Bounds on key appearance equivocation for substitution ciphers
The average conditional entropy of the key given the message and its corresponding cryptogram, H (K vertical bar 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 (S-M vertical bar M-L C-L) 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 Sm 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.
known plaintext attack simple substitution ciphers key equivocation memoryless message source message equivocation