Substitution Cipher - Homophonic Substitution

Homophonic Substitution

An early attempt to increase the difficulty of frequency analysis attacks on substitution ciphers was to disguise plaintext letter frequencies by homophony. In these ciphers, plaintext letters map to more than one ciphertext symbol. Usually, the highest-frequency plaintext symbols are given more equivalents than lower frequency letters. In this way, the frequency distribution is flattened, making analysis more difficult.

Since more than 26 characters will be required in the ciphertext alphabet, various solutions are employed to invent larger alphabets. Perhaps the simplest is to use a numeric substitution 'alphabet'. Another method consists of simple variations on the existing alphabet; uppercase, lowercase, upside down, etc. More artistically, though not necessarily more securely, some homophonic ciphers employed wholly invented alphabets of fanciful symbols.

An interesting variant is the nomenclator. Named after the public official who announced the titles of visiting dignitaries, this cipher combined a small codebook with large homophonic substitution tables. Originally the code was restricted to the names of important people, hence the name of the cipher; in later years it covered many common words and place names as well. The symbols for whole words (codewords in modern parlance) and letters (cipher in modern parlance) were not distinguished in the ciphertext. The Rossignols' Great Cipher used by Louis XIV of France was one; after it went out of use, messages in French archives were unbroken for several hundred years.

Nomenclators were the standard fare of diplomatic correspondence, espionage, and advanced political conspiracy from the early fifteenth century to the late eighteenth century; most conspirators were and have remained less cryptographically sophisticated. Although government intelligence cryptanalysts were systematically breaking nomenclators by the mid-sixteenth century, and superior systems had been available since 1467, the usual response to cryptanalysis was simply to make the tables larger. By the late eighteenth century, when the system was beginning to die out, some nomenclators had 50,000 symbols.

Nevertheless, not all nomenclators were broken; today, cryptanalysis of archived ciphertexts remains a fruitful area of historical research.

The Beale Ciphers are another example of a homophonic cipher. This is a fascinating story of buried treasure that was described in the 1819-21 period by use of a ciphered text that was keyed to the Declaration of Independence. Here each ciphertext character was represented by a number. The number was determined by taking the plaintext character and finding a word in the Declaration of Independence that started with that character and using the numerical position of that word in the Declaration of Independence as the encrypted form of that letter. Since many words in the Declaration of Independence start with the same letter, the encryption of that character could be any of the numbers associated with the words in the Declaration of Independence that start with that letter. Deciphering the encrypted text character X (which is a number) is as simple as looking up the Xth word of the Declaration of Independence and using the first letter of that word as the decrypted character.

Another homophonic cipher was described by Stahl and was one of the first attempts to provide for computer security of data systems in computers through encryption. In Stahl's method, since plaintext and ciphertext were stored as binary strings of digits, he constructed the cipher in such a way that the number of homophones for a given character was in proportion to the frequency of the character, thus making frequency analysis much more difficult.

The book cipher and straddling checkerboard are types of homophonic cipher.