On a fallacious bound for authentication codes (Q1304974)

An authentication code provides a way to transmit information over an insecure channel. A possible attack by an opponent is to try to deceive the receiver by replacing the legitimate message by a different one, hoping the receiver will accept it as valid. For this so-called substitution attack one can compute the probability of success. A lower bound on this probability was derived in \textit{M. De Soete} [J. Cryptology 3, No. 3, 173-186 (1991; Zbl 0739.94010)]. In the current paper it is shown that the lower bound by De Soete is false. Firstly, the authors introduce a small counterexample. Then the flaw in the original proof by De Soete is spotted and corrected, resulting in a new lower bound. Finally, some published results from the theory of authentication codes and secret sharing schemes, that were originally based on the flawed bound by De Soete, are corrected.