Editing Unicity distance (section)

==Relation with key size and possible plaintexts==
In general, given 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]] English characters, so if we assume that the [[plaintext]] has this form, then there are 26 possible letters for each position in the string. Likewise if we assume five-character upper case keys, there are K=26<sup>5</sup> possible keys, of which the majority will not "work".

A tremendous number of possible messages, N, can be generated using even this limited set of characters: N = 26<sup>L</sup>, 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 &times; (M/N) of them will "work". One of these is the correct key, the rest are spurious.

Since M/N gets arbitrarily small as the length L of the message increases, there is eventually some L that is large enough to make the number of spurious keys equal to zero. Roughly speaking, this is the L that makes KM/N=1. This L is the unicity distance.