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How to Base Security on the Perfect/Statistical Binding Property of Quantum Bit Commitment?

Authors Junbin Fang, Dominique Unruh, Jun Yan, Dehua Zhou

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Author Details

Junbin Fang
  • Jinan University, Guangzhou, China
Dominique Unruh
  • University of Tartu, Estonia
Jun Yan
  • Jinan University, Guangzhou, China
Dehua Zhou
  • Jinan University, Guangzhou, China

Funding

  • Fang, Junbin: Junbin Fang was supported by National Natural Science Foundation of China (Grant No. 62171202).
  • Unruh, Dominique: Dominique Unruh was supported by the ERC consolidator grant CerQuS (Grant No. 819317), by the Estonian Centre of Exellence in IT (EXCITE) funded by ERDF, by PUT team grant PRG946 from the Estonian Research Council.
  • Yan, Jun: Jun Yan was supported by National Natural Science Foundation of China (Grant No. 61602208), by PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (Grant No. 2014A030310333).
  • Zhou, Dehua: Dehua Zhou was supported by Science and Technology Project of Guangzhou City (Grant No. 201707010320).

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Junbin Fang, Dominique Unruh, Jun Yan, and Dehua Zhou. How to Base Security on the Perfect/Statistical Binding Property of Quantum Bit Commitment?. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 26:1-26:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ISAAC.2022.26

Abstract

The concept of quantum bit commitment was introduced in the early 1980s for the purpose of basing bit commitments solely on principles of quantum theory. Unfortunately, such unconditional quantum bit commitments still turn out to be impossible. As a compromise like in classical cryptography, Dumais et al. [Paul Dumais et al., 2000] introduce the conditional quantum bit commitments that additionally rely on complexity assumptions. However, in contrast to classical bit commitments which are widely used in classical cryptography, up until now there is relatively little work towards studying the application of quantum bit commitments in quantum cryptography. This may be partly due to the well-known weakness of the general quantum binding that comes from the possible superposition attack of the sender of quantum commitments, making it unclear whether quantum commitments could be useful in quantum cryptography.
In this work, following Yan et al. [Jun Yan et al., 2015] we continue studying using (canonical non-interactive) perfectly/statistically-binding quantum bit commitments as the drop-in replacement of classical bit commitments in some well-known constructions. Specifically, we show that the (quantum) security can still be established for zero-knowledge proof, oblivious transfer, and proof-of-knowledge. In spite of this, we stress that the corresponding security analyses are by no means trivial extensions of their classical analyses; new techniques are needed to handle possible superposition attacks by the cheating sender of quantum bit commitments.
Since (canonical non-interactive) statistically-binding quantum bit commitments can be constructed from quantum-secure one-way functions, we hope using them (as opposed to classical commitments) in cryptographic constructions can reduce the round complexity and weaken the complexity assumption simultaneously.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Theory of computation → Cryptographic primitives
Keywords
  • Quantum bit commitment
  • quantum zero-knowledge
  • quantum proof-of-knowledge
  • quantum oblivious transfer

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