### Batch Verification for Statistical Zero Knowledge Proofs

Inbar Kaslasi, Guy N. Rothblum, Ron D. Rothblum, Adam Sealfon, and Prashant Nalini Vasudevan

##### Abstract

A statistical zero-knowledge proof (SZK) for a problem $\Pi$ enables a computationally unbounded prover to convince a polynomial-time verifier that $x \in \Pi$ without revealing any additional information about $x$ to the verifier, in a strong information-theoretic sense. Suppose, however, that the prover wishes to convince the verifier that $k$ separate inputs $x_1,\dots,x_k$ all belong to $\Pi$ (without revealing anything else). A naive way of doing so is to simply run the SZK protocol separately for each input. In this work we ask whether one can do better -- that is, is efficient batch verification possible for SZK? We give a partial positive answer to this question by constructing a batch verification protocol for a natural and important subclass of SZK -- all problems $\Pi$ that have a non-interactive SZK protocol (in the common random string model). More specifically, we show that, for every such problem $\Pi$, there exists an honest-verifier SZK protocol for batch verification of $k$ instances, with communication complexity $poly(n) + k \cdot poly(\log{n},\log{k})$, where $poly$ refers to a fixed polynomial that depends only on $\Pi$ (and not on $k$). This result should be contrasted with the naive solution, which has communication complexity $k \cdot poly(n)$. Our proof leverages a new NISZK-complete problem, called Approximate Injectivity, that we find to be of independent interest. The goal in this problem is to distinguish circuits that are nearly injective, from those that are non-injective on almost all inputs.

Available format(s)
Category
Cryptographic protocols
Publication info
A minor revision of an IACR publication in TCC 2020
Keywords
Zero-knowledge proofsSZKbatch verification
Contact author(s)
kaslasi inbar @ gmail com
inbar kaslasi @ gmail com
History
Short URL
https://ia.cr/2020/1167

CC BY

BibTeX

@misc{cryptoeprint:2020/1167,
author = {Inbar Kaslasi and Guy N.  Rothblum and Ron D.  Rothblum and Adam Sealfon and Prashant Nalini Vasudevan},
title = {Batch Verification for Statistical Zero Knowledge Proofs},
howpublished = {Cryptology ePrint Archive, Paper 2020/1167},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/1167}},
url = {https://eprint.iacr.org/2020/1167}
}

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