Deception in authentication channels with multiple usage

By considering a simple but very general authentication code, we obtain some lower bounds on the probability of successful deception, through impersonation or substitution, if an authentication channel is used without a change of key after each message. In particular an authentication scheme proposed by Johanssen (see Designs, Codes and Cryptography, vol.4, p.69-81, 1994) is analysed, and found to be extremely vulnerable in multiple usage.