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Practical Sublinear Proofs for R1CS from Lattices

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13508))

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Abstract

We propose a practical sublinear-size zero-knowledge proof system for Rank-1 Constraint Satisfaction (R1CS) based on lattices. The proof size scales asymptotically with the square root of the witness size. Concretely, the size becomes 2–3 times smaller than Ligero (ACM CCS 2017), which also exhibits square root scaling, for large instances of R1CS. At the core lies an interactive variant of the Schwartz-Zippel Lemma that might be of independent interest.

This work is supported by the EU H2020 ERC Project 101002845 PLAZA.

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Notes

  1. 1.

    In particular, [ALS20, ENS20] computed that for \(q \approx 2^{32}\), the maximum probability for each coefficient of \(c \bmod X^4-\zeta ^{8j+4}\) is around \(2^{-31.4}\).

  2. 2.

    We provide more background on commitment schemes in the full version.

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Authors and Affiliations

  1. IBM Research Europe, Rüschlikon, Switzerland

    Ngoc Khanh Nguyen & Gregor Seiler

  2. ETH Zurich, Zürich, Switzerland

    Ngoc Khanh Nguyen

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  1. Ngoc Khanh Nguyen
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  2. Gregor Seiler
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Correspondence to Gregor Seiler .

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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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Nguyen, N.K., Seiler, G. (2022). Practical Sublinear Proofs for R1CS from Lattices. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13508. Springer, Cham. https://doi.org/10.1007/978-3-031-15979-4_5

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