Improved Generic Attacks against Hash-Based MACs and HAIFA

The security of HMAC (and more general hash-based MACs) against state-recovery and universal forgery attacks was very recently shown to be suboptimal, following a series of surprising results by Leurent

et al.

and Peyrin

et al.

. These results have shown that such powerful attacks require much 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 properties of concrete hash functions such as a limited message length, and 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

4ℓ/5

. Then, we describe improved trade-offs between the message length and the complexity of a state-recovery attack on HMAC. Consequently, we obtain improved attacks on several HMAC constructions used in practice, in which the hash functions limit 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

.