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In analogy to the well - known notion of finite - state compressibility of individual sequences, due to Lempel and Ziv, the authors define a similar notion of "Finite - state encryptability" of an individual plain-text sequence, as the minimum asymptotic key rate that must be consumed by finite - state encrypters so as to guarantee perfect secrecy in a well - defined sense. Their main basic result is that the finite - state encryptability is equal to the finite - state compressibility for every individual sequence. This is in parallelism to Shannon's classical probabilistic counterpart result, asserting that the minimum required key rate is equal to the entropy rate of the source.
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