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Pseudorandomness with Proof of Destruction and Applications

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14372))

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Abstract

Two fundamental properties of quantum states that quantum information theory explores are pseudorandomness and provability of destruction. We introduce the notion of quantum pseudorandom states with proofs of destruction (PRSPD) that combines both these properties. Like standard pseudorandom states (PRS), these are efficiently generated quantum states that are indistinguishable from random, but they can also be measured to create a classical string. This string is verifiable (given the secret key) and certifies that the state has been destructed. We show that, similarly to PRS, PRSPD can be constructed from any post-quantum one-way function. As far as the authors are aware, this is the first construction of a family of states that satisfies both pseudorandomness and provability of destruction.

We show that many cryptographic applications that were shown based on PRS variants using quantum communication can be based on (variants of) PRSPD using only classical communication. This includes symmetric encryption, message authentication, one-time signatures, commitments, and classically verifiable private quantum coins.

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Notes

  1. 1.

    In this primitive, the verification is quantum, but sending the proof of possession to the verifier only requires classical communication.

  2. 2.

    One may be concerned that true random states are infeasible to generate, however for our purposes here we can use so-called “state-designs” instead of true random states.

  3. 3.

    For technical reasons which are outside the scope of this work, the algorithm can output abort.

  4. 4.

    The pseudorandom security guarantee implies that with overwhelming probability over the chosen key, the state should be negligibly close to a pure state in trace distance; otherwise, pseudorandomness of the state can be violated via Swap-test.

  5. 5.

    We believe that the distributions are in fact, statistically close due to the strong concentration of the Haar measure, but we have not been able to prove it. The lemma is a weaker version of this statement, but it suffices for our purposes.

  6. 6.

    This is referred to as d-restricted \(\textsf{MAC} \) in [14].

  7. 7.

    We use the term strong in place of super because strong is the more colloquially accepted term.

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Acknowledgments

Amit Behera and Or Sattath were supported by the Israeli Science Foundation (ISF) grant No. 682/18 and 2137/19, and by the Cyber Security Research Center at Ben-Gurion University. Zvika Brakerski is supported by the Israel Science Foundation (Grant No. 3426/21), and by the European Union Horizon 2020 Research and Innovation Program via ERC Project REACT (Grant 756482). Omri Shmueli is supported by the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme (grant agreements No. 101042417, acronym SPP, and No. 756482, acronym REACT), by Israeli Science Foundation (ISF) grants 18/484 and 19/2137, by Len Blavatnik and the Blavatnik Family Foundation, and by the Clore Israel Foundation. The authors would like to thank the anonymous reviewers for their valuable and insightful comments.

This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 756482).

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Authors and Affiliations

  1. Department of Computer Science, Ben Gurion University of the Negev, Beersheba, Israel

    Amit Behera & Or Sattath

  2. Weizmann Institute of Science, Rehovot, Israel

    Zvika Brakerski

  3. Tel-Aviv University, Tel Aviv, Israel

    Omri Shmueli

Authors
  1. Amit Behera
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  2. Zvika Brakerski
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Correspondence to Amit Behera .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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© 2023 International Association for Cryptologic Research

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Behera, A., Brakerski, Z., Sattath, O., Shmueli, O. (2023). Pseudorandomness with Proof of Destruction and Applications. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14372. Springer, Cham. https://doi.org/10.1007/978-3-031-48624-1_5

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  • DOI: https://doi.org/10.1007/978-3-031-48624-1_5

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