added in Fig. 52. In this figure, two combinations may be discarded, because of trigrams KTY and YTY. The others appear acceptable. At this point, however, the sequence XTY of combination 16-5-14 begins to draw attention because of its very few possibilities (SIXTY, NEXT YEAR, etc.), making it likely that one of these will quickly select or discard the entire combination. For building SIXTY, row 3 of the set-up contains two I’s and one S. The two I’s, columns 13 and 19, when inspected visually, are found to bring out, on the top row, the two sequences I O C K and T O C K, while the S, column 21, brings out, on the top row, another S, which would extend these, respectively, to read S I O C K and S T O C K, the latter surely the more acceptable. The results of these additions, with subsequent development, can be examined in Fig. 53. The completion of the word SIXTY has brought out also: STOCK, MITED, SMITH, DOING. The presence of the word STOCK suggests extending the
| Figure 52 12-5-14 13-5-14 15-5-14 16-5-14 25-5-14 O C K I C K A C K O C K O C K U E D X E D N E D T E D O E D L T Y I T Y K T Y X T Y Y T Y A T H O T H R T H I T H S T H I N G E N G E N G I N G O N G |
sequence MITED to read LIMITED, and the addition of two more columns on the left brings out another CK, suggesting another appearance of the word STOCK. The chances are that we have already been building on this other word STOCK, but if not, we may build it now to the point shown in the figure, where the top row suggests RAILROAD STOCK, the third row, FIFTY TO SIXTY, and the second may or may not suggest MEXICO. Thus we are well on our way to solution, and
| Figure 53 11 8 25 6 3 21 19 16 5 14 L R O A D S T O C K I C O L I M I T E D F T Y T O S I X T Y N E S O R S M I T H S T O C K D O I N G |
have not once had recourse to a long prepared list of probable words: division, regiment, battalion, attack, advance, report, forward, artillery, ammunition, communication, enemy, signal, retreat, troops, and so on.
Naturally, there are times when the matching of the columns, for one reason or another, proves troublesome. We are thrown off by errors, by the presence of nulls, initials, abbreviations, etc., or by the encipherer’s use of cover-up devices, such as the writing of YH instead of TH. Or we find that the handling of many paper strips, caused by message length, is awkward and confusing. But if, in the eyes of the decryptor, there is any good reason for finding out the contents of such messages, he can always succeed, even with only two letters per column.
So far, nothing has been said about helping ourselves to the serial numbers of the columns, which, during the rearrangement of letters, are automatically forming in a certain sequence across the top of the set-up. Regardless of the cipher, it can do no harm to examine these, and find out what information, if any, they are able to give. In some cases, they will provide us with both the system and its key, enabling us to throw away the strips and start deciphering. Suppose, for instance, we have correctly matched sixteen columns, and find their numbers in the following order: 31-10-24-37-17-3-32-11-25-38-18-4-33-12-26-39. A careful examination shows that the numbers are running in sets of six. After the first six are passed, the next six have repeated them with an increase of 1, and another six appear to be forming up which will repeat them with an increase of 2. We may verify this by finding the columns which have numbers 19-5-34-13, etc., and, if the set-up continues to show plaintext, we know that we are dealing with a simple columnar transposition. Notice that if the above series were marked into segments of six numbers each, and the segments placed one below another, we should have six columns, each one made up of numbers which are consecutive. Thus, we may sometimes learn from a series of numbers: (1) the system, which is straight columnar transposition; (2) the key-length, which is 6; and (3) the key itself, which, taking the six numbers according to size, is 5-2-4-6-3-1, possibly with the wrong numbers coming first, though it happens that in this case they do not. This is our old friend SCOTIA, used on forty numbers, in case the student cares to verify it.
The trail of the columns is not so plain where a second transposition has done something to the first. But it is still present; the most complex of ciphers has method of some kind, provided we can find it. Consider, for instance, the series of numbers, 11-8-25-6-3-21-19-16-5-14, which has been forming in Fig. 53. Examination here shows pairs of consecutive numbers, 11-8, 6-3, and 19-16, all having the same numerical difference of 3; that is, the plan of our present encipherment, whatever it is, has, on three separate occasions, caused some plaintext digram to appear in the cryptogram reversed, and with its letters three positions apart. Irrespective of the type of transposition, this constant numerical difference of 3 might be found again; perhaps we can set some two columns together correctly simply by reproducing this numerical difference in the two column-numbers. A glance ahead at the next figure will show that we actually could, by setting together columns 12-9 or columns 20-17. Where we cannot discover a repeated numerical difference, perhaps we can discover a progressing difference, or some other signs of regularity.
Now, returning to the particular case, let us pass on to Fig. 54, in which the matching of the 25 columns has finally been completed, and make a careful comparison between the two numerical series 12-9-10-15 and 20-17-18-23. What can these represent but the fragments of four columns, belonging to a first encipherment block, which have been laid down along the rows of a second encipherment block, and taken out in slices? And since the lineal distance apart of any pair of numbers, as 12 and 20, is seen from the figure to be six positions, it would be possible, by writing the series of numbers in lines of six numbers each, to place each pair of corresponding numbers in a same column. The trail, usually, is not so wide, but there is little doubt here that we have been dealing with a case of double columnar transposition in which the key-length of the original block was 6. We shall come back to this in a moment.
Suppose, now, we give our attention to the various series of numbers which appear in Fig. 54, and make sure that we understand what they are. The numbers running across the tops of the columns were, originally, the serial numbers of cryptogram letters (or columns). When we restored these letters to their plaintext order, we disarranged their serial numbers, causing these to come out in the order 1-7-24-22-12-9, etc. This series, then, is made up of cryptogram serial numbers. But it is also a key, since it shows us exactly the order in which we might take off a plaintext in order to form a cryptogram. It is a key of the Myszkowsky type, according to which every letter in the text has its individual key-number, as we saw in Fig. 46 (imagine that encipherment accomplished twice in succession). We do not desire, however, to take off plaintext. And, to use this same key on a cryptogram, we should have to use it in the writing-in manner; that is, first lay out the series of key-numbers, and then, taking the cryptogram letters in their 1-2-3 order, place them, one by one, below their key-numbers. But once the plaintext has been restored, the plaintext letters (or columns) may also have serial numbers, and these new serial numbers, in the figure, have been added at the bottoms of the columns. Should we now restore these columns to the order in which we found them, that is, to their cryptogram order, each column taking with it its new serial number, we should find, running across the bottom of the set-up, another mixed series of numbers