A Tight Bound for EMAC

We prove a new upper bound on the advantage of any adversary for distinguishing the encrypted CBC-MAC (EMAC) based on random permutations from a random function. Our proof uses techniques recently introduced in [BPR05], which again were inspired by [DGH+04] The bound we prove is tight — in the sense that it matches the advantage of known attacks up to a constant factor — for a wide range of the parameters: let n denote the block-size, q the number of queries the adversary is allowed to make and l an upper bound on the length (i.e. number of blocks) of the messages, then for l≤2n/8 and q≥l2 the advantage is in the order of q2/2n (and in particular independent of l). This improves on the previous bound of q2lΘ(1/lnln l)/2n from [BPR05] and matches the trivial attack (which thus is basically optimal) where one simply asks random queries until a collision is found