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2020 | OriginalPaper | Chapter

Shorter Non-interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages

Authors : Geoffroy Couteau, Dominik Hartmann

Published in: Advances in Cryptology – CRYPTO 2020

Publisher: Springer International Publishing

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Abstract

We put forth a new framework for building pairing-based non-interactive zero-knowledge (\(\mathsf {NIZK}\)) arguments for a wide class of algebraic languages, which are an extension of linear languages, containing disjunctions of linear languages and more. Our approach differs from the Groth-Sahai methodology, in that we rely on pairings to compile a \(\varSigma \)-protocol into a \(\mathsf {NIZK}\). Our framework enjoys a number of interesting features:

conceptual simplicity, parameters derive from the \(\varSigma \)-protocol;
proofs as short as resulting from the Fiat-Shamir heuristic applied to the underlying \(\varSigma \)-protocol;
fully adaptive soundness and perfect zero-knowledge in the common random string model with a single random group element as CRS;
yields simple and efficient two-round, public coin, publicly-verifiable perfect witness-indistinguishable (WI) arguments(ZAPs) in the plain model. To our knowledge, this is the first construction of two-rounds statistical witness-indistinguishable arguments from pairing assumptions.

Our proof system relies on a new (static, falsifiable) assumption over pairing groups which generalizes the standard kernel Diffie-Hellman assumption in a natural way and holds in the generic group model (GGM) and in the algebraic group model (AGM).

Replacing Groth-Sahai \(\textsf {NIZKs}\) with our new proof system allows to improve several important cryptographic primitives. In particular, we obtain the shortest tightly-secure structure-preserving signature scheme (which are a core component in anonymous credentials), the shortest tightly-secure quasi-adaptive \(\mathsf {NIZK}\) with unbounded simulation soundness (which in turns implies the shortest tightly-mCCA-secure cryptosystem), and shorter ring signatures.

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previous chapter NIZK from LPN and Trapdoor Hash via Correlation Intractability for Approximable Relations

next chapter Non-interactive Zero-Knowledge Arguments for QMA, with Preprocessing

Alternatively, the Fiat-Shamir transform offers provable security in the random oracle model; we note that there have been recent developments regarding instantiating Fiat-Shamir in the standard model under strong assumptions [16, 55].

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Title: Shorter Non-interactive Zero-Knowledge Arguments and ZAPs for Algebraic Languages
Authors: Geoffroy Couteau
Dominik Hartmann
Publisher: Springer International Publishing
Book: Advances in Cryptology – CRYPTO 2020
Print ISBN: 978-3-030-56876-4

Electronic ISBN: 978-3-030-56877-1

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-56877-1_27

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