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;
| 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 |
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.
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.