Particularly interesting is the assistance he receives from the symmetrical pattern into which the letters of his four units are written; position 3 is position 1 reversed, and position 4 is position 2 reversed. Thus, having tentatively selected the letters of a probable word, or fairly long sequence, he can check the correctness of his observations by examining another sequence which would automatically build up, traveling in the opposite direction, in the reverse position of the grille.
For a clear understanding of these matters, suppose we consider the decryptment of the block just enciphered, on the assumption that we suspect the presence there of the word VIADUCT. Fig. 21 shows a 6 x 6 block carrying consecutive cell-numbers, which are also the serial numbers of the cryptogram letters, as these appear in a separate block beside the first. It is understood that our first move would be that of ascertaining whether or not the seven letters of this word are all present. It must be remembered, too, that a long word is not necessarily altogether in one unit; the grille might have been turned before the word was completed.
In the present case, however, our first letter, V, is found near the top of the square, and only once, so that if the word VIADUCT is present, a substantial portion of it must have been written before the grille was turned. We expect to find letters I, A, D, U, and so on, following the letter V in just that order, and without any very great distance between any two of them; and if, approaching the bottom of the square, we find it necessary to proceed backward for U, C, or T, then the grille was surely turned before that U, C, or T, was written.
Now, considering together the two blocks of Fig. 21, we find that our first letter, V, occupies cell No. 7. In imagination, we revolve a grille in which the only aperture has been cut in cell 7, and find that this aperture exposes the cells numbered 5, 30, and 32. These three cells, then, were surely covered from sight when the letter V was written into cell 7, and regardless of what the letters are that occupy these three cells, it is definitely impossible that any one of the three could have been used in the same minor unit with the V of cell 7.
Looking for a letter I, we find several within a very short range. But the block contains only one A, and since we cannot proceed backward after selecting the I, the position of A (cell 10) tells us that only the I of cell 9 is possible. We accept, then, the I of cell 9, and, again revolving an imaginary grille with its only aperture cut in cell 9, we eliminate the letters found in cells 17, 28, and 20. Similarly, accepting A of cell 10, we eliminate whatever letters are occupying cells 23, 27, and 14. So far, none of the letters eliminated have been wanted for the development of the word VIADUCT; but notice that the fourth letter, D, found only once in the block, occupies cell 15, thus eliminating the letters of cells 16, 22, and 21, one of which is U, the next letter needed. Thus, we are not forced to make a decision as between the U of cell 16 and the U of cell 18.
| Figure 21 1 2 3 4 5 6 B T M R X5 U 7 8 9 10 11 12 V7 C I9 A10 I S 13 14 15 16 17 18 R F D15 U S U18 19 20 21 22 23 24 T19 I R I22 H E 25 26 27 28 29 30 I N O27 N28 C S30 31 32 33 34 35 36 T O32 J S O N |
We have put together, then, the letters V I A D U in the only manner which is possible at all, and their cell-numbers, taken in order, are 7-9-10-15-18. If the grille is reversed, these same openings, named in the same order, will uncover cells 30-28-27-22-19; these new cells, however, will not be seen in reverse order; they will be in straight order like their letters. If, then, our sequence V I A D U is correct, the five letters found in cells 19-22-27-28-30, taken in normal order, should form an acceptable English combination. A glance at the right-hand block of Fig. 21 will show that this check-sequence is T I O N S.
When we selected V, we automatically selected S of cell 30 as its check-letter. When we added I on the right-hand side of V, we obtained with it the N of cell 28 on the left side of S, giving the check-digram as NS, entirely acceptable. With A, we added the O of cell 27, giving the check-trigram as ONS, still acceptable; and so on to IONS, TIONS. Our complete word VIADUCT produces the check-sequence UCTIONS. It must not be objected that the fact of having only one each of letters V, A, D, has too greatly facilitated the search. This is an entirely legitimate expectation in a case where we deal with one unit, and the decryptor, when possible, chooses his probable word with this in mind. In the absence of a probable word, we are never without probable sequences: the list of frequent trigrams, and the various common affIxes, such as -TION, -MENT, -ENCE, -ABLE, CON-, PRE-, etc. For the first three or four letters, where decisions are sometimes uncertain, it is more satisfactory to work directly on the square (prepared in ink), so that impossible cells may be canceled in pencil, and the pencil marks erased when wrong; but once well started, a paper or celluloid grille can be prepared to fit the block, and the chosen cells actually cut out as they are selected. Having found seven out of nine apertures, we may, if we like, turn the paper grille and experiment with its other two positions. The letters, in this case, will show gaps in sequence, and may indicate by these gaps just where the new openings ought to be cut. With one full unit determined, we have the grille for reading the others. The only remaining problem would be that of deciding the exact sequence of these four units, with their context as a guide.
For the case in which it is necessary to begin with letter-sequences, particularly if driven back to the digram list, the device shown in Fig. 22 may prove of considerable assistance: The cryptogram is written in both directions, and thus pairs every letter with its check-letter, so that check-sequences here would be written backward. This idea is adapted from General Givierge’s Cours de cryptographie.
| Figure 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 B T M R X U V C I A I S R F D U S U N O S J O T S C N O N I E H I R I T 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 T I R I H E I N O N C S T O J S O N U S U D F R S I A I C V U X R M T B 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 |