Alphabet 3: The tens-half of the third column contains the “giveaway” digit 2, and the units-half contains this digit also. The key which produced the third cipher alphabet is 11.

Alphabet 4: The tens-half of the fourth column ranges only over the digits 5-6-7-8, with nothing to indicate whether the missing one is 4 or 9. Thus, the key to the tens might have been either 3 or 4, though it could not have been anything else. The units have the full range of digits, 5-6-7-8-9, key 4. In the fourth cipher alphabet, then, we cannot tell immediately whether the key is 34 or 44. Granting, however, that the arrangement of letters in Lindquist’s key-square was the same as that of Fig. 136, the substitution of letters for numbers may suggest which of the two numbers, 34 or 44, is the correct key. With one of these we obtain letters C O A O, and, with the other, C O A T, a word (The student might find it of interest to decipher this cryptogram and learn what the minister had to say).

Any sufficiently long cryptogram, then, will reveal both its period and its key, and this regardless of how the letters were arranged in the encipherer’s checkerboard. It may then be deciphered with its own key, and the case, at worst, becomes one of simple substitution. With shorter cryptograms, we often find, as here, that some one or more of the cipher alphabets could have had two or more possible keys. This happening, presuming that the alphabetical arrangement of the square is a known one, or one easily reconstructed, presents no real problem; a little experimentation on the cryptogram will show which keys bring out a message. When the alphabet of the square is an unknown mixed one, the problem may vary according to length, and the number of key-combinations which are found to be possible. If, for instance, the case resembles that of our preceding cryptogram, where only one alphabet out of four was in doubt, then, remembering that the Nihilist cipher alphabets are of a kind whose frequency counts can be “lined up,” we might take frequency counts on the several alphabets, and supply the missing numbers of the doubtful one by making its pattern match that of the rest. With several alphabets in doubt, which could only happen when frequency counts are too scant to betray their graph, it might become necessary to decipher the periodic cryptogram with each possible combination of key-numbers, each time obtaining a new cryptogram, and accept, among these new cryptograms, the one whose general frequency count seems most likely to be that of a simple substitution. The correct cryptogram, in this case, should also contain some fresh repetitions; that is, repetitions which were not present in the periodic one. As to the three examples which follow, there should be little difficulty in deciding whether or not the Nihilist cipher is represented.

131. By B. NATURAL.
45 68 48 46 60 78 45 78 24 59 35 67 50 75 38 58 53 60 65 26 54 46 68 55 38 67 42
69 56 59 24 59 70 54 30 85 32 90 44 46 45 56 79 54 30 86 22 78 27 26 44 49 78 75
38 54 55 78 47 27 45 49 89 44 49 88 42 59 56 49 42 86 50 52 26 55 42 60 47 36 22
50 78 65 50 76 35 78 28 59 26 50 68 54 60 76 25 87 28 29 55 58 59 73 59 97 54 69
66 57 26 46 78 65 48 76 45 57 47 29 65 79 77 55 30 57 35 89 45 49 53 46 66 75 57
97 55 68 28 47 22 66 66.
132. By PICCOLA. (Keyword, CRYPT. Fifth alphabet contains Q. But: Can you rearrange the numbers on the strip before taking frequencies?
15 20 23 18 03 15 26 12 26 25 03 30 40 14 20 09 20 25 11 15 17 25 16 02 29
30 25 21 18 03 11 16 27 30 26 10 02 21 17 01 06 25 13 01 25 03 30 23 26 23
06 27 12 11 20 12 22 16 18 03 29 20 19 01 19 17 19 12 12 20 02 11 14 18 19
13 20 38 11 23 19 01 19 01 27 30 16 21 01 23 17 24 22 25 03 19 26 21 11 28
11 17 16 21 03 13 20 28 05 20 06 26 13 11 26 11 16 27 26 16 02 26 18 05 25
06 03 16 03 03 30 26 16 27 28 10 02 16 02 29 06 26 27 11 24 15 20 23 13 15
11 25 13 05 24 28 20 40 27 19 19 30 27 19 19 13 02 23 21 28 11 30 14 28 03
18 26.
133. By PICCOLA. (If you recognize this gem of literature, you are beyond the draft age. It got around the censor in 1918).
20 08 17 29 15 09 01 05 08 29 24 11 06 05 10 26 13 22 06 01 18 19 05 03 16 24 13
16 04 08 07 19 12 18 24 11 17 09 07 27 26 22 01 15 21 21 10 03 06 22 03 18 04 22
20 06 07 24 12 19 10 19 10 30 10 19 16 24 13 16 04 08 23 01 10 10 23 10 09 05 08
17 21 22 09 15 21 21 10 03 06 06 21 20 12 22 21 08 18 19 23 05 02 01 11 34 19 27
12 06 02 15 10 22 03 03 02 11 12 19 10 11 19 27 13 12 18 24 19 13 24 15 07 16 16
16 26 20 04 05 11 29 26 20 03 10 19 10 23 11 16 19 13 16 04 08 25 17 05 24 20 20
23 09 10 25 20 25 02 05 07 16 26 20 04 05 11.
134. By DAN SURR. (Should you be worried at finding this in Daughter's boudour?)
A B C D E F G E H D G E F J E K H D L J D G J M M J D G J M E
E F J E O J E L F A C B D G. - P G M G.

CHAPTER XVIII
Periodic Ciphers with Mixed Alphabets

Periodic cryptograms in which the cipher alphabets are mixed are nearly always produced by means of slides. Before discussing these ciphers, it may be well to clarify a few terms which otherwise could leave room for uncertainty. We have, for instance, two, and sometimes three, key-words. There is a primary one (sometimes two) used in the preparation of the slide, and a secondary one, often called the “specific” key, which is used, as in Vigenère, for the encipherment of cryptograms. Since we shall have practically no occasion to mention the primary key-word (or words), any references which are made here to a key-word, unless clearly seen to refer to the preparation of a mixed alphabet, can be understood as meaning the secondary one, that is, the specific key which selects the cipher alphabets. Perhaps it is also advisable to call attention once more to the existence of a primary cipher alphabet (the basic one which is written twice in succession on the slide) and of the 26 secondary cipher alphabets which can be derived from it by placing it in its 26 possible positions. These are usually referred to simply as “the alphabets,” while the basic one is more commonly called “the sliding alphabet.” All, of course, are the same alphabet except for their points of beginning.

To see clearly what is meant by an “equivalent slide,” the student may make an experiment: First, form a temporary slide, using any two 26-letter alphabets, and use the slide to encipher a short message. Now form another temporary slide on which the two alphabets of the preceding slide (both treated by exactly the same plan) have been rearranged so that their letters are taken at every interval 3 (or at every interval 5, or 7, or 9 — any interval whatever that is not divisible by 2 or 13), and with care taken always to maintain this constant interval even when the 26th letter is reached and the 1st reappears. Then, using this new slide in the same way as before, encipher the same message with the same key, and compare this new cryptogram with the first. Finally, an alphabetical interval (or distance) between two letters will mean their distance apart in the normal alphabet, while a lineal interval (or distance) will mean their distance apart in any alphabet whatever. That is, the alphabetical distance from A to B is invariably 1 (position), while their lineal distance apart on a slide, or in the rows or columns of a tableau, could be anything from 1 to 25. Where these intervals must be mentioned often, the distance from A to B will be referred to more briefly as “the distance AB.”

Now let us consider the four slides of Fig. 138, which are being designated (arbitrarily) as belonging to Types I, II, III, and IV, in what would seem to be the order of their potential resistance to decryptment. Their actual resistance, however, might depend largely upon the manner of their use, and we are assuming throughout the chapter that the encipherment process is identically that described for the Saint-Cyr cipher: The upper alphabet, in all cases, is to be the plaintext one; the index-letter is always the initial one of this plaintext alphabet; and, for the encipherment of cryptograms, the letters of the chosen key-word are to be found in the lower alphabet and brought one by one to stand below the index-letter in order to set up their cipher alphabets. Also, for our immediate purposes, we are neglecting certain precautions the advisability of which will be seen later: First, the mixed