We extend a commitment scheme based on the learning with errors over rings (RLWE) problem, and present efficient companion zeroknowledge proofs of knowledge. Our scheme maps elements from the ring (or equivalently, n elements fro

A Banerjee

A Fiat

A Jain

C Peikert

D Stehlé

E Fujisaki

F Benhamouda

G Asharov

I Damgård

IB Damgård

J Boyar

J Groth

J Katz

J Kilian

J Stern

L Ducas

M Bellare

M Rückert

O Goldreich

R Cramer

R Lindner

S Ling

V Lyubashevsky

X Xie

Z Brakerski

English

We design an efficient commitment scheme, and companion zero-knowledge proofs of knowledge, based on the learning with errors over rings (RLWE) problem.  In particular, for rings in which almost all elements have inverses, we construct a perfectly binding commitment scheme whose hiding property relies on the RLWE assumption. Our scheme maps elements from the ring (or equivalently, n elements from F_q) to a small constant number of ring elements.  We then construct Sigma-protocols for proving, in a zero-knowledge manner, knowledge of the message contained in a commitment.  We are able to further extend our basic protocol to allow us to prove additive and multiplicative relations among committed values.

Our protocols have a communication complexity of O(Mn\log q) and achieve a negligible knowledge error in one run.
Here M is the constant from a rejection sampling technique that we employ, and can be set close to 1 by adjusting other parameters.
Previously known Sigma-protocols for LWE-related languages either relied on ``smudging\u27\u27 out the error (which necessitates working over large fields, resulting in poor efficiency) or only achieved a noticeable or even constant knowledge error (thus requiring many repetitions of the protocol)

Fabrice Benhamouda

Stephan Krenn

Vadim Lyubashevsky

Krzysztof Pietrzak

Cryptology ePrint Archive

Efficient Zero-Knowledge Proofs for Commitments from Learning With Errors over Rings

Benhamouda, Fabrice

Krenn, Stephan

Lyubashevsky, Vadim

Pietrzak, Krzysztof Z 

IST Austria: PubRep (Institute of Science and Technology)

LNCS

Pietrzak, Krzysztof

Hal-Diderot

Efficient Zero-Knowledge Proofs for Commitments from Learning with Errors over Rings

Crossref

Pietrzak, Krzysztof Z

HAL: Hyper Article en Ligne

IST PubRep

Efficient zero-knowledge proofs for commitments from learning with errors over rings

ISTA Research Explorer (Institute of Science and Technology Austria)

INRIA a CCSD electronic archive server

https://research-explorer.ista.ac.at/download/1649/4883

LNCS

Abstract

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Cryptology ePrint Archive

IST Austria: PubRep (Institute of Science and Technology)

Hal-Diderot

Crossref

IST Austria: PubRep (Institute of Science and Technology)

HAL: Hyper Article en Ligne

IST PubRep

ISTA Research Explorer (Institute of Science and Technology Austria)

INRIA a CCSD electronic archive server