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, key and/or size:
“Much poetry seems to be aware of its situation in time and of its relation to the metronome, the clock, and the calendar. ... The season or month is there to be felt; the day is there to be seized. Poems beginning “When” are much more numerous than those beginning “Where” of “If.” As the meter is running, the recurrent message tapped out by the passing of measured time is mortality.”
—William Harmon (b. 1938)
“I cannot tell what I am as much afraid of, as a woman who invariably washes on Monday. It is a kind of key to character; and if her mouth is not puckered and her brow wrinkled, they will be, unless she repents.”
—Jane Grey Swisshelm (1815–1884)
“Beauty depends on size as well as symmetry. No very small animal can be beautiful, for looking at it takes so small a portion of time that the impression of it will be confused. Nor can any very large one, for a whole view of it cannot be had at once, and so there will be no unity and completeness.”
—Aristotle (384 B.C.–322 B.C.)