Error probabilities for simple substitution ciphers

Unlike recent works by Blom and Dunham on simple substitution ciphers, papers, we do not consider equivocations (conditional entropies given the cryptogram) but rather the probability that the enemy makes an error when he tries to decipher the cryptogram or to identify the key by means of optimal identification procedures. This approach is suggested by the usual approach to coding problems taken in Shannon theory, where one evaluates error probabilities with respect to optimal encoding-decoding procedures. The main results are asymptotic; the same relevant parameters are obtained as in Blom or Dunham.