Passing on to irregular types, we find these in all degrees of difficulty, from the very simple “rail fence” to the formidable “U. S. Army” double transposition.
The “rail fence” family is outlined sketchily in Fig. 8. The writing in of the plaintext follows a zig-zag route, downward by so many letters, then upward to the line of beginning, as indicated by the series A B C . . . . . , and the taking off of the cryptogram is done by straight lines. In explanation of the character &, this has been used here as a signal to show the ends of the straight lines. No such signal is needed if a proper understanding exists between correspondents as to the construction of the “fence” and the length of it which may occupy one line of writing; and in some cases the straight lines are all equal in length.
In Fig. 9, we have a suggested grille-transposition, of a kind described by Mario Zanotti as “indefinite.” This kind of grille, we believe, is the invention of General Sacco. To picture it complete, we may imagine a flat surface, such as a piece of cardboard, marked off into squares, having dimensions 12 x 6, and turned sidewise. Assuming this to be shown in full, we are looking at 12 columns, and each column has 6 of the small squares, or cells. To convert this piece of cardboard into an encipherment grille, we clip out three squares from each one of its 12 columns, always in the most haphazard manner possible. The resulting grille will thus have 36 openings, and, if placed over a sheet of paper (preferably also marked into cells), enables us to transpose the first 36 letters of a message by writing them one at a time into the 36 apertures in some one order and taking them off in another. The original plan was the reverse of the usual: write the letters by columns and take them off by rows.
In the figure, a 9-letter message, STRIKE NOW, has been written into the first three columns of such a grille, and, taken off by rows, comes out in the order N, SO, TI, K, RE, W. While the figure shows this cryptogram regrouped in the usual fives, the original method, as prescribed with the device, would have grouped it in threes, that is, to correspond with the number of apertures per column. This
| Figure 9
Cryptogram: N S O T I K R E W. |
would facilitate the operation of decipherment, which is as follows: Count the number of letters in the cryptogram and divide this number by 3, in order to find how many columns were used. Cover (or ignore) the unused portion of the grille, write the cryptogram by straight horizontals into the uncovered portion, then read, or copy, by descending verticals. The recipient of the present cryptogram, for instance, finds nine letters, divides this number by 3, thus ascertaining that three columns were used, covers up the other nine columns, then, proceeding by straight horizontals, places one cryptogram-letter wherever he sees a hole. Having thus restored all letters to their proper columns, he has the plaintext message before him. It will be noticed that an encipherer uses only the number of columns that he needs. His last column does not have to be completed with nulls, as in the case of complete-unit ciphers.
As this grille has just been described, its full capacity is 36 letters, and it has a repeating cycle of that length, presuming that, after the transposition of the first
Figure 10 |
36 letters, another 36-letter unit is to be transposed by the same grille standing in the same position. But this grille, reversed, provides a new pattern; and the opposite side of the grille provides two additional patterns. These positions may be numbered, thus providing for the encipherment of 144 letters, even assuming that the positions are to be used in 1, 2, 3, 4 order and without varying the method of use. Add to this that the cryptographic offices may have provided half-a-dozen different grilles to be used interchangeably and not always in exactly the same way, and it becomes plain that such an encipherment, in the hands of an operator who knows his business, could be made to furnish a very effective form of transposition.
Zanotti, and others, have also described mechanical devices of a patentable type for accomplishing very involved transpositions. The principle on which most of these operate can be seen in Fig. 10. A certain number of pointers, or narrow sliding rulers, all carrying the same progression of numbers, are so attached to a framework that they can be set, by means of a numerical key, to project at irregular lengths over a sheet of quadrille paper cut to fit into the frame. Thus, each pointer indicates a certain number of empty cells, as nine on the first line, six on the next, and so on. In the example of the figure, presuming that each pointer carries only ten numbers, and that the full number of these pointers is seven, the numerical key would be the column of numbers at the extreme left: 2-5-0-7-3-4-7. The message here is written in the usual horizontals, with a null (not strictly necessary) completing the last line. It could be taken off by columns: L, EC, TEN, UFCI, etc. The decipherer, having a duplicate apparatus, would set this according to the pre-arranged key, copy the cryptogram by columns, and read it by rows. The exact method, of course, can be varied.