The exact PRF-security of NMAC and HMAC

P. Gazi, K.Z. Pietrzak, M. Rybar, in:, J. Garay, R. Gennaro (Eds.), Springer, 2014, pp. 113–130.

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Conference Paper | Published | English
Garay, Juan; Gennaro, Rosario
Series Title
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].
Publishing Year
Date Published
113 - 130
CRYPTO: International Cryptology Conference
Conference Location
Santa Barbara, USA
Conference Date
2014-08-17 – 2014-08-21

Cite this

Gazi P, Pietrzak KZ, Rybar M. The exact PRF-security of NMAC and HMAC. In: Garay J, Gennaro R, eds. Vol 8616. Springer; 2014:113-130. doi:10.1007/978-3-662-44371-2_7
Gazi, P., Pietrzak, K. Z., & Rybar, M. (2014). The exact PRF-security of NMAC and HMAC. In J. Garay & R. Gennaro (Eds.) (Vol. 8616, pp. 113–130). Presented at the CRYPTO: International Cryptology Conference, Santa Barbara, USA: Springer.
Gazi, Peter, Krzysztof Z Pietrzak, and Michal Rybar. “The Exact PRF-Security of NMAC and HMAC.” edited by Juan Garay and Rosario Gennaro, 8616:113–30. Springer, 2014.
P. Gazi, K. Z. Pietrzak, and M. Rybar, “The exact PRF-security of NMAC and HMAC,” presented at the CRYPTO: International Cryptology Conference, Santa Barbara, USA, 2014, vol. 8616, no. 1, pp. 113–130.
Gazi P, Pietrzak KZ, Rybar M. 2014. The exact PRF-security of NMAC and HMAC. CRYPTO: International Cryptology Conference, LNCS, vol. 8616. 113–130.
Gazi, Peter, et al. The Exact PRF-Security of NMAC and HMAC. Edited by Juan Garay and Rosario Gennaro, vol. 8616, no. 1, Springer, 2014, pp. 113–30, doi:10.1007/978-3-662-44371-2_7.
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