Characterization of Optimal Authentication Codes with Arbitration

In this paper we study authentication codes with arbitration (A2-codes). An A2-code is called optimal if its cheating probabilities achieve their information-theoretic lower bounds, and has minimum number of keys. We give characterization of optimal A2 -codes in terms of combinatorial designs. This means that construction of optimal A2- codes is reduced to the construction of the corresponding combinatorial structures.