Abstract
The average conditional entropy of the key given the message and its corresponding cryptogram, ff(K|M, C), which is refer as a key appearance equivocation, was proposed as a theoretical measure of the strength of the cipher system under a known plaintext attack by Dunham in 1980. In the same work (among other things), lower and upper bounds for H(SM |MLCL) are found and its asymptotic behavior as a function of cryptogram length L is described for simple substitution ciphers, i.e., when the key space SLambda1, Is the symmetric group acting on a discrete alphabet M. In the present paper we consider the same problem when the key space is an arbitrary subgroup K < S,M and generalize Dunham's result.
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