Cryptology ePrint Archive: Report 2021/918

The Round Complexity of Quantum Zero-Knowledge

Orestis Chardouvelis and Giulio Malavolta

Abstract: We study the round complexity of zero-knowledge for QMA (the quantum analogue of NP). Assuming the quantum quasi-polynomial hardness of the learning with errors (LWE) problem, we obtain the following results: - 2-Round statistical witness indistinguishable (WI) arguments for QMA. - 4-Round statistical zero-knowledge arguments for QMA in the plain model, additionally assuming the existence of quantum fully homomorphic encryption. This is the first protocol for constant-round statistical zero-knowledge arguments for QMA. - 2-Round computational (statistical, resp.) zero-knowledge for QMA in the timing model, additionally assuming the existence of post-quantum non-parallelizing functions (time-lock puzzles, resp.).

All of these protocols match the best round complexity known for the corresponding protocols for NP with post-quantum security. Along the way, we introduce and construct the notions of sometimes-extractable oblivious transfer and sometimes-simulatable zero-knowledge, which might be of independent interest.

Category / Keywords: cryptographic protocols / quantum cryptography, zero-knowledge, timing model

Date: received 7 Jul 2021, last revised 17 Sep 2021

Contact author: orestischar at gmail com, giulio malavolta at hotmail it

Available format(s): PDF | BibTeX Citation

Version: 20210917:163250 (All versions of this report)

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