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Chain Reductions for Multi-signatures and the HBMS Scheme

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Advances in Cryptology – ASIACRYPT 2021 (ASIACRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13093))

Abstract

Existing proofs for existing Discrete Log (DL) based multi-signature schemes give only weak guarantees if the schemes are implemented, as they are in practice, in 256-bit groups. This is because the underlying reductions, which are mostly in the standard model and from DL, are loose. We show that relaxing either the model or the assumption suffices to obtain tight reductions. Namely we give (1) tight proofs from DL in the Algebraic Group Model, and (2) tight, standard-model proofs from well-founded assumptions other than DL. We first do this for the classical 3-round schemes, namely \(\mathsf {BN} \) and \(\mathsf {MuSig} \). Then we give a new 2-round multi-signature scheme, \(\mathsf {HBMS} \), as efficient as prior ones, for which we do the same. These multiple paths to security for a single scheme are made possible by a framework of chain reductions, in which a reduction is broken into a chain of sub-reductions involving intermediate problems. Overall our results improve the security guarantees for DL-based multi-signature schemes in the groups in which they are implemented in practice.

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Acknowledgments

We thank the ASIACRYPT 2021 reviewers for their careful reading and valuable comments.

Bellare was supported in part by NSF grant CNS-1717640 and a gift from Microsoft. Dai was supported in part by a Powell Fellowship and grants of the first author.

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Authors and Affiliations

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

    Mihir Bellare & Wei Dai

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  1. Mihir Bellare
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Correspondence to Mihir Bellare or Wei Dai .

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Editors and Affiliations

  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Bellare, M., Dai, W. (2021). Chain Reductions for Multi-signatures and the HBMS Scheme. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13093. Springer, Cham. https://doi.org/10.1007/978-3-030-92068-5_22

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  • DOI: https://doi.org/10.1007/978-3-030-92068-5_22

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