New Combinatorial Bounds for Authentication Codes and Key Predistribution Schemes

This paper provides new combinatorial bounds and characterizations of authentication codes (A-codes) and key predistribution schemes (KPS). We first prove a new lower bound on the number of keys in an A-code without secrecy, which can be thought of as a generalization of the classical Rao bound for orthogonal arrays. We also prove a new lower bound on the number of keys in a general A-code, which is based on the Petrenjuk, Ray-Chaudhuri and Wilson bound for t-designs. We also present new lower bounds on the size of keys and the amount of users' secret information in KPS, the latter of which is accomplished by showing that a certain A-code is hiding inside any KPS.