Unicity distance is a term used in cryptography referring to the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key, there should be just one decipherment that makes sense. Cryptography has had a long and colourful history. ... This article is about algorithms for encryption and decryption. ... The EFFs US$250,000 DES cracking machine contained over 18,000 custom chips and could brute force a DES key in a matter of days — the photograph shows a DES Cracker circuit board fitted with several Deep Crack chips In cryptanalysis, a brute force attack is a method... A key is a piece of information that controls the operation of a cryptography algorithm. ...

Consider an attack on the ciphertext string "WNAIW" encrypted using a Vigenere cipher with a five letter key. Conceivably, this string could be deciphered into any other string — RIVER and WATER are both possibilities for certain keys. This is a general rule of cryptanalysis: with no additional information it is impossible, even in theory, to decode this message. The Vigenère cipher is named for Blaise de Vigenère (pictured), although the cipher had been invented earlier by Giovan Batista Belaso. ... Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ...

Of course, even in this case, only a certain number of five letter keys will result in English words. Trying all possible keys we will not only get RIVER and WATER, but SXOOS and KHDOP as well. The number of "working" keys will likely be very much smaller than the set of all possible keys. The problem is knowing which of these "working" keys is the right one; the rest are spurious.

In general, given any particular assumptions about the size of the key and the number of possible messages, there is an average ciphertext length where there is only one key (on average) that will generate a readable message. In the example above we see only upper case Roman characters, so if we assume this is the input then there are 26 possible letters for each position in the string. Likewise if we assume five-character upper case keys, there are K=26⁵ possible keys, of which the majority will not "work". Majuscules or capital letters (in the Roman alphabet: A, B, C, ...) are one type of case in a writing system. ... Jump to: navigation, search The Latin alphabet, also called the Roman alphabet, is the most widely used alphabetic writing system in the world today. ...

A tremendous number of possible messages, N, can be generated using even this limited set of characters: N = 26^L, where L is the length of the message. However only a smaller set of them is readable plaintext due to the rules of the language, perhaps M of them, where M is likely to be very much smaller than N. Moreover M has a one-to-one relationship with the number of keys that work, so given K possible keys, only K × (M/N) of them will "work". One of these is the correct key, the rest are spurious. The plain text term has a different meaning. ...

Since N is dependent on the length of the message L, whereas M is dependent on the number of keys, K, there is some L where the number of spurious keys is zero. This L is the unicity distance.

External links

• Bruce Schneier: How to Recognize Plaintext (Crypto-Gram Newsletter December 15, 1998)