International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Lattice-Based SNARKs: Publicly Verifiable, Preprocessing, and Recursively Composable

Martin R. Albrecht , Information Security Group, Royal Holloway, University of London
Valerio Cini , AIT Austrian Institute of Technology
Russell W. F. Lai , Chair of Applied Cryptography, Friedrich-Alexander-Universität Erlangen-Nürnberg
Giulio Malavolta , Max Planck Institute for Security and Privacy
Sri AravindaKrishnan Thyagarajan , Carnegie Mellon University
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Conference: CRYPTO 2022
Abstract: A succinct non-interactive argument of knowledge (SNARK) allows a prover to produce a short proof that certifies the veracity of a certain NP-statement. In the last decade, a large body of work has studied candidate constructions that are secure against quantum attackers. Unfortunately, no known candidate matches the efficiency and desirable features of (pre-quantum) constructions based on bilinear pairings. In this work, we make progress on this question. We propose the first lattice-based SNARK that simultaneously satisfies many desirable properties: It (i) is tentatively post-quantum secure, (ii) is publicly-verifiable, (iii) has a logarithmic-time verifier and (iv) has a purely algebraic structure making it amenable to efficient recursive composition. Our construction stems from a general technical toolkit that we develop to translate pairing-based schemes to lattice-based ones. At the heart of our SNARK is a new lattice-based vector commitment (VC) scheme supporting openings to constant-degree multivariate polynomial maps, which is a candidate solution for the open problem of constructing VC schemes with openings to beyond linear functions. However, the security of our constructions is based on a new family of lattice-based computational assumptions which naturally generalises the standard Short Integer Solution (SIS) assumption.
Video from CRYPTO 2022
  title={Lattice-Based SNARKs: Publicly Verifiable, Preprocessing, and Recursively Composable},
  author={Martin R. Albrecht and Valerio Cini and Russell W. F. Lai and Giulio Malavolta and Sri AravindaKrishnan Thyagarajan},