Editing Unicity distance (section)

{{Short description|Length of ciphertext needed to unambiguously break a cipher}}
{{More citations needed|date=October 2007}}

In [[cryptography]], '''unicity distance''' is 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 (cryptography)|key]], there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy.<ref name=hac>{{Cite book |title=Handbook of Applied Cryptography |author=[[Alfred J. Menezes]] |author2=[[Paul C. van Oorschot]] |author3=[[Scott A. Vanstone]] |chapter=Chapter 7 - Block Ciphers |page=246 |url=http://cacr.uwaterloo.ca/hac/ |chapter-url=http://cacr.uwaterloo.ca/hac/about/chap7.pdf }}</ref>

[[Claude Shannon]] defined the unicity distance in his 1949 paper "[[Communication Theory of Secrecy Systems]]".<ref>{{Cite journal |last=Deavours |first=C.A. |date=1977 |title=Unicity Points in Cryptanalysis |url=http://www.tandfonline.com/doi/abs/10.1080/0161-117791832797 |journal=[[Cryptologia]] |language=en |volume=1 |issue=1 |pages=46–68 |doi=10.1080/0161-117791832797 |issn=0161-1194|url-access=subscription }}</ref>

Consider an attack on the ciphertext string "WNAIW" encrypted using a [[Vigenère cipher]] with a five letter key. Conceivably, this string could be deciphered into any other string&mdash;RIVER and WATER are both possibilities for certain keys. This is a general rule of [[cryptanalysis]]: with no additional information it is impossible to decode this message.

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.