Abstract  We suggest some simple variants of the CBC MAC that enable the efficient authentication of arbitrary-length messages. Our constructions use three keys, K1, K2, K3, to avoid unnecessary padding and MAC any message M {0,1}* using max{1, |M|/n} applications of the underlying n-bit block cipher. Our favorite construction, XCBC, works like this: if |M| is a positive multiple of n then XOR the n-bit key K2 with the last block of M and compute the CBC MAC keyed with K1; otherwise, extend Ms length to the next multiple of n by appending minimal 10 padding ( 0), XOR the n-bit key K3 with the last block of the padded message, and compute the CBC MAC keyed with K1. We prove the security of this and other constructions, giving concrete bounds on an adversarys inability to forge in terms of his inability to distinguish the block cipher from a random permutation. Our analysis exploits new ideas which simplify proofs compared with prior work.