A Tight Bound for EMAC

Abstract

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 ≤ 2^n/8 and q≥ł² the advantage is in the order of q ²/2ⁿ (and in particular independent of ℓ). This improves on the previous bound of q ²ℓ^{Θ(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.