beginning block by adding to each pair of letters a few of the letters which immediately precede and follow it. Thus, our block begins to build up as at (b); and, for each time that a partial column is set up in (b), the segment which contained it is promptly circled out of the cryptogram itself, which now begins to assume the appearance indicated at (c). Thus some words have automatically formed on the new lines which tell us plainly that the final column must contain a sequence L T E, followed by S or W, and the appearance of the cryptogram tells us plainly where to look for it; the final segment is the only one having enough letters to furnish another nine- or ten-letter column.
| Figure 33 Letter Examined & Distance Apart Sequences Found In Word I IS 6 ID 8 IR 3 IC 2 N NS 5 NV 8 C CO 8 CR 1 CS 4 R RE 1 4 11 RA 2 RL 8 E EM 9 (6)* EU 8 (5)* EO 6 (3)* ES 2 (*) Distances from the second E Proving up: I N C R E . . . (8) D V O L U |