Tighter bounds on entropy of secret keys in authentication codes

The traditional theory of information-theoretically secure authentication codes (A-codes) developed by Simmons and others usually assumes that a uniformly random source for truly random keys is available. However, if we consider the scenario without the assumption, previously known bounds on key-entropy are not tight. In this paper, tighter lower bounds of A-codes with non-uniformly random secret keys are investigated and derived in terms of the Rényi entropy.