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Publication . Part of book or chapter of book . Conference object . 2019

Algebraic Techniques for Short(er) Exact Lattice-Based Zero-Knowledge Proofs

Jonathan Bootle; Vadim Lyubashevsky; Gregor Seiler;
Open Access
Published: 28 Aug 2019
Publisher: Springer International Publishing
Abstract

A key component of many lattice-based protocols is a zeroknowledge proof of knowledge of a vector ~s with small coe cients satisfying A~s = ~u mod q. While there exist fairly e cient proofs for a relaxed version of this equation which prove the knowledge of ~s0 and c satisfying A~s0 = ~uc where k~s0k k~sk and c is some small element in the ring over which the proof is performed, the proofs for the exact version of the equation are considerably less practical. The best such proof technique is an adaptation of Stern's protocol (Crypto '93), for proving knowledge of nearby codewords, to larger moduli. The scheme is a -protocol, each of whose iterations has soundness error 2=3, and thus requires over 200 repetitions to obtain soundness error of 2-128, which is the main culprit behind the large size of the proofs produced. In this paper, we propose the rst lattice-based proof system that signicantly outperforms Stern-type proofs for proving knowledge of a short ~s satisfying A~s = ~u mod q. Unlike Stern's proof, which is combinatorial in nature, our proof is more algebraic and uses various relaxed zeroknowledge proofs as sub-routines. The main savings in our proof system comes from the fact that each round has soundness error of 1=n, where n is the number of columns of A. For typical applications, n is a few thousand, and therefore our proof needs to be repeated around 10 times to achieve a soundness error of 2-128. For concrete parameters, it produces proofs that are around an order of magnitude smaller than those produced using Stern's approach.

Subjects by Vocabulary

Microsoft Academic Graph classification: Discrete mathematics Mathematical proof Zero-knowledge proof Mathematics Small element Proof of knowledge Lattice (order) Large size Algebraic number Moduli

arXiv: Nuclear Experiment Nuclear Theory

Subjects

Lattices,, Zero-Knowledge Proofs,, Commitments

Related Organizations
Funded by
EC| FutureTPM
Project
FutureTPM
Future Proofing the Connected World: A Quantum-Resistant Trusted Platform Module
  • Funder: European Commission (EC)
  • Project Code: 779391
  • Funding stream: H2020 | RIA
Validated by funder
,
EC| FutureTPM
Project
FutureTPM
Future Proofing the Connected World: A Quantum-Resistant Trusted Platform Module
  • Funder: European Commission (EC)
  • Project Code: 779391
  • Funding stream: H2020 | RIA
Validated by funder
Related to Research communities
Social Science and Humanities
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