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CRYPTO 2020: Advances in Cryptology – CRYPTO 2020 pp 500–529Cite as

Lattice-Based Blind Signatures, Revisited

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12171)

Abstract

We observe that all previously known lattice-based blind signature schemes contain subtle flaws in their security proofs (e.g., Rückert, ASIACRYPT ’08) or can be attacked (e.g., BLAZE by Alkadri et al., FC ’20). Motivated by this, we revisit the problem of constructing blind signatures from standard lattice assumptions.

We propose a new three-round lattice-based blind signature scheme whose security can be proved, in the random oracle model, from the standard SIS assumption. Our starting point is a modified version of the (insecure) BLAZE scheme, which itself is based Lyubashevsky’s three-round identification scheme combined with a new aborting technique to reduce the correctness error. Our proof builds upon and extends the recent modular framework for blind signatures of Hauck, Kiltz, and Loss (EUROCRYPT ’19). It also introduces several new techniques to overcome the additional challenges posed by the correctness error which is inherent to all lattice-based constructions.

While our construction is mostly of theoretical interest, we believe it to be an important stepping stone for future works in this area.

Keywords

  • Blind signatures
  • Forking lemma
  • Lattices

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Notes

  1. 1.

    ROS stands for Random inhomogenities in an Overdetermined, Solvable system of linear equations.

  2. 2.

    It is not even clear how much better our scheme performs compared to generic constructions using non-interactive zero-knowledge proofs [23].

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Acknowledgments

We would like to thank Vadim Lyubashevsky for pointing out the flaw in BLAZE and Dominique Schröder for helping us with previous work on blind signatures. We are furthermore very grateful for the anonymous comments by the CRYPTO 2020 reviewers. Eduard Hauck was supported by DFG SPP 1736 Big Data. Eike Kiltz was supported by the BMBF iBlockchain project, the EU H2020 PROMETHEUS project 780701, DFG SPP 1736 Big Data, and the DFG Cluster of Excellence 2092 CASA. Ngoc Khanh Nguyen was supported by the SNSF ERC Transfer Grant CRETP2-166734 FELICITY. Julian Loss was supported by the financial assistance award 70NANB19H126 from U.S. Department of Commerce, National Institute of Standards and Technology.

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Authors and Affiliations

  1. Ruhr-Universität Bochum, Bochum, Germany

    Eduard Hauck & Eike Kiltz

  2. University of Maryland, College Park, USA

    Julian Loss

  3. ETH Zurich, Zürich, Switzerland

    Ngoc Khanh Nguyen

  4. IBM Research, Zurich, Rüschlikon, Switzerland

    Ngoc Khanh Nguyen

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  1. Eduard Hauck
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Correspondence to Eduard Hauck .

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  1. UC San Diego, La Jolla, CA, USA

    Daniele Micciancio

  2. Cornell Tech, New York, NY, USA

    Thomas Ristenpart

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Hauck, E., Kiltz, E., Loss, J., Nguyen, N.K. (2020). Lattice-Based Blind Signatures, Revisited. In: Micciancio, D., Ristenpart, T. (eds) Advances in Cryptology – CRYPTO 2020. CRYPTO 2020. Lecture Notes in Computer Science(), vol 12171. Springer, Cham. https://doi.org/10.1007/978-3-030-56880-1_18

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