CHAPTER XIII
The Gronsfeld, Porta, and Beaufort Ciphers
Now let us have a brief look at other classic ciphers of the multiple-alphabet type, and see to what extent these will differ from the Vigenère. The Gronsfeld cipher, as may be seen from the specimen encipherment of Fig. 92, uses a number-key. Its ten alphabets are governed by the ten digits. To encipher _S_, using key-digit 2, simply begin at _S_ and count forward 2 in the normal alphabet; the substitute is _U_. To encipher _E_ with key 8, begin at _E_ and count forward 8 in the normal alphabet; the substitute is _M_. For decipherment, count backward in the alphabet. A very superficial investigation will show that the Gronsfeld key of the figure, 28105, and the Vigenère key _CIBAF_ will produce identically the same cryptograms. The key-digit _zero_ governs the _A_-alphabet of the Vigenère, the key-digit 1 governs the _B_-alphabet, and so on to the _J_-alphabet. If it is found convenient to use a tableau (as it may be for the decipherment), the first ten cipher alphabets of the Vigenère tableau can be ruled off from the rest, and the key-digits, in the order 0 to 9, can be added beside the key-letters _A_ to _J_. Or, if the slide is the preferred method, these digits can be written beneath the first ten letters of the sliding alphabet; it is then possible to slide them into position below the index (the stationary _A_), in the same way as the letter-keys. The Gronsfeld cipher, then, is no more than a minor variation of the Vigenère, and requires no separate discussion other than a simple reminder that its possibilities are far more limited than those of the Vigenère proper. That is, it covers a range of only ten cipher alphabets where the Vigenère covers 26, and this limitation more than compensates for the fact that its key is not a plaintext word (presuming, that is, that we know what cipher has been used. Otherwise, the difficulties are about the same for both). To understand how this limitation may modify the case, let us examine the work-sheet shown in Fig. 93.
Figure 92
GRONSFELD Encipherment
Key: 2 8 1 0 5 2 8 1 0 5 2 8... Plaintext: S E N D S U P P L I E S... Cryptogram: U M O D X W X Q L N G A...
Here, we have exactly the routine of Fig. 90, except that our search must be made for probable trigrams, and not for a probable word. We have begun with the most likely trigram, _THE_. But here we do not find it possible to do as we did in Fig. 90; that is, _decipher every letter_, first as _T_, then as _H_, then as _E_. Of the twelve cryptogram-letters present, only seven can be deciphered as _T_; the rest are too far away from it in the normal alphabet, and would require keys larger than 9. Of the six letters which immediately follow the possible _T_’s (the seventh is not shown), only three can be deciphered as _H_. And of the three letters which immediately follow a possible _TH_, only two can be deciphered as _E_ or as _A_. It is often possible, in these ciphers, to investigate simultaneously the trigrams _THE_ and _THA_. So far as the cryptogram is shown, then, there are only two points at which a trigram _THE_ can be present, while a Vigenère cryptogram of the same length would have presented ten possibilities. Thus, we have no real need for a second work-sheet; the only possible key-fragments, 114 and 790, can be tested by any hit-or-miss method which happens to be quickest.
Figure 93
Decrypting a Known Gronsfeld
Cryptogram Fragment: X U I I A Q E U U Y J W....... Trigram tried: T 4 1/ 7/ 1 1 5/ 3 H 1/ 9/ 2/ E 4/ 0/
The sequences U I I and A Q E are the only points at which the trigram T H E could possibly be present, so that only the key-sequences 1 1 4 and 7 9 0 are to be tried. The digram T H alone may be present at Y J.
This cipher is often decrypted in much the same way as a “Caesar” simple substitution (shown in Fig. 61). The cryptogram, or a convenient portion of it, is copied on a single line of writing; then, with each letter as a point of beginning, a series of alphabets is extended (written in reverse order), but only for a distance which includes ten letters. That is, the ten possible decipherments for each cryptogram-letter are written in the form of a ten-letter column. The decryptor may then inspect the ten rows of decipherment to see what he can find. At any point where it is possible to find _T_, _H_, and _E_ in three consecutive columns, the correctness of this possible _THE_ can be checked by finding out whether or not it has a series of companion-trigrams standing at some regular interval on exactly the same three rows.
* * *
In Fig. 94, we have the tableau of Giovanni Battista della Porta, adjusted to suit the modern 26-letter alphabet. Here we have only thirteen cipher alphabets, each of which may be governed by either of two key-letters; these pairs of keys may be seen at the left of their respective alphabets. In all thirteen of these cipher alphabets, the encipherment is _reciprocal_. In the _AB_-alphabet, for instance, which is the first one on the chart, the substitute for _A_ is _N_, and the substitute for _N_ is _A_. The Porta cipher, the oldest known of its kind, employs a key-word, applied as in Vigenère. If the key-letter in use is either _A_ or _B_, the topmost alphabet is the one to be used; if the key-letter is either _C_ or _D_, the second alphabet must be used; and so on. Where this encipherment is illustrated in Fig. 95, it may be of some interest to observe that it is not totally impossible for two different key-words to produce identical cryptograms. As to decipherment, we have already mentioned the fact of reciprocal substitution. Whenever the alphabets are reciprocal (in any cipher), the decipherment is identically the same process as encipherment.
Figure 94
The PORTA Tableau
AB 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
CD A B C D E F G H I J K L M O P Q R S T U V W X Y Z N
EF A B C D E F G H I J K L M P Q R S T U V W X Y Z N O
GH A B C D E F G H I J K L M Q R S T U V W X Y Z N O P
IJ A B C D E F G H I J K L M R S T U V W X Y Z N O P Q
KL A B C D E F G H I J K L M S T U V W X Y Z N O P Q R
MN A B C D E F G H I J K L M T U V W X Y Z N O P Q R S
OP A B C D E F G H I J K L M U V W X Y Z N O P Q R S T
QR A B C D E F G H I J K L M V W X Y Z N O P Q R S T U
ST A B C D E F G H I J K L M W X Y Z N O P Q R S T U V
UV A B C D E F G H I J K L M X Y Z N O P Q R S T U V W
WX A B C D E F G H I J K L M Y Z N O P Q R S T U V W X
YZ A B C D E F G H I J K L M Z N O P Q R S T U V W X Y
The Porta tableau, being smaller than the Vigenère, is not at all inconvenient to prepare and use as it stands. It can be made still more compact: The upper half being alike for all thirteen cipher alphabets, this half can be written _once only_, at the top of the chart. The lower halves can be written below this on thirteen parallel lines, with their pairs of keys at the left. A ruler may then be used, as suggested for Vigenère, to point out any given lower half. But when it is noticed that these lower halves are identically the same series of letters, with its point of beginning shifted one letter at a time, it is promptly seen that a slide is possible, on which the _N_-to-_Z_ half of the normal alphabet, if written twice in succession, could be placed in 13 different positions with reference to the _A_-to-_M_ half; and a slide is more convenient still. The slide shown in Fig. 96 is another of Ohaver’s devices. The only new feature in connection with the Porta slide lies in the handling of the key-letters, which, in this cipher, are no longer the first letters of their cipher alphabets. Mr. Ohaver has added them on the sliding portion of the device, each pair of keys being placed directly below the letter which must stand beneath the index (_A_) whenever one or the other of the pair is the key-letter in use.
Figure 95
Porta Encipherment
Keyword: E A S T E A S T Plaintext: S E N D S U P P... Cipher: D R E Z D H G G...
(Compare:)
Keyword: F A T S F A T S Plaintext: S E N D S U P P... Cipher: D R E Z D H G G...
The Porta cipher, aside from its purely historical interest, provides a most interesting decryptment study in the formation of its alphabets. Notice that because of the encipherment scheme itself, it becomes totally impossible that the substitute for any letter, in any cipher alphabet, can ever be taken from its own half of the normal alphabet. This limitation is far more visible than that of the Gronsfeld. We have, say, a cryptogram sequence _H E P_. Can this represent the trigram _THE_? No, because _E_ cannot represent _H_; for the same reason, it cannot represent _THA_. Can it represent _AND_? No, because _H_ cannot represent _A_. Can it represent _ENT_? No, because _H_ cannot represent _E_. Can it represent _ION_? _TIO_? _FOR_? _NDE_? _HAS_? It is not until we reach _STH_ that we find a normally frequent trigram which could have the substitutes _HEP_. But to gather the full significance of this Porta limitation, and also a suggestion concerning the detail work when taking advantage of it, let us picture the case of a probable word: INFANTRY.
Figure 96
A Slide for PORTA - Devised by OHAVER
┌─────────────────────────────────┐ │ A B C D E F G H I J K L M │ ┌───────────┤ ┌───────────────────────────┐ ├───────────┐ │ N O P Q │ │ T U V W X Y Z N O P Q R S │ │ V W X Y │ │ │ │ │ │ │ │ │ │ (Keys) │ │ │ │ A C E G │ │ M O Q S U W Y │ │ │ │ B D F H │ │ N P R T V X Z │ │ │ └───────────┤ └───────────────────────────┘ ├───────────┘ │ │ └─────────────────────────────────┘
Using digits 1 and 2 to mean, respectively, the first and the second half of the normal alphabet, this probable word INFANTRY has the alphabetical pattern 1 2 1 1 2 2 2 2. And, since every substitute must have been taken from the other half of the normal alphabet, it will certainly be represented in any Porta cryptogram by eight letters having the opposite alphabetical pattern: 2 1 2 2 1 1 1 1. Moreover, a pattern as long as this is not going to be found very often in any one cryptogram. The decryptor, then, may proceed as in Fig. 97. Each cryptogram letter is marked I or 2, or imagined to be so marked, and this series of digits is examined in the hope of finding a sequence 2 1 2 2 1 1 1 1. If it cannot be found, the word is not present; if it is found, it can be assumed to represent the word INFANTRY. Here, we meet with a slight difference between the procedure for Vigenère and the procedure for Porta.
Figure 97
THE PROBABLE WORD METHOD IN PORTA
Pattern of word INFANTRY: 1 2 1 1 2 2 2 2 Pattern of substitute: 2 1 2 2 1 1 1 1
The cryptogram, with pattern:
F J I D T U V S S L F F I T X M S T M E D L 1 1 1 1 2 2 2 2 2 1 1 1 1 2 2 1 2 2 1 1 1 1
Determining the KEYWORD:
.....X M S T M E D L..... I N F A N T R Y
E C A M C E C A F D B N D F D B D A N C E
In Vigenère, we found it possible to discover the key by simply taking the probable word and deciphering with it. In Porta, we cannot do this. We must first pair the two letters, that is, a supposed substitute with its supposed original, and then find out what key would cause this. In the figure, for instance, we have a sequence _X M S T_, assumed to represent _I N F A_. The first corresponding pair is _X_ = _I_. If we are using the tableau of Fig. 94, one of these letters, _I_, is never found anywhere except in the 9th column. We find the _I_-column, and trace down until we find _X_; the key, in this case, must be _E_ or _F_, The next corresponding pair of letters (_M_ representing _N_) demands that we find the _M_-column and trace down to _N_; key _C_ or _D_. The third pair (_S_ representing _F_) demands that we find the _F_-column, and trace down to _S_; key _A_ or _B_. The fourth pair (_T_ representing _A_) demands that we find the _A_-column, and trace down to _T_; key _M_ or _N_.
Using the slide of Fig. 96: Place _X_ and _I_ together, and note that the key-letters standing below the index (stationary _A_) are _EF_. Place _M_ and _N_ together, and note key-letters _CD_. Place _S_ and _F_ together, and note key-letters _AB_. Place _T_ and _A_ together, and note key-letters _MN_. From the recovered pairs of key-letters, we are to select one each in order to recover the key-word, using somewhat the logic we might apply in dealing with a key-phrase cryptogram. In the given case, where we need the two vowels to form any word at all, it is not difficult to surmise that the key-word was DANCE. It might not be so easy to decide as between EAST and FATS; but key-words, as a rule, are seldom so short as those we have been using, and the longer the word, the fewer the possibilities. Concerning keys, however, there is one contingency which may have to be considered: The various modernized versions of this tableau are not always duplicates. The cipher alphabets will be the same as those given here; but where we have caused these to shift in the normal direction, another tableau may show them shifting in reverse. The first alphabet will be the same as here, but the second, still showing key-letters _CD_, will show its lower half beginning _Z N O P_. . . ; the third, still showing key-letters _EF_, will show its lower half beginning _Y Z N O P_. . . ; and so on. The recovery of the key-word, of course, is not vital.
* * *
Coming now to the two ciphers which are called Beaufort, we return to a tableau so closely resembling Vigenère’s tableau that the two can be used interchangeably. Fig. 98 shows only enough of the Beaufort tableau to bring out the difference in form. Here, we find no separate plaintext alphabet and no separate key-alphabet. Those which form the square have been lengthened by repeating their first letters; and a 27th alphabet, added at the bottom of the tableau, repeats the alphabet shown at the top. In this way, we have a 27 x 27 alphabet square in which _all four of the outside alphabets are exactly alike_. These ciphers, also, make use of a key-word, applied as in Vigenère and in Porta. As Sir Francis Beaufort himself is said to have used the tableau, the encipherment of a given plaintext-letter, using a given key-letter, was accomplished as follows: To encipher plaintext _S_ with key _C_, find the letter _S_ in any one of the four outside alphabets, trace into the square along the _S_-column (or row) as far as the key-letter _C_; at that point, turn a right angle, in either direction, and trace outward along that row (or column), emerging from the square at the substitute, which, in the given case, is _K_. Or: To _decipher_ _K_ with key _C_, begin with _K_, and _follow identically the encipherment process_, emerging this time at the plaintext letter, _S_. This process we have called the _true Beaufort_ cipher. Notice that we have _reciprocal encipherment_; encipherment and decipherment are identically the same thing.
Figure 98
Upper Portion of the BEAUFORT Tableau
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 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 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 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 A B C D E F G H I J K L M.... (Etc.) ....W X Y Z A B C D E
There are no external alphabets. The four outer alphabets of the square are exactly alike, with A in each of the four corners.
TRUE BEAUFORT Encipherment VARIANT BEAUFORT Encipherment
Key: C O M E T C O M E T C O Key: C O M E T C O M E T C O Plaintext: S E N D S U P P L I E S Plaintext: S E N D S U P P L I E S Cipher: K K Z B B I Z X T L Y W Cipher: Q Q B Z Z S B D H P C E
As to the companion cipher, the student will promptly have guessed this for himself: Instead of starting with the plaintext-letter, _S_, and tracing inward to the key-letter, it is entirely feasible to begin with key-letter _C_ and trace inward to the plaintext-letter _S_, emerging at _Q_ instead of at _K_. This cipher, too, is called Beaufort, since its method of accomplishment is Beaufort’s method. But there is a difference in the two resulting ciphers; notice here that the encipherment is no longer reciprocal; should we start at key-letter _C_, trace inward to the new cipher-letter, _Q_, and then trace outward, we do not emerge from the square at the plaintext letter _S_, but at _O_, an entirely new letter. In order to distinguish the two ciphers, we have referred to this second process as the _variant Beaufort_, or sometimes, more briefly, as “the variant.” There is some justification, also, for calling it the “Vigenère-Beaufort.” To see why, the student may turn back to his Vigenère tableau, and actually perform the encipherment, using only the two sides of this tableau in which the alphabets run from _A_ to _Z_.
In applying the variant encipherment, in which key-letters are found first, he need find a given key-letter but once, then lay a ruler along the row (or column) indicated by that key-letter, and encipher at a single writing all plaintext letters which are going to have that particular key. But if, as previously recommended, he has familiarized himself with the use of the Vigenère tableau, he will see instantly that the operation which, in the variant Beaufort he is calling _encipherment_, is identical, in every particular, with the operation which, in Vigenère, he would have called _decipherment_, and that, in order to decipher the variant, he must perform the operation which, in Vigenère, is called encipherment. Neither of these operations provides a reciprocal substitution; instead, they are reciprocal to each other. Once it is seen that this is true, it becomes equally plain that the Saint-Cyr slide serves just as well for the variant as for the Vigenère. To make use of it in applying the variant encipherment, set key-letters below index-letter _A_, exactly as if making ready to encipher in Vigenère, but reverse the functions of the two alphabets; that is, find all plaintext letters in the lower one, and take their substitutes from the upper one.
Figure 99
How to find the C-alphabet of each Beaufort
TRUE BEAUFORT VARIANT BEAUFORT
Key: C C C C C C C C Key: C C C C C C C C Plaintext: A B C D E F G H... Plaintext: A B C D E F G H... Cipher ALPHABET: C B A Z Y X W V... Cipher ALPHABET: Y Z A B C D E F...
Now, consider the true Beaufort cipher: Here, plaintext letters are found first, and keys are found by tracing into the square, so that encipherment is more or less a letter-by-letter process, and hardly so convenient as in the other two ciphers. It is true that every ascending diagonal in the tableau is made up of only one key-letter, so that a ruler, laid diagonally across this tableau, will point out a whole line of _C_’s, or _O_’s, or _M_’s. But practically every one of these diagonals is broken into two portions, so that in attempting to encipher by one key-letter at a time, we find it rather confusing to make the necessary adjustments. Is there not, then, a more convenient method for applying the Beaufort? Every cipher of this family, remember, provides a certain number of individual simple substitution cipher-alphabets. For every key (whether it is a letter or a number) there is some kind of cipher alphabet showing a substitute for _A_, a substitute for _B_, a substitute for _C_, and so on. To isolate one of these cipher alphabets, and find out what it is like, we have merely to take some one key-letter (or some one key-number) and discover what these substitutes are, and what their order is; that is, we need merely _encipher the normal alphabet_, using this one key. This is true of every cipher of the multiple-alphabet type. The process can be seen in Fig. 99, where the _C_-alphabet (that is, the alphabet governed by key-letter _C_) is being isolated for each of the Beaufort ciphers.
In the Beaufort proper, we find that the _C_-alphabet will begin with _C_ and come out in the order _C B A Z Y X_. . . . , which is merely the normal alphabet reversed. Should we investigate the _D_-alphabet, we should find that this begins at _D_ and comes out in the order _D C B A Z Y_. . . . , again the normal alphabet reversed; or, investigating the _E_-alphabet, we should find _E D C B A Z_. . . . , always the normal alphabet written backward, and always beginning with whatever letter is called the key. This being the case, it becomes quite evident that a slide is possible, and the formation of this slide is clearly indicated in the left-hand tabulation of the figure: Its upper alphabet must run in one direction and its lower alphabet in the other; if one of the two is made of double length, it becomes possible to place any one of the 26 key-letters in juxtaposition with index _A_, thus bringing into position any one of the 26 cipher-alphabets which are governed by these keys. Nor does it make a particle of difference which of the two _A_’s, the upper or the lower, is regarded as the index-letter; when _C_ is standing below _A_, then _A_ is also standing below _C_. We saw, in the tableau itself, that the true Beaufort encipherment gives reciprocal substitution. This, however, was not our first meeting with one of the Beaufort alphabets; in Chapter IX, we met the _Z_-alphabet. We saw there that whenever a cipher alphabet is merely the plaintext alphabet written backward, it makes no difference which of the two is called a cipher alphabet; we may see here that this fact is not altered by shifting one of the alphabets. Since a slide is possible, it follows that a disk is also possible. This particular cipher disk, on which one alphabet runs forward and the other backward, was used long ago in our own army, and is widely known in this country as “The United States Army Cipher Disk.” Most persons, apparently, prefer the slides, on which the letters are always right-side up, and the preparation of which does not involve the division of a circle into 26 equal arcs. Of those who prefer the disks, practically all will make the smaller disk _reversible_, with the normal alphabet on one side and the reversed alphabet on the other.
Figure 100
A Pair of COMPLEMENTARY Alphabets:
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 A Z Y X W V U T S R Q P O N M L K J I H G F E D C B
By doubling the length of one or the other of these two alphabets, we may use them to form a slide which will encipher and decipher the true BEAUFORT.
Now, returning to our Fig. 99, and examining its right-hand tabulation: We find that, in isolating the _C_-alphabet of the variant Beaufort, we have merely reproduced the _Y_-alphabet of the Vigenère. Should we now isolate its _Y_-alphabet, we should find that we have obtained the _C_-alphabet of the Vigenère. Further investigation will show that the _D_-alphabet of one is the _X_-alphabet of the other, that the _E_-alphabet of one is the _W_-alphabet of the other; and so on. Only their _A_-alphabets and their _N_-alphabets are keyed alike. Thus we seem to have here a case of “reciprocal” key-letters. These particular pairs of corresponding letters, _B_ and _Z_, _C_ and _Y_, _D_ and _X_, and so on, are called _complements_, one letter of each pair being _complementary_ to the other. Since the letters _A_ and _N_ have no complements (or serve as their own complements), the normal alphabet will furnish only twelve such pairs, and these are shown complete in Fig. 100. In this same set-up, it can be seen that the _A_-alphabet of the Beaufort cipher is the complement of the normal alphabet. Thus, having provided ourselves with a Beaufort slide (or disk), we have always at hand a means for finding out the complements of letters. Once it is clearly understood that the chief difference between a Vigenère cryptogram and a variant cryptogram lies in the names of their respective cipher alphabets, it becomes evident that we might decrypt a variant, believing it to be a Vigenère, and have no trouble whatever in reading its message, though finding that it has an _incoherent key_. Vigenère keys, of course, can be incoherent; occasionally they are based in some way on numbers, following the Gronsfeld scheme. But usually, this is not true; the incoherency is only apparent, and a little investigation will discover what the trouble is. In the case just mentioned, the variant key-word COMET will come out in Vigenére as _Y M O W H_, or vice versa; all that is necessary, in order to discover the original key-word, is to set the Beaufort slide at the _A_-alphabet, and perform a bit of simple substitution. Another cause for the apparently incoherent key lies in the use of some other index-letter than the stationary _A_. Say, for instance, that the encipherer has used the key-word COMET, but has placed his key-letters beneath index _D_. The key recovered by the decryptor is _Z L J B Q_; to find the original key-word, he need merely “run it down the alphabet.”
Figure 101
Applying a PROBABLE WORD to BEAUFORT (a) Cryptogram, TRUE BEAUFORT: K K Z B B I Z X T L Y W T Q
Probable word.......... S C C R T T A R P L D Q O L I U E T V V C T R N F S Q N K P O Q Q X O M I A N L I F P Q . . . M I A N . I . L E I T E C S O
Use the word SUPPLIES as a trial key, exactly as in Vigenère, but make use of the VARIANT method, and not tho TRUE BEAUFORT.
*** *** (b) Cryptogram, VARIANT BEAUFORT: Q Q B Z Z S B D H P C E H K
Probable word............. S Y Y J H H A J L P X K M P S U W H F F Y H J N V I K N Q P M K K D M O S A N P S V P . . . . O S . N . P . L W I H E Y S M
This was deciphered as a Vigenère, and showed the repeating of a scrambled key: Y M O W H. Had it been deciphered with the BEAUFORT SLIDE, suggested in Figure 100, it would have reproduced the plaintext keyword, C O M E T.
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.