Expected loss bounds for authentication in constrained channels

We derive bounds on the expected loss for authenti-cation protocols in channels which are constrained due to noisyconditions and communication costs. This is motivated by anumber of authentication protocols, where at least some partof the authentication is performed during a phase, lasting nrounds, with no error correction. This requires assigning anacceptable threshold for the number of detected errors andtaking into account the cost of incorrect authentication andof communication. This paper describes a framework enablingan expected loss analysis for all the protocols in this family.Computationally simple methods to obtain nearly optimal valuesfor the threshold, as well as for the number of rounds aresuggested and upper bounds on the expected loss, holdinguniformly, are given. These bounds are tight, as shown by amatching lower bound. Finally, a method to adaptively selectboth the number of rounds and the threshold is proposed for acertain class of protocols