Bounds on message equivocation for simple substitution ciphers

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.