Relation With Key Size and Possible Plaintexts
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".
A tremendous number of possible messages, N, can be generated using even this limited set of characters: N = 26L, 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.
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.
Read more about this topic: Unicity Distance
Famous quotes containing the words relation with, relation, key and/or size:
“There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
—Umberto Eco (b. 1932)
“To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.”
—Henry James (1843–1916)
“They have thrown away her electric toothbrush, someone else slips
The key into the lock of her safety-deposit box
At the Crocker-Anglo Bank; her seat at the cricket matches
Is warmed by buttocks less delectable than hers.”
—Randall Jarrell (1914–1965)
“There are obvious places in which government can narrow the chasm between haves and have-nots. One is the public schools, which have been seen as the great leveler, the authentic melting pot. That, today, is nonsense. In his scathing study of the nation’s public school system entitled “Savage Inequalities,” Jonathan Kozol made manifest the truth: that we have a system that discriminates against the poor in everything from class size to curriculum.”
—Anna Quindlen (b. 1952)