Paper 2014/441

Improved Generic Attacks Against Hash-based MACs and HAIFA

Itai Dinur and Gaëtan Leurent


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 \emph{et al.} and Peyrin \emph{et al.}. These results have shown that such powerful attacks require much less than $2^{\ell}$ computations, contradicting the common belief (where $\ell$ 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 $2^{4\ell/5}$. 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.

Available format(s)
Secret-key cryptography
Publication info
A major revision of an IACR publication in CRYPTO 2014
Hash functionsMACHMACMerkle-DamgårdHAIFAstate-recovery attackuniversal forgery attackGostStreebogSHA family.
Contact author(s)
gaetan leurent @ normalesup org
2014-06-14: revised
2014-06-13: received
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Short URL
Creative Commons Attribution


      author = {Itai Dinur and Gaëtan Leurent},
      title = {Improved Generic Attacks Against Hash-based MACs and HAIFA},
      howpublished = {Cryptology ePrint Archive, Paper 2014/441},
      year = {2014},
      note = {\url{}},
      url = {}
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