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When Messages Are Keys: Is HMAC a Dual-PRF?

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14083))

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Abstract

In Internet security protocols including TLS 1.3, KEMTLS, MLS and Noise, \(\textsf{HMAC}\) is being assumed to be a dual-PRF, meaning a PRF not only when keyed conventionally (through its first input), but also when “swapped” and keyed (unconventionally) through its second (message) input. We give the first in-depth analysis of the dual-PRF assumption on \(\textsf{HMAC}\). For the swap case, we note that security does not hold in general, but completely characterize when it does; we show that \(\textsf{HMAC}\) is swap-PRF secure if and only if keys are restricted to sets satisfying a condition called feasibility, that we give, and that holds in applications. The sufficiency is shown by proof and the necessity by attacks. For the conventional PRF case, we fill a gap in the literature by proving PRF security of \(\textsf{HMAC}\) for keys of arbitrary length. Our proofs are in the standard model, make assumptions only on the compression function underlying the hash function, and give good bounds in the multi-user setting. The positive results are strengthened through achieving a new notion of variable key-length PRF security that guarantees security even if different users use keys of different lengths, as happens in practice.

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Acknowledgments

Bellare was supported in part by NSF grant CNS-2154272 and KACST.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Matilda Backendal, Felix Günther & Matteo Scarlata

  2. Department of Computer Science and Engineering, University of California, San Diego, USA

    Mihir Bellare

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  1. Matilda Backendal
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  2. Mihir Bellare
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Correspondence to Matilda Backendal .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Backendal, M., Bellare, M., Günther, F., Scarlata, M. (2023). When Messages Are Keys: Is HMAC a Dual-PRF?. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14083. Springer, Cham. https://doi.org/10.1007/978-3-031-38548-3_22

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