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A Note on the Post-quantum Security of (Ring) Signatures

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13178))

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Abstract

This work revisits the security of classical signatures and ring signatures in a quantum world. For (ordinary) signatures, we focus on the arguably preferable security notion of blind-unforgeability recently proposed by Alagic et al. (Eurocrypt’20). We present two short signature schemes achieving this notion: one is in the quantum random oracle model, assuming quantum hardness of SIS; and the other is in the plain model, assuming quantum hardness of LWE with super-polynomial modulus. Prior to this work, the only known blind-unforgeable schemes are Lamport’s one-time signature and the Winternitz one-time signature, and both of them are in the quantum random oracle model.

For ring signatures, the recent work by Chatterjee et al. (Crypto’21) proposes a definition trying to capture adversaries with quantum access to the signer. However, it is unclear if their definition, when restricted to the classical world, is as strong as the standard security notion for ring signatures. They also present a construction that only partially achieves (even) this seeming weak definition, in the sense that the adversary can only conduct superposition attacks over the messages, but not the rings. We propose a new definition that does not suffer from the above issue. Our definition is an analog to the blind-unforgeability in the ring signature setting. Moreover, assuming the quantum hardness of LWE, we construct a compiler converting any blind-unforgeable (ordinary) signatures to a ring signature satisfying our definition.

X. Liang—Part of this work was done while visiting Max Planck Institute.

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Notes

  1. 1.

    To avoid confusion, we henceforth denote this model as CROM (“C” for “classical”).

  2. 2.

    [5] also claimed that blind-unforgeability implies one-more unforgeability. But their proof was flawed [29]. The relation between these two notions is an open problem.

  3. 3.

    Indeed, \(\mathsf {R} \) may even contain “illegitimate” or “non-existent” members faked by \(\mathcal {A} \). Note that we do not require \(\mathsf {R} \subseteq \mathcal {R}\).

  4. 4.

    Inspired by J. R. R. Tolkien. Indeed, this is a “ring” signature paper.

  5. 5.

    The N has to be super-polynomial to support rings of arbitrary polynomial size.

  6. 6.

    Of course, the challenger also needs to check if \(\mathsf {VK} _{i_0} \in \mathsf {R} \) and \(\mathsf {VK} _{i_1} \in \mathsf {R} \). But we can safely ignore this for our current discussion.

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Acknowledgments

We thank the anonymous PKC 2022 reviewers for their valuable comments.

Rohit Chatterjee and Xiao Liang are supported in part by Omkant Pandey’s DARPA SIEVE Award HR00112020026 and NSF grants 1907908 and 2028920. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, DARPA, or NSF.

Kai-Min Chung is supported by Ministry of Science and Technology, Taiwan, under Grant No. MOST 109-2223-E-001-001-MY3.

Giulio Malavolta is supported by the German Federal Ministry of Education and Research BMBF (grant 16K15K042, project 6GEM).

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Authors and Affiliations

  1. Stony Brook University, Stony Brook, USA

    Rohit Chatterjee & Xiao Liang

  2. Academia Sinica, Taipei, Taiwan

    Kai-Min Chung

  3. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta

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  1. Rohit Chatterjee
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  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

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Chatterjee, R., Chung, KM., Liang, X., Malavolta, G. (2022). A Note on the Post-quantum Security of (Ring) Signatures. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13178. Springer, Cham. https://doi.org/10.1007/978-3-030-97131-1_14

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