Equivocations for homophonic ciphers

Abstract

Substitution ciphers can be quite weak when the probability distribution of the message letters is distinctly non-uniform. A time-honoured solution to remove this weakness is to “split” each high-probability letter into a number of “homophones” and use a substitution cipher for the resulting extended alphabet. Here the performance of a homophonic cipher is studied from a Shannon-theoretic point of view. The key and message equivocations (conditional entropies given the intercepted cryptogram) are computed both for finite-length messages and “very long” messages. The results obtained are strictly related to those found by Blom and Dunham for substitution ciphers. The key space of a homophonic cipher is specified carefully, so as to avoid misunderstandings which appear to have occurred on this subject.