Prof. Itai Dinur

The security of HMAC (and more general hash-based MACs) against state-recovery and universal forgery attacks was shown to be suboptimal, following a series of results by Leurent et al. and Peyrin et al. These results have shown that such powerful attacks require significantly less than 2 ^ℓ computations, contradicting the common belief (where ℓ denotes the internal state size). In this work, we revisit and extend these results, with a focus on concrete hash functions that limit the message length, and apply special iteration modes. We begin by devising the first state-recovery attack on HMAC with a HAIFA hash function (using a block counter in every compression function call), with complexity 2 ^{4 ℓ / 5}. Then, we describe improved tradeoffs between the message length and the complexity of a state-recovery attack on HMAC with a Merkle–Damgård hash function. Consequently, we obtain improved attacks on several HMAC constructions used in practice, in which the hash functions limits the maximal message length (e.g., SHA-1 and SHA-2). Finally, we present the first universal forgery attacks, which can be applied with short message queries to the MAC oracle. In particular, we devise the first universal forgery attacks applicable to SHA-1 and SHA-2. Despite their theoretical interest, our attacks do not seem to threaten the practical security of the analyzed concrete HMAC constructions.