Nichole Robinson
MATH 478.01
September 15, 2004
Digraphic Ciphers
In cryptography, one of the simplest ways to encode something would be by the use of a cipher. A cipher is a cryptographic system in which units of plain text of regular length, usually letters, are arbitrarily transposed or substituted according to a predetermined code. As interest and need increased, many variations of simple ciphers began to evolve. In 1563, Giovanni Battista Porta's work on cryptography entitled De furtivis notis was published. His work paved the way for many different ideas in cryptography including the first digraphic cipher. He premiered encrypting two letters into a single symbol instead of substituting letters individually. A major advantage to do this is that the frequency distribution of digraphs is much flatter than that of individual letter. Though, like the single letters e, t, a, o, n, s, and i, certain letter combinations, such as th, sh, le, and so on, occur much more frequently than other combinations increasing the frequency distribution for these sets. Another advantage digraphic ciphers have over single letter ciphers is that the number of elements available for the cryptanalyst to decode is only half of what it would be other wise. This means that if a message were quiet long (making it easier to encode with single letter frequencies) the length of the message become shortened and when encoding se, e becomes c, but in the following combination el, e becomes k. This leads to another advantage. To decode the message, a cryptanalyst would depend on a digraph frequency chart. But instead of only having 26 possibilities, there are now 26*26=676 possible combinations to keep track of. This same chart of 676 choices could also be used to encrypt messages, but many used algebraic or geometric methods over the bulky chart.
One of the earliest practical digraphic substitutions was created by Charles Wheatstone, but named after Lyon Playfair, who was a close friend of Wheatstone. Playfair first demonstrated the Playfair Cipher at a dinner in January 1854 given by Lord Granville, president of the governing council. Queen Victoria's husband, Prince Albert, and Lord Palmerston were also guests at this dinner. Both Granville and Palmerston mastered the encryption technique and wrote letters using it. The cipher was the first literal on in history to be digraphic. The first step to encrypt the message is to select a keyword. In the first line of a 5*5 square, enter the keyword from left to right skipping letters already used and continuing to the second row, or more, if necessary. After entering the keyword the other letters of the alphabet are entered in order to fill in the rest of the chart. (Note that in some ciphers a letter, such as q, is left out, or two letters, such as i and j are combine into one square) The text to be encoded is then divided into digraphs with null letters, ie x, are added to the end to make an even amount or between double letters. The three rules for enciphering are then used. 1. If both letters of the digraph lie in the same row, each letter is enciphered by the letter immediately to its right. 2. If both letters of the digraph lie in the same column, then each letter is enciphered by the letter immediately below it. 3. In the remaining case, each letter is exchanged by the letter at the intersection of its row and the other letter's column. The recipient of the Playfair Cipher would also know the keyword and thus the 5*5 square and would simply decipher it using the same rules, but in reverse.
Of course, the Playfair Cipher is only one of the many digraphic ciphers available. Each different method abides by different tools to encode and decode. Some, as mentioned before, can cut down the number of letters used. Others use more than one square with similar rules.
Regardless of the method of enciphering and deciphering the message, there are still many advantages to using a digraphic cipher to encode messages to be kept secret much longer than those that would be encoded with a single letter cipher.