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Threshold Raccoon: Practical Threshold Signatures from Standard Lattice Assumptions

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Advances in Cryptology – EUROCRYPT 2024 (EUROCRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14652))

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Abstract

Threshold signatures improve both availability and security of digital signatures by splitting the signing key into N shares handed out to different parties. Later on, any subset of at least T parties can cooperate to produce a signature on a given message. While threshold signatures have been extensively studied in the pre-quantum setting, they remain sparse from quantum-resilient assumptions.

We present the first efficient lattice-based threshold signatures with signature size 13 KiB and communication cost 40 KiB per user, supporting a threshold size as large as 1024 signers. We provide an accompanying high performance implementation. The security of the scheme is based on the same assumptions as Dilithium, a signature recently selected by NIST for standardisation which, as far as we know, cannot easily be made threshold efficiently.

All operations used during signing are due to symmetric primitives and simple lattice operations; in particular our scheme does not need heavy tools such as threshold fully homomorphic encryption or homomorphic trapdoor commitments as in prior constructions. The key technical idea is to use one-time additive masks to mitigate the leakage of the partial signing keys through partial signatures.

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Notes

  1. 1.

    More precisely, we rely on the recent \(\mathsf {Hint\text {-}MLWE}_{}\) problem by Kim et al. [44] and the \(\textsf{SelfTargetMSIS}_{}\) problem underlying the security of Dilithium [43]. Both problems are known to be as hard as the \(\textsf{MLWE}_{}\) and \(\textsf{MSIS}_{}\) problems, respectively.

  2. 2.

    We choose not to do so yet as the parameters of both schemes are still subject to improvements.

  3. 3.

    This is an upper limit of the “large” requirements of NIST preliminary call for threshold [57]. Note that our parameters support any \(1 \le T \le N \le 1024\).

  4. 4.

    From a security proof perspective, a proof with rejection sampling requires slightly more work due to subtle issues [7, 32].

  5. 5.

    This step prevents the adversary from maliciously generating its commitment after learning all the honest users commitments (see for instance [9]).

  6. 6.

    See Fig. 1 for why we call it row and column masks.

  7. 7.

    This is not to be confused with [59], having the same signature name \(\textsf{Raccoon}\). While [59] also considers a variant of the Lyubashevsky’s signature scheme without rejection sampling, [58] can be viewed as a major simplification and refinement of it.

  8. 8.

    Strictly speaking, the underlying signature scheme is not \(\textsf{Raccoon}\) as we use discrete Gaussians instead of sum of uniforms. However, we attribute \(\textsf{Raccoon}\) as the core features (i.e., removing rejection sampling and optimisations) are the same.

  9. 9.

    The Threshold Raccoon implementation used to generate these benchmarking results is available to reviewers: https://anonymous.4open.science/r/ec24-thrc-F64C.

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Acknowledgement

This work has been supported in part by JSPS KAKENHI Grant Numbers JP23KJ0548 and JPMJCR22M1.

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Authors and Affiliations

  1. PQShield, Oxford, UK

    Rafael del Pino, Shuichi Katsumata, Mary Maller, Thomas Prest & Markku-Juhani Saarinen

  2. AIST, Tokyo, Japan

    Shuichi Katsumata

  3. Ethereum Foundation, Zug, Switzerland

    Mary Maller

  4. XWiki/CryptPad, Bruxelles, Belgium

    Fabrice Mouhartem

  5. Tampere University, Tampere, Finland

    Markku-Juhani Saarinen

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    Marc Joye

  2. Ruhr University Bochum, Bochum, Germany

    Gregor Leander

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del Pino, R., Katsumata, S., Maller, M., Mouhartem, F., Prest, T., Saarinen, MJ. (2024). Threshold Raccoon: Practical Threshold Signatures from Standard Lattice Assumptions. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14652. Springer, Cham. https://doi.org/10.1007/978-3-031-58723-8_8

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