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PI-Cut-Choo and Friends: Compact Blind Signatures via Parallel Instance Cut-and-Choose and More

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13509))

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Abstract

Blind signature schemes are one of the best-studied tools for privacy-preserving authentication. Unfortunately, known constructions of provably secure blind signatures either rely on non-standard hardness assumptions, or require parameters that grow linearly with the number of concurrently issued signatures, or involve prohibitively inefficient general techniques such as general secure two-party computation.

Recently, Katz, Loss and Rosenberg (ASIACRYPT’21) gave a technique that, for the security parameter n, transforms blind signature schemes secure for \(O(\log n)\) concurrent executions of the blind signing protocol into ones that are secure for any \(\textsf{poly}(n)\) concurrent executions.

This transform has two drawbacks that we eliminate in this paper: 1) the communication complexity of the resulting blind signing protocol grows linearly with the number of signing interactions; 2) the resulting schemes inherit a very loose security bound from the underlying scheme and, as a result, require impractical parameter sizes.

In this work, we give an improved transform for obtaining a secure blind signing protocol tolerating any \(\textsf{poly}(n)\) concurrent executions from one that is secure for \(O(\log n)\) concurrent executions. While preserving the advantages of the original transform, the communication complexity of our new transform only grows logarithmically with the number of interactions. Under the CDH  and RSA  assumptions, we improve on this generic transform in terms of concrete efficiency and give (1) a BLS-based blind signature scheme over a standard-sized group where signatures are of size roughly 3 KB and communication per signature is roughly 120 KB; and (2) an Okamoto-Guillou-Quisquater-based blind signature scheme with signatures and communication of roughly 9 KB and 8 KB, respectively.

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Notes

  1. 1.

    We instantiate \(\textsf{PRF}\) efficiently using random oracles [18].

  2. 2.

    In a different context, namely secure multi-party computation, the combination of puncturable pseudorandom functions and cut-and-choose has been used before.

  3. 3.

    If we rely on these proof systems, our scheme can be proven secure assuming that both the RSA assumption and either of these assumptions hold.

  4. 4.

    Note that without this optimization, the security loss would be exponential in K.

  5. 5.

    In our concrete instantiation, \(\log (K) \approx 6.5\).

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Authors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Lucjan Hanzlik, Julian Loss & Benedikt Wagner

  2. Brown University, Providence, RI, 02906, USA

    Rutchathon Chairattana-Apirom & Anna Lysyanskaya

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  1. Rutchathon Chairattana-Apirom
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Correspondence to Benedikt Wagner .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Chairattana-Apirom, R., Hanzlik, L., Loss, J., Lysyanskaya, A., Wagner, B. (2022). PI-Cut-Choo and Friends: Compact Blind Signatures via Parallel Instance Cut-and-Choose and More. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13509. Springer, Cham. https://doi.org/10.1007/978-3-031-15982-4_1

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