Concretely-Efficient Zero-Knowledge Arguments for Arithmetic Circuits and Their Application to Lattice-Based Cryptography

Carsten Baum, Ariel Nof

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

25 Scopus citations

Abstract

In this work we present a new interactive Zero-Knowledge Argument of knowledge for general arithmetic circuits. Our protocol is based on the “MPC-in-the-head”-paradigm of Ishai et al. (STOC 2009) and follows the recent “MPC-in-the-head with Preprocessing” as proposed by Katz, Kolesnikov and Wang (ACM CCS 2018). However, in contrast to Katz et al. who used the “cut-and-choose” approach for pre-processing, we show how to incorporate the well-known “sacrificing” paradigm into “MPC-in-the-head”, which reduces the proof size when working over arithmetic circuits. Our argument system uses only lightweight symmetric-key primitives and utilizes a simplified version of the so-called SPDZ-protocol. Based on specific properties of our protocol we then show how it can be used to construct an efficient Zero-Knowledge Argument of Knowledge for instances of the Short Integer Solution (SIS) problem. We present different protocols that are tailored to specific uses of SIS, while utilizing the advantages of our scheme. In particular, we present a variant of our argument system that allows the parties to sample the circuit “on the fly”, which may be of independent interest. We furthermore implemented our Zero-Knowledge argument for SIS and show that using our protocols it is possible to run a complete interactive proof, even for general SIS instances which result in a circuit with gates, in less than 0.5 s.

Original languageEnglish
Title of host publicationPublic-Key Cryptography – PKC 2020 - 23rd IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings
EditorsAggelos Kiayias, Markulf Kohlweiss, Petros Wallden, Vassilis Zikas
PublisherSpringer
Pages495-526
Number of pages32
ISBN (Print)9783030453732
DOIs
StatePublished - 2020
Externally publishedYes
Event23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2020 - Edinburgh, United Kingdom
Duration: 4 May 20207 May 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12110 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2020
Country/TerritoryUnited Kingdom
CityEdinburgh
Period4/05/207/05/20

Bibliographical note

Publisher Copyright:
© 2020, International Association for Cryptologic Research.

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