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General Properties of Quantum Bit Commitments (Extended Abstract)

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13794))

Abstract

While unconditionally-secure quantum bit commitment (allowing both quantum computation and communication) is impossible, researchers turn to study the complexity-based one, a.k.a. computational quantum bit commitment. A computational canonical (non-interactive) quantum bit commitment scheme refers to a kind of schemes such that the commitment consists of just a single (quantum) message from the sender to the receiver that later can be opened by uncomputing the commit stage. In this work, we study general properties of computational quantum bit commitments through the lens of canonical quantum bit commitments. Among other results, we in particular obtain the following two:

  1. 1.

    Any computational quantum bit commitment scheme can be converted into the canonical (non-interactive) form (with its sum-binding property preserved).

  2. 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 computational 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.

The full version of this paper is referred to [50].

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Notes

  1. 1.

    Even in case, it is still legal to call it “quantum bit commitment scheme”. This is because classical computation and communication can be simulated by quantum computation and communication, respectively, in a standard way.

  2. 2.

    That is, any quantum cheating sender cannot generate a commitment that can be opened as both 0 and 1 successfully with non-negligible probability.

  3. 3.

    In the prior work (e.g. [18, 51, 52]) and an earlier draft of this paper (back in 2020), it is called “generic” form. However, this name is misleading as pointed out by Ananth, Qian, and Yuen [4], who also suggest the current name “canonical” to us. And we accept.

  4. 4.

    In [18], a quantum oblivious transfer with a security that is weaker than the full simulation-security [5, 22] but still very useful in many scenarios was achieved.

  5. 5.

    We do not claim that this holds for a general quantum bit commitment; the two simple schemes presented in [50, Appendix C] also serve as two counterexamples in this regard.

  6. 6.

    Then it suffices to show its semi-honest security.

  7. 7.

    Strictly speaking, we simplify the security analysis of the DMS scheme after it is firstly converted into the canonical form (which is straightforward).

  8. 8.

    This symmetry is in the same sense as that of oblivious transfer [48].

  9. 9.

    To the best of our knowledge, however, no impossibility result is known yet. In [12], authors only vaguely argue that this seems impossible for quantum computationally-binding commitments.

  10. 10.

    After the upload of the first preprint of this work to Cryptology ePrint Archive [50] in 2020.

  11. 11.

    This is also observed in [36, Appendix B].

  12. 12.

    We do not expect that quantum bit commitments can imply quantum-secure one-way functions, simply because a canonical quantum bit commitment scheme concerns quantum states rather than any sort of functions.

  13. 13.

    Their size depend on the security parameter n.

  14. 14.

    Strictly speaking, it should be understood as the corresponding two quantum state ensembles indexed by the security parameter n are indistinguishable.

  15. 15.

    Here the notation \(\left| 0 \right\rangle \) should be understood as multiple \(\left| 0 \right\rangle \)’s, the number of which depends on the security parameter; we just write a single \(\left| 0 \right\rangle \) to simplify the notation. We will follow this rule throughout this paper.

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Acknowledgements

We thank Dominique Unruh and Takeshi Koshiba for bringing the reference [48] to our attention. Many thanks also go to Dominique Unruh, Takeshi Koshiba, Prabhanjan Ananth, Luowen Qian, Henry Yuen, and the anonymous referees of ICALP 2021, Crypto 2022 and Asiacrypt 2022 for their useful suggestions and valuable comments on earlier drafts of this paper.

This work 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), by Major Program of Guangdong Basic and Applied Research Project (Grant No. 2019B030302008), by National Joint Engineering Research Center of Network Security Detection and Protection Technology, and by Guangdong Key Laboratory of Data Security and Privacy Preserving. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of funding agencies.

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Yan, J. (2022). General Properties of Quantum Bit Commitments (Extended Abstract). In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13794. Springer, Cham. https://doi.org/10.1007/978-3-031-22972-5_22

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