Welcome to the resource topic for 2023/1405
Title:
Lattice-based Succinct Arguments from Vanishing Polynomials
Authors: Valerio Cini, Russell W. F. Lai, Giulio Malavolta
Abstract:Succinct arguments allow a prover to convince a verifier of the validity of any statement in a language, with minimal communication and verifier’s work. Among other approaches, lattice-based protocols offer solid theoretical foundations, post-quantum security, and a rich algebraic structure. In this work, we present some new approaches to constructing efficient lattice-based succinct arguments. Our main technical ingredient is a new commitment scheme based on vanishing polynomials, a notion borrowed from algebraic geometry. We analyse the security of such a commitment scheme, and show how to take advantage of the additional algebraic structure to build new lattice-based succinct arguments. A few highlights amongst our results are:
- The first recursive folding (i.e. Bulletproofs-like) protocol for linear relations with polylogarithmic verifier runtime. Traditionally, the verifier runtime has been the efficiency bottleneck for such protocols (regardless of the underlying assumptions).
- The first verifiable delay function (VDF) based on lattices, building on a recently introduced sequential relation.
- The first lattice-based \emph{linear-time prover} succinct argument for NP, in the preprocessing model. The soundness of the scheme is based on (knowledge)-k-R-ISIS assumption [Albrecht et al., CRYPTO'22].
ePrint: https://eprint.iacr.org/2023/1405
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