Paper 2022/941
Lattice-Based SNARKs: Publicly Verifiable, Preprocessing, and Recursively Composable
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.
Metadata
- Available format(s)
- Category
- Cryptographic protocols
- Publication info
- A major revision of an IACR publication in CRYPTO 2022
- Keywords
- lattice-based cryptographysnarkvector commitmentfunctional commitment
- Contact author(s)
- valerio cini @ ait ac at
- History
- 2023-02-08: last of 2 revisions
- 2022-07-20: received
- See all versions
- Short URL
- https://ia.cr/2022/941
- License
-
CC0
BibTeX
@misc{cryptoeprint:2022/941, author = {Martin R. Albrecht and Valerio Cini and Russell W. F. Lai and Giulio Malavolta and Sri AravindaKrishnan Thyagarajan}, title = {Lattice-Based {SNARKs}: Publicly Verifiable, Preprocessing, and Recursively Composable}, howpublished = {Cryptology {ePrint} Archive, Paper 2022/941}, year = {2022}, url = {https://eprint.iacr.org/2022/941} }