Expected loss bounds for authentication in constrained channels

We derive bounds on the expected loss for authentication protocols in channels which are constrained due to noisy conditions and communication costs. This is motivated by a number of authentication protocols, where at least some part of the authentication is performed during a phase, lasting n rounds, with no error correction. This requires assigning an acceptable threshold for the number of detected errors and taking into account the cost of incorrect authentication and of communication. This paper describes a framework enabling an expected loss analysis for all the protocols in this family. Computationally simple methods to obtain nearly optimal values for the threshold, as well as for the number of rounds are suggested and upper bounds on the expected loss, holding uniformly, are given. These bounds are tight, as shown by a matching lower bound. Finally, a method to adaptively select both the number of rounds and the threshold is proposed for a certain class of protocols.