Often, two ciphers will differ from each other only in the method by which their cryptograms are produced; oftener, there will be an actual difference, but one which is purely superficial. For instance, we have just mentioned a plaintext unit A B C D E F as having been transposed with a key 6 2 1 4 3 5 to result in the order F B A D C E. Identically the same numerical key, used in another way, will transpose this unit in the order C B E D F A. The two resulting cryptograms would be different, but the kind of cryptogram would not.
An extremely common form of complete-unit transposition is that indicated in Fig. 7, where a short message, LET US HEAR FROM YOU AT ONCE CONCERNING JEWELS QQ (38 letters plus 2 nulls), has been written into an oblong, or block, in one order and taken off in another. Both the writing in and the taking off follow a route, rather than a key and, for that reason, the cipher is often spoken of as route transposition, rather than rectangular transposition.
Three of the many possible routes are shown in the three (partial) cryptograms of the figure. In this connection, the American popular terminology seems to favor horizontals and verticals, rather than “rows” and “columns.” The writing in or
| Figure 7 L E T U S Cryptograms: H E A R F R O M Y O (a) By descending verticals, from the left: L H R U C U A T O N C E C O N C N E E E O A E E G L T A M T C R J S U, etc. C E R N I N G J E W (b) By alternating verticals from the right, top: E L S Q Q S F O N N I W Q Q E N O O Y R U T A M T, etc. (c) By diagonals: L H E R E T U O A U C A M R S C E T Y F N E C O O, etc. |
the taking out of a text is said to be done by straight horizontals, or by reversed horizontals (backward), or by alternate (or alternating) horizontals (written alternately in both directions). Similarly, we find ascending, or descending, or alternate verticals; and again the diagonal routes will be described as ascending, descending, or alternate. The route may also be a spiral one, and in this case it is said to be clockwise or counter-clockwise.
For all of these routes, the point of beginning is nearly always one of the four corners, except in the case of the two spiral routes, which are just as likely to begin with a central letter, particularly when the rectangle is a square. Colonel Parker Hitt, in his Manual for the Solution of Military Ciphers, shows the same series of letters written into forty different blocks, always beginning at one of the four corners.
Rectangular transposition, when used as cipher and not simply as a puzzle, requires that one dimension of the oblong be fixed, the other dimension being entirely dependent on the length of the message to be conveyed. In the figure, the pre-arranged width of the block, called its key-length, was 5, and the filling of the block required 8 complete units. These were written one by one as simple bits of plaintext, and were then broken up in the method of taking off. Occasionally it will be the vertical dimension of the block which is fixed, and the plaintext will be written in by columns, beginning at the left or at the right. But there is so little difference in the results of the two procedures that a decryptor may solve and read a cryptogram without learning which of the two was actually followed. Ordinarily, it is the simple operation which comes first, the writing in of intact units one after another. Sometimes the opposite is true, the operation of writing in being made very complex, so that the whole block is the unit, the taking off being done by simple rows or columns. Frequently both operations are complex. This kind of transposition belongs rather to the category of puzzles than to cipher; any reasonably intelligent person can decrypt it, knowing what it is. However, it has not infrequently been applied to serious purposes, and a decryptor, encountering an unknown transposition, would not overlook the possibility of simple rectangular encipherment.
Decryptment, here, is merely a matter of trying out the known routes, and it would never be actually necessary to write out the entire forty-plus blocks, or even half of these, for any one rectangle. The decryptor begins by counting the letters of his cryptogram and factoring the number of these, to find out what oblongs are possible. A 36-letter cryptogram, for instance, might mean dimensions 6 x 6, or dimensions 4 x 9. It could, conceivably, represent dimensions 3 x 12, or 2 x 18. But key-lengths are hardly ever shorter than 5, or as long as 18. He would seize upon the square as the object of his first investigation, writing the cryptogram into that block by various known routes, and also reading by various known routes, diagonally, horizontally, vertically, backward, or upside down, until he begins to find words. As a rule, this does not take him very long; often the very efforts of an encipherer to achieve complexity will result in an easier task for the decryptor. However, a spiral will sometimes give trouble.
| Figure 8 A E I B D F H J C G K........etc. Taken off: A E I & B D F H J & C G K... |
The examples appended to this chapter are all of the complete-unit type, and require little knowledge of cryptanalysis for their solution.