Classical Binding for Quantum Commitments

Nir Bitansky, Zvika Brakerski

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In classical commitments, statistical binding means that for almost any commitment transcript there is at most one possible opening. While quantum commitments (for classical messages) sometimes have benefits over their classical counterparts (e.g. in terms of assumptions), they provide a weaker notion of binding. Essentially that the sender cannot open a given commitment to a random value with probability noticeably greater than 1/2. We introduce a notion of classical binding for quantum commitments which provides guarantees analogous to the classical case. In our notion, the receiver performs a (partial) measurement of the quantum commitment string, and the outcome of this measurement determines a single value that the sender may open. We expect that our notion can replace classical commitments in various settings, leaving the security proof essentially unchanged. As an example we show a soundness proof for the GMW zero-knowledge proof system. We construct a non-interactive quantum commitment scheme which is classically statistically-binding and has a classical opening, based on the existence of any post-quantum one-way function. Prior candidates had inherently quantum openings and were not classically binding. In contrast, we show that it is impossible to achieve classical binding for statistically hiding commitments, regardless of assumption or round complexity. Our scheme is simply Naor’s commitment scheme (which classically requires a common random string, CRS), but executed in superposition over all possible values of the CRS, and repeated several times. We hope that this technique for using quantum communication to remove a CRS may find other uses.

Original languageEnglish
Title of host publicationTheory of Cryptography - 19th International Conference, TCC 2021, Proceedings
EditorsKobbi Nissim, Brent Waters, Brent Waters
PublisherSpringer Science and Business Media Deutschland GmbH
Pages273-298
Number of pages26
ISBN (Print)9783030904586
DOIs
StatePublished - 2021
Event19th International Conference on Theory of Cryptography, TCC 2021 - Raleigh, United States
Duration: 8 Nov 202111 Nov 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13042 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Theory of Cryptography, TCC 2021
Country/TerritoryUnited States
CityRaleigh
Period8/11/2111/11/21

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