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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.

The equivocation of the key for a simple substitution cipher is upper and lower hounded, when the message source is memoryless. The hounds are shown to be exponentially tight. The results are compared with random ciphering. It is observed that the exponential behavior of the equivocation of the key is not determined by the redundancy in the message source, but by the symbol probabilities which are closest in a certain sense. The title is incorrect in the IEEE version. The first word is Bounds, not Sounds.

For simple substitution ciphers an exact expression and bounds are derived for the message equivocation in terms of the key equivocation. It is established that the message equivocation approaches the key equivocation exponentially fast for discrete memoryless sources. It is observed that the exponential behavior of the message equivocation is not determined by redundancy in the message source but by either the symbol probabilities which are closest in a certain sense or the sum of the two smallest symbol probabilities.