The exact PRF-security of NMAC and HMAC

Gaži, Peter and Pietrzak, Krzysztof and Rybar, Michal (2014) The exact PRF-security of NMAC and HMAC. In: CRYPTO: International Cryptology Conference, August 17-21, 2014, Santa Barbara, CA, USA.

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Official URL: http://dx.doi.org/10.1007/978-3-662-44371-2_7

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].

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Message authentication codes, HMAC, NI, NMAC, pseudorandom functions
Subjects: 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems
000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems > 004 Data processing & computer science
Research Group: Pietrzak Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 02 Dec 2016 08:35
Last Modified: 05 Sep 2017 14:44
URI: https://repository.ist.ac.at/id/eprint/682

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