The exact PRF-security of NMAC and HMAC Conference Paper

Author(s): Gaži, Peter; Pietrzak, Krzysztof; Rybar, Michal
Title: The exact PRF-security of NMAC and HMAC
Title Series: LNCS
Affiliation IST Austria
Abstract: NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). Security proofs and attacks for NMAC can typically be lifted to HMAC. NMAC was introduced by Bellare, Canetti and Krawczyk [Crypto'96], who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto'06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: If f is an ε-secure PRF (against q queries) and a δ-non-adaptively secure PRF (against q queries), then NMAC f is an (ε+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto'99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto'05].
Keywords: Message authentication codes; HMAC; NI; NMAC; pseudorandom functions
Conference Title: CRYPTO: International Cryptology Conference
Volume: 8616
Issue 1
Conference Dates: August 17-21, 2014
Conference Location: Santa Barbara, CA, USA
Publisher: Springer  
Date Published: 2014-01-01
Start Page: 113
End Page: 130
Sponsor: This work was partly funded by the European Research Council under an ERC Starting Grant (259668-PSPC).
DOI: 10.1007/978-3-662-44371-2_7
Notes: We thank the anonymous reviewers for useful comments and suggestions.
Open access: yes (repository)
IST Austria Authors
  1. Michal Rybar
    4 Rybar
  2.  Peter Gazi
    9 Gazi
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