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2020 | OriginalPaper | Buchkapitel

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

verfasst von : Carsten Baum, Ariel Nof

Erschienen in: Public-Key Cryptography – PKC 2020

Verlag: Springer International Publishing

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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 \({>}10^6\) gates, in less than 0.5 s.

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This is to obtain the smallest possible argument size while avoiding attacks such as [DN19]. A generalization of our scheme without this assumption can be obtained by generating the randomness for commitments independent of the message.

It works like SPDZ in the sense that it considers dishonest majority, uses an additive secret sharing and multiplication triples, but without the information-theoretic MAC.

The analysis for \( {\varPi }_{\textsf {c \& c}}\) is described in the full version.

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Titel: Concretely-Efficient Zero-Knowledge Arguments for Arithmetic Circuits and Their Application to Lattice-Based Cryptography
verfasst von: Carsten Baum
Ariel Nof
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2020
Print ISBN: 978-3-030-45373-2

Electronic ISBN: 978-3-030-45374-9

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-45374-9_17

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