The theory of polyalphabetical substitution is as follows: The encipherer has at his disposal several simple substitution alphabets, usually 26. He uses one such alphabet to encipher only one letter; for the next letter, he may use another cipher alphabet; for the third letter, a third alphabet; and so on, until some preconcerted plan has been followed out. The earliest known ciphers of this kind, the Porta (1563) and the Vigenère (1586), made use of a chart, or tableau, on which all of the available cipher alphabets were written out in full one below another. The Gronsfeld cipher (1655) used a purely mental encipherment plan; but the Beaufort ciphers, arriving two hundred years later (1857), again made use of a tableau, and something of the same idea survives in the use of strips; that is, a set of long narrow cards, each card carrying a simple substitution key. Slides, however, must have been in use near the time of Beaufort, since the best-known of the slide-ciphers, the Saint-Cyr, was being taught in 1880 at the French military school from which it takes its name. As to cipher disks, these appear to have been known even in Porta’s time, and have passed through many complications, though it has not been a great many years since a very simple disk was in use in our own army. (A drawing of the United States Army Cipher Disk may be seen in Webster’s New International Dictionary.)
To know thoroughly any one of these ciphers is to understand the fundamental principles of all, and we are going to base our studies chiefly upon the Vigenère, most perfect of the simpler types, and the basis upon which others have been founded. Fig. 85 shows, in full, the Vigenère tableau, or “alphabet square.” The alphabet standing horizontally across the top of this figure is the plaintext alphabet, and serves for the whole tableau. Below this, and parallel to it, are the 26 “Caesar” alphabets, the first one being a duplicate of the plaintext alphabet, while the remaining 25 have been shifted, one letter at a time, until the last one begins with Z. These are the 26 available cipher alphabets, and each one is named according to its first letter, which is also spoken of as its key. Thus, the key-letter A points out the A-alphabet; the key-letter B points out the B-alphabet, and so on. The alphabet standing vertically on the left side of the tableau is merely a list of these key-letters, and so is called the key-alphabet. Except where cipher machines are employed, the ordinary plan of encipherment does not make use of the full 26 available cipher alphabets; only a few of these are used, and these few are taken always in a given rotation, so that the cipher becomes periodic. If the rotation includes, say, twelve of the cipher alphabets (whether or not these are all different), the cryptograms are said to have a period of 12. (The word “cycle” is also used in this connection.) Since each letter of the normal alphabet is the key to one of the Vigenère cipher alphabets, the encipherer, wishing to make use of several different cipher alphabets, is able to remember their sequence by means of a key-word, in which each letter will point out one particular cipher alphabet. If today’s key-word is BED, only three cipher alphabets will be used, the B-alphabet, the E-alphabet, and the D-alphabet, and the cryptograms will all have a period of 3. But if, tomorrow, the key-word is changed to CONSTANTINOPLE, the complete rotation will include fourteen alphabets, and the cryptograms will have a period of 14.
| Figure 85 THE VIGENÈRE 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 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 B 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 C 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 D 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 E 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 F 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 G 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 H 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 I 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 J 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 K 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 L 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 M 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 N 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 O 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 P 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 Q 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 R 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 S 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 T 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 U 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 V 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 W 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 X 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 Y 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 Z 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 |
To make use of a cipher alphabet, say the B-alphabet, we may lay a ruler across the tableau in such a way that this one alphabet is pointed out. Then, to encipher any letter, as S, we may find this letter, S, in the plaintext alphabet at the top, and trace down its column as far as the B-alphabet which is being pointed out by the ruler; we find that the substitute, in this alphabet, is T. Or, wishing to decipher T, we find this letter in the B-alphabet and trace upward to the plaintext alphabet in order to find that its original is S. While the foregoing explains the principle, it has not been expressed in the usual language. Where we have mentioned the use of the B-alphabet, it is much commoner to hear that a certain letter has been enciphered or deciphered “with key-letter B,” and the usual description of the encipherment will be somewhat as follows: To encipher S by B, find S in the plaintext alphabet, find B in the key-alphabet, and use the substitute which is found at the intersection of the S-column with the B-row. Or: To decipher T by B, first find the key-letter B, trace horizontally to the right as far as the cipher-letter T, then trace upward to its original, S. This, we believe, is the original description, as explained by Blaise de Vigenère himself, and the original encipherment plan was that indicated in Fig. 86. The message of this figure is SEND SUPPLIES TO MORLEY’S STATION. The key-word, BED, has been repeated often enough to pair one
| Figure 86 Original Method of VIGENÈRE Encipherment Key: B E D B E D B E D B E D B E D B E D B E D B E D B E D B Message: S E N D S U P P L I E S T O M O R L E Y S S T A T I O N Cipher: T I Q E W X Q T O J I V U S P P V O F C V T X D U M R O |
| Figure 87 Modern Enciphernent B E D B E D B E D S E N D S U P P L T I Q E W X Q T O I E S T O M O R L J I V U S P P V O E Y S S T A T I O F C V T X D U M R N O 5 10 15 20 25 30 T I Q E W X Q T O J I V U S P P V O F C V T X D U M R O X X |
key-letter with each text-letter, and these pairs are handled one at a time: S is enciphered by B, E is enciphered by E, N is enciphered by D, and so on, following the original description.
The modern method would be that of Fig. 87. Knowing that a great many letters are going to be enciphered by B, a great many others by E, and a great many others by D, and having no wish to preserve word-divisions, we begin by writing our plaintext into three columns (or by grouping it conveniently), and then encipher at a single writing all of those letters which are to be enciphered by any one same key-letter. That is, we apply one cipher alphabet at a time, as first explained. The modern practice will also require that the cryptogram be taken off in five-letter groups, and that the final group be made complete. This is another of those cases in which the decryptor will number his letters, as shown in the figure. The student who has not previously met the Vigenère cipher is urged to perform the two operations of encipherment and decipherment and thus familiarize himself with the use of a tableau; it is possible that in most of his subsequent reading he will find explanations based on the “columns” and “rows” of a “tableau,” when, as a matter of fact, no tableau has been used. To understand how this might be, suppose we take a look now at the Saint-Cyr cipher.