There are, of course, many ways in which a key could be applied. The method used here is one published several years ago by Ohaver, and can be studied in Fig. 19. First, as shown at (a), we have a quick mechanical method for selecting apertures that cannot conflict. The square is divided into four quarters, and each quarter, treated as if it were the one occupying the upper left-hand corner, receives its consecutive cell numbers, 1 to 9 (or 1 to 4, 1 to 16, 1 to 25, 1 to 36, etc.). If the route of writing-in is made exactly the same for all four of the quarters, it becomes possible to clip one each of the numerals 1, 2, 3, 4, 5 . . . . . . . etc., taken absolutely at pleasure, and each resulting aperture will expose only its particular four cells. This can be seen at (b).
The grille shown at (b), however, was based on the key-phrase FRIENDLY GROUPS, and the method can be studied at (c), following Ohaver’s plan, even to its minute details. The fact that the square is based on 6 is told in the initial letter of the key-word, F, 6th letter of the alphabet. This key-word must yield nine letters, one for each proposed aperture in the grille. A short word, such as FRIEND, can be lengthened by a partial repetition, as FRIENDFRI, while a longer word is cut off after its ninth letter, as it was in Fig. 19. This literal key is next converted to a numerical key, as explained in the [preceding chapter], and the nine resulting numbers are divided as evenly as possible into four sections. Finally, considering the four quarters of the grille in some definitely agreed rotation, each section of key-numbers will show what numerals are to be clipped from a given quarter. In the figure, the numerals 3 and 8 were clipped from the first quarter, numerals 5 and 2 from the second — proceeding in a clockwise direction, — numerals 7 and 1 from the third quarter, and numerals 6, 9, and 4 from the remaining quarter.
Figure 19 - Preparation of a Grille
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Another method for selecting cells, proposed by Edward Nickerson, dispenses with numerals, using in their places the letters of a key-word which must be without repetitions, as FRIENDLY G happens to be. If these nine letters, all different, be written into the nine cells of each quarter, following exactly the same route in each case, it becomes possible to clip one each of the letters F, R, I, E, N, D, L, Y, G, taken wherever desired. The choice can be made as follows: Taking the four quarters of the grille in the agreed rotation, follow the normal alphabet, clipping A, (when present,) from the first quarter, B, (when present,) from the second quarter, C, (when present,) from the third quarter, and so on. Or, to insure a more even distribution, rearrange the nine letters in alphabetical sequence: D E, F G, I L, N R Y, and divide as in the former plan, clipping D and E from the first quarter, F and G from the second, and so on. While it is possible to provide key-phrases of sixteen letters, without repeating, it is probably more convenient to take whatever number of letters is needed from a key-mixed alphabet of the following type: F R I E N D L Y G O U P S A B C . . . . . . W X Z f r i e . . . . . .
In Fig. 20, at (a), (b), (c), (d), we have a detailed picture of the operation of this grille on the 36-letter plaintext unit: MISFIRE ON VIADUCT JOB X RUSH INSTRUCTIONS. One definite edge of the grille must be designated as the top, and there is a right and a wrong side. Taking precautions in these respects, we place the grille over a sheet of paper and mark its outline with a pencil (or otherwise make sure of maintaining this one location). We write the first nine letters as at (a), and give the grille a quarter-turn to the right. We add the second nine letters as at (b) — where the newly-written letters are the capitals; the others, in lower case, are presumed to be hidden from sight by the solid portion of the grille. Another quarter-turn makes ready for the next nine letters (c), and a remaining quarter-turn completes the revolution (d). The writing-in, at all times, is straight ahead: cells taken from left to right, and lines taken from top to bottom.
Figure 20 - Four Stages of Encipherment
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In the Jules Verne story, the three units of his cryptogram were left standing in their blocks. Verne’s heroes were clever enough to unearth a ready-made grille, and, by laying this, in its four successive positions, above each of the three blocks, were able to read the message through the apertures. Today, such blocks would be taken off in five-letter groups, and possibly by a devious route. A little concealment can be afforded, too, by completing the last five-letter group with nulls, or, better, by adding these nulls at the beginning of the cryptogram. It is also possible to make the final 36-letter unit incomplete by blanking out its bottom cells before putting in the letters.
A grille can be used in other ways. Negligible changes can be produced in its cryptograms by altering the customary order of its four positions. A more substantial change is introduced by departures from the straight horizontal direction of the writing-in. It is possible to revolve the paper instead of the grille, setting the letters right-side-up at the time of their taking off. And in all of these cases, the grille is still serving as an instrument for writing-in; there would be corresponding cases in which it is used as an instrument for taking out the letters of a prepared block. Each variation, perhaps, would require its own separate analysis before its individual inherent weaknesses could be spotted and used as the basis for a special method. If the student, after observing some special methods applied to ordinary grille encipherment, cares to try his hand at analyzing some one of its variations, we suggest that he take a series of numbers, 1 to 36, 1 to 64, etc., and carry these through a complete encipherment to see what becomes of each one.
Grille transposition, like the Nihilist, involves a major unit composed of minor units. But here, the four minor units are never left intact, and if the type of encipherment is not known in advance, the decryptment of a single block will give somewhat more trouble than the decryptment of a single Nihilist block, for the reason that the decryptor usually exhausts the simpler possibilities before trying the complex. With grille encipherment known, or suspected, we have a cipher bristling with points of attack.
The strictly horizontal writing-in of each minor unit has had to be done within a fairly short compass, and no two consecutive letters of this unit can have been placed very far apart without causing other letters to draw closer together. Their average distance apart is four cells. For the decryptor, this actual distance apart of letters is made shorter by his knowledge that for each letter considered, there are three others which cannot have been written into the same unit with it, and that he knows definitely what these three letters are.