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Compact Ring Signatures from Learning with Errors

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12825))

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Abstract

Ring signatures allow a user to sign a message on behalf of a “ring” of signers, while hiding the true identity of the signer. As the degree of anonymity guaranteed by a ring signature is directly proportional to the size of the ring, an important goal in cryptography is to study constructions that minimize the size of the signature as a function of the number of ring members.

In this work, we present the first compact ring signature scheme (i.e., where the size of the signature grows logarithmically with the size of the ring) from the (plain) learning with errors (LWE) problem. The construction is in the standard model and it does not rely on a common random string or on the random oracle heuristic. In contrast with the prior work of Backes et al.  [EUROCRYPT’2019], our scheme does not rely on bilinear pairings, which allows us to show that the scheme is post-quantum secure assuming the quantum hardness of LWE.

At the heart of our scheme is a new construction of compact and statistically witness indistinguishable ZAP arguments for NP \(\cap \) coNP, that we show to be sound based on the plain LWE assumption. Prior to our work, statistical ZAPs (for all of NP) were known to exist only assuming sub-exponential LWE. We believe that this scheme might find further applications in the future.

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Acknowledgments

We thank anonymous reviewers for pointing out issues in Definition 4 and Definition 8 in an earlier version of this work.

Omkant Pandey is supported in part by DARPA SIEVE Award HR00112020026, NSF grants 1907908 and 2028920, and a Cisco Research Award.

Sanjam Garg is supported in part by DARPA under Agreement No. HR00112020026, AFOSR Award FA9550-19-1-0200, NSF CNS Award 1936826, and research grants by the Sloan Foundation and Visa Inc.

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, AFOSR, NSF, Cisco, Sloan Foundation, or Visa Inc.

Dakshita Khurana is supported in part by DARPA SIEVE Award HR00112020024.

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Authors and Affiliations

  1. Stony Brook University, Stony Brook, USA

    Rohit Chatterjee, Xiao Liang, Omkant Pandey & Sina Shiehian

  2. University of California, Berkeley, USA

    Sanjam Garg & Sina Shiehian

  3. NTT Research, Tokyo, Japan

    Sanjam Garg

  4. University of Waterloo, Waterloo, Canada

    Mohammad Hajiabadi

  5. University of Illinois Urbana-Champaign, Champaign, USA

    Dakshita Khurana

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

    Giulio Malavolta

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  1. Rohit Chatterjee
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Correspondence to Rohit Chatterjee .

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

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Chatterjee, R. et al. (2021). Compact Ring Signatures from Learning with Errors. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12825. Springer, Cham. https://doi.org/10.1007/978-3-030-84242-0_11

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  • DOI: https://doi.org/10.1007/978-3-030-84242-0_11

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