| Figure 143 (a) a b c d e f g h i j k l m n o p q r s t u v w x y z 1 - B G Z 2 - E D 3 - A B 4 - Z K 5 - C (b) a b c d e f g h i j k l m n o p q r s t u v w x y z 1 - B G K Z A 2 - E D 3 - A B G K Z 4 - Z A B G K 5 - C |
satisfactory as that of w. With G and Z added to alphabet 3, and with A added to alphabet 1, we may now turn our attention to alphabet 4, which contains a Z, and, by making similar observations there, we may add to the 4th cipher alphabet the letters A B G, and, to the 1st and 3d alphabets, the letter K. Thus we arrive at (b) through what is ordinarily referred to as the “symmetry of position” existing among the several cipher alphabets.
But the second and fifth alphabets cannot yet be combined with the other three, since neither of these contains any letter in common with them, and thus we have no point from which to measure lineal distances. We know, however, that if our hypothesis is correct, the letters A B G K Z, in these alphabets also, will be found at exactly the same lineal distances as before. It would be possible to prepare a sort of slide on which these letters, written twice in succession, are spaced as in the other three alphabets, and use this in experimenting with alphabets 2 and 5.
The cryptogram, as we first saw it, showed all substitutions which are possible from (b) of Fig. 143, together with a few v-c notations which were listed in Fig. 142 but not further investigated. In case the student cares to complete solution, he might refer to certain precautions mentioned at the beginning of the chapter. Notice, in the last figure, the lineal distance from G to K; what letters would you feel inclined to try in the three intervening positions? Or notice the distance BG. What letter is very likely to have been taken here for use in the key-word, and where is it likely to stand in that word? If the index-letter was A, does it seem possible that the a-substitutes could all be selected in advance directly from the contact sheets? Would this be possible if the encipherment process were varied so that an index, selected in the sliding alphabet, were brought to stand below keys in the stationary one? The cryptogram is known to contain the word SUPPOSE, and the period is 5. Is there any room here for pattern methods?
Our Type II slide, then, unlike the remaining three, builds up automatically in the key-frame, owing to the simple fact that we are able to set down the plaintext alphabet in the encipherer’s original order. The method of solution, so far as we know, was first published (1883) by Auguste Kerckhoffs, who seems to have originated the term “symmetry of position.” The invention of the cipher is credited to “a member of the (French) Commission on Military Telegraphy.”
If these parallel cipher alphabets are to be avoided in the key-frame, but still using a Type II slide, General Sacco has suggested that the encipherment process be altered as follows: Let the index-letter and the key-letter both be found in the upper alphabet. Slide the plaintext letter to stand below the index-letter, and use the substitute which will then be standing below the key-letter. This, of course, would have to be letter-by-letter encipherment, and represents one of those rare cases in which a slide is less convenient and rapid than its equivalent tableau. If this tableau be laid out in full, as explained for Beaufort alphabets, it shows, on its 26 rows, 26 cipher alphabets not one of which appears to be at all related to the others. One of these (the one in which index-letter and key-letter are the same) will be the normal alphabet. We may find the original sliding alphabet, however, by looking at columns. Such a tableau is exactly equivalent to the Delastelle tableau if the Z-alphabet be made the normal one. Delastelle’s tableau was described as follows: Using the mixed alphabet, fill in the tableau by columns, beginning each column with whatever letter, in the mixed alphabet, follows the plaintext letter shown above the column. This causes the final alphabet to come out in A B C order. The Delastelle tableau is not nearly so easy to reconstruct as that of the ordinary Type II slide; the method, however, will be plain enough when we have understood the reconstruction of Types III and IV.
The Type I slide, as pointed out in the beginning, is somewhat out of place in the present chapter; every frequency count will follow the graph of the mixed plaintext alphabet, so that all can be “lined up” by their common pattern. Having letters, and not numbers, the “top” of a frequency count may be anywhere; it is usually best to prepare at least one of the frequency counts of double length in order to effect the alignment. Granting, however, that for some reason the common pattern of the frequency counts has not been recognized, then the method of decryptment would be exactly the same as for any other case of mixed alphabets.
Fig. 144 shows the development of the key-frame in this case. At (a), some substitutes have been correctly identified in each of four cipher alphabets. But long before reaching this stage, the most careless of decryptors must have noticed that the difference between any two cipher alphabets is purely a matter of alphabetical shift. This is particularly visible as between alphabets 3 and 4, where the alphabetical interval is only 1; examination of alphabets 1 and 2 shows that wherever both substitutes are present, their alphabetical difference is 14; and further examination shows that the alphabetical distance from alphabet 2 to alphabet 3 is 17. The use, here, of a Saint-Cyr slide enables us to arrive very quickly at (b). The alphabets of (b) are, of course, secondary cipher alphabets, and the primary one obviously runs in normal order (or, at worst, in a strictly methodized order which is easily obtainable from the normal one). What we still lack, in order to reconstruct the slide, is the mixed plaintext alphabet, and this can be recovered as at (c). Write out the normal alphabet (known to be the original cipher alphabet), then, using any one of the secondary alphabets, place originals above their substitutes wherever these are known. In the given example, all missing letters can be filled in by alphabetical sequence; and even though the index-letter was one of low frequency, and thus was not used in the message, the student should have no trouble whatever in discovering the key-word which governs the four cipher alphabets.
In considering the reconstruction of the remaining two slides, we shall have to keep clearly in mind the imaginary tableau on which the plaintext alphabet has exactly the order of the one on the slide, so that cipher alphabets, also, have exactly the order of the one on the slide, and are shifted one letter at a time, as in the Vigenère tableau. For one thing, we are going to call some of these alphabets by numbers, or refer to them as odd-numbered and even-numbered alphabets. Thus, with
| Figure 144 The Alphabets from a TYPE I Slide: (a) a b c d e f g h i j k l m n o p q r s t u v w x y z 1 - L . . J Q . H G F . . . . B A . . R Y X . . . . . . 2 - Z . . . E . . . T . . C Q . O . . . . . B . . . . . 3 - Q P . O V N . . . . I . . G F U . . D C . B A . Y . 4 - R . . P W . . M L . J . . . G . . . . D . . . . . . (b) a b c d e f g h i j k l m n o p q r s t u v w x y z 1 - L K . J Q I H G F . D O C B A P . R Y X N W V . T . 2 - Z Y . X E W V U T . R C Q P O D . F M L B K J . H . 3 - Q P . O V N M L K . I T H G F U . W D C S B A . Y . 4 - R Q . P W O N M L . J U I H G V . X E D T C B . Z . (c) Alphabet No. 1: Plaintext: o n m k . i h g f d b a . u l p e r . y . w v t s . CIPHER (Rearranged): A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |