Paper 2020/1488

General Properties of Quantum Bit Commitments

Jun Yan, Jinan University
Abstract

While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one. A complexity-based canonical (non-interactive) quantum bit commitment scheme refers to a kind of scheme such that the commitment consists of just a single (quantum) message from the sender to the receiver that can be opened later by uncomputing the commit stage. In this work, we study general properties of complexity-based quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two: 1. Any complexity-based quantum bit commitment scheme can be converted into the canonical (non-interactive) form (with its sum-binding property preserved). 2. Two flavors of canonical quantum bit commitments are equivalent; that is, canonical computationally-hiding statistically-binding quantum bit commitment exists if and only if the canonical statistically-hiding computationally-binding one exists. Combining this result with the first one, it immediately implies (unconditionally) that complexity-based quantum bit commitment is symmetric. Canonical quantum bit commitments can be based on quantum-secure one-way functions or pseudorandom quantum states. But in our opinion, the formulation of canonical quantum bit commitment is so clean and simple that itself can be viewed as a plausible complexity assumption as well. We propose to explore canonical quantum bit commitment from perspectives of both quantum cryptography and quantum complexity theory in the future.

Note: This version is almost the same as all versions uploaded in 2022. However, there are two significant differences between versions uploaded in 2022 and pre-2022. Specifically, versions in 2022 add a new discussion and a new result as follows. New discussion: we propose to study quantum bit commitments not only as a cryptographic primitive in the MiniQCrypt world, but also as a basic (quantum) complexity-theoretic object whose existence is an interesting open problem in its own right. In particular, two flavors of canonical quantum bit commitments can be formulated as two complexity-theoretic objects that are clean and simple to state. New result: quantum bit commitment is symmetric.

Metadata
Available format(s)
PDF
Category
Cryptographic protocols
Publication info
Published by the IACR in ASIACRYPT 2022
Keywords
quantum bit commitment binding round collapse parallel composition
Contact author(s)
tjunyan @ jnu edu cn
History
2022-10-17: last of 7 revisions
2020-11-29: received
See all versions
Short URL
https://ia.cr/2020/1488
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2020/1488,
      author = {Jun Yan},
      title = {General Properties of Quantum Bit Commitments},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1488},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1488}},
      url = {https://eprint.iacr.org/2020/1488}
}
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