Of the ciphers we have seen, then, those three which are complete, that is, which employ a full 26 alphabets, are curiously interrelated to one another. In the matter of substitution (encipherment and decipherment), the Beaufort stands alone, in that it is reciprocal, while the other two ciphers are reciprocal to each other in this respect. But in the matter of keys, it is the Vigenère which stands alone, in that it can be deciphered indifferently by key-letter or message-letter, where this is not true of either Beaufort. In this respect, these two ciphers are reciprocal. To see this plainly, we may examine our three encipherments, each one showing a different cryptogram obtained from the plaintext fragment SEND SUPPLIES, using key COMET. The Vigenère version was seen in Fig. 90. If this be deciphered with its message, SEND SUPPLIES, the result is a repeating key-word COMET COMET CO. The other two cryptograms were those of Fig. 98. Here, the Beaufort cryptogram, beginning K K Z B B, if deciphered with the key COMET, gives the message-letters S E N D S. But when we attempt to decipher it using S E N D S as our key, we obtain: I U O C R. It becomes necessary, in order to find out our key-letters, that we proceed as we did for Porta: Assuming that the slide is being used, place message S beside cipher K, and find out what key-letter is standing beside the index A. Place E and K together, and find the next key, and so on. That is, change the position of the slide for every decipherment.

In this same figure, the variant cryptogram begins Q Q B Z Z. If it be deciphered with the correct key-word COMET, we obtain the correct message-letters, S E N D S. But if we attempt to decipher it with a key S E N D S, we obtain the same series as in the other case: I U O C R. To decipher it as a variant, we must again proceed letter by letter. How, then, are we going to apply a probable word as we did with the Vigenère in Fig. 90? How are we going to decipher a whole row of letters, first as S, then as U, then as P, and so on? Must we do this letter by letter, shifting the slide for every letter on every row? And suppose it is a page of trigrams, where we wish to decipher every trigram on the page as THE? Is there no way in which we can decipher all first-letters as T, all second letters as H, and all third letters as E, with only three settings of a slide? The answer is simple. Switch the slides. We have said (and shown) that in this respect the two Beauforts are reciprocal. Where the cryptogram is true Beaufort, and you desire to use your probable word as a trial key, do this with your Saint-Cyr slide (used in reverse, that is, as if enciphering in Vigenère). If your cryptogram is variant Beaufort, use the Beaufort slide (or treat it as a Vigenère, and obtain the key later). Both cases can be looked at in Fig. 101. The cryptogram at (a) is our same Beaufort cryptogram; that at (b) is our same variant. In [another chapter], we shall look a little more closely into this odd triangle of Vigenère-variant-Beaufort. Meanwhile, the interested student might like to investigate for himself a few of the curious angles:

Would it be possible to prepare a tableau for the true Beaufort, and use it in exactly the manner described for Vigenère? Recalling the appearance of the Vigenère tableau (Fig. 85): Suppose we should add to this another vertical alphabet, this time on the right-hand side, causing this new alphabet to begin at A and run backward, A Z Y X. . . . Could this new alphabet be made to serve any useful purpose? More than one? What about the reversible cipher-disk? Is there any way at all in which it would be possible to encipher and decipher Vigenère cryptograms with a Beaufort slide, or Beaufort cryptograms with a Vigenère slide? Could you make a cipher disk for the Porta?

110. By NEON. (Gronsfeld).
J Q Q Y P I R S F Q Y J N E U R U V E F V W P E B Q F G T E M K U K G
R W E T Z I D V I Q Q S Z I H K W M C E K B F J Q Q X T R F V R J K O
A T E E N J U M S N G L P I B S O A S R Y S A X R U O J G W M V R U S
V D Q Q R D P P K P L I C.
111. By B. NATURAL. (Gronsfeld).

L N P L G S Y R U A I R I Q X R E N D I U U N H D
Y M S U U O Q N S T I T U G L W R E R V B Z D U Q
S I C T U Q B T F X J F E H J W N I K U N H A Y H
I E P R G X K W M P U K U L F N G Q P R B X Z R E
T E U U W T R X J F N H J Y O J U V S P N W O Z G
S O Q C J N W K G E B X Z R I P U N X B N A W O -

112. By B. NATURAL. (Porta).
I O U K J G F Y S M Q S X H W W D P K M M J E S P Y W Y L B X B V U D
X T V L V O G Q K S L W W Q S E U D K W J I A M G W Z C W F O U I M M
V Z F U Q K S O X D S E L E E P T I O T U L U L W W P K Q K S Z E U.
113. By KRIS KROST. (Beaufort. Probable word: AMERICA).
N D L H T I E Y R K F M F H L C S Z Q A H B H T Y H A F P I V I D C S
X P Z E X N K W Q R M S A H E Q X G R E H A U H G D S O O A G X U G D
W G T I L S A P D V H A Q W E W Z M I M Y Y Q O B F E K C M M T F N E
V H W Z Y B G P W V E H R Z V U O O N B K X F O Z J A Z I Q N Z T T O
P R V I T.
114. By WHOSIT. (Variant Beaufort).
K O A S Y B B S G P A R Y A T F R F D U L W H J A R G H S G U W D B C
J R V M C U P S T Q W M B Y S I W Y I F H B A A F I A N Y H J L S B T
J O C Z E E N N R U A S R U I E J N O E P S G C G W V U M E A K W R L
Y H N S R G H B A H.
115. By PICCOLA. (Short Simple Substitution. - No keyword).
O F T D A F F B E H Z H W G W F O M; M F W R J D E D N V F P Z K
W F D Y F M Z Q K K Z T.

CHAPTER XIV
The Kasiski Method for Periodic Ciphers

Prior to the 1860’s, the ciphers of the past two chapters had been regarded as entirely safe. A radical change of opinion took place in 1863, when Major F. W. Kasiski, a German cryptanalyst, was so indiscreet as to publish certain of his observations. The student will surely have noticed, among the examples of Chapters [XII] and [XIII], the happening which is suggested in Fig. 102. Some sequence, usually a digram, is repeated in the plaintext, and happens to be enciphered more than once by exactly the same few key-letters; the result is a repeated sequence in the cryptogram. What he may have failed to notice is the periodicity of such repeated sequences. In order that the same few key-letters be used again, the key-word must have been repeated an exact number of times, so that, in these cases of repeated cryptogram-sequences, the distance from first-letter to first-letter is evenly divisible by the key-length — or period (in the figure, the distance from V to V is 10,