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.
In this primitive, the verification is quantum, but sending the proof of possession to the verifier only requires classical communication.
- 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.
For technical reasons which are outside the scope of this work, the algorithm can output abort.
- 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.
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.
This is referred to as d-restricted \(\textsf{MAC} \) in [14].
- 7.
We use the term strong in place of super because strong is the more colloquially accepted term.
References
Amos, R., Georgiou, M., Kiayias, A., Zhandry, M.: One-shot signatures and applications to hybrid quantum/classical authentication. In: Makarychev, K., Makarychev, Y., Tulsiani, M., Kamath, G., Chuzhoy, J. (eds.) Proceedings of the Annual ACM SIGACT Symposium on Theory of Computing, pp. 255–268. ACM (2020). https://doi.org/10.1145/3357713.3384304
Ananth, P., Gulati, A., Qian, L., Yuen, H.: Pseudorandom (function-like) quantum state generators: new definitions and applications. In: Kiltz, E., Vaikuntanathan, V. (eds.) Theory of Cryptography, TCC 2022. LNCS, vol. 13747, pp. 237–265. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22318-1_9
Ananth, P., Lin, Y., Yuen, H.: Pseudorandom strings from pseudorandom quantum states (2023)
Ananth, P., Qian, L., Yuen, H.: Cryptography from pseudorandom quantum states (2021)
Bartusek, J., Coladangelo, A., Khurana, D., Ma, F.: One-way functions imply secure computation in a quantum world. In: Malkin, T., Peikert, C. (eds.) Advances in Cryptology - CRYPTO 2021–41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, 16–20 August 2021, Proceedings, Part I. LNCS, vol. 12825, pp. 467–496. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_17
Behera, A., Sattath, O.: Almost public coins. In: QIP 2021 (2020)
Ben-David, S., Sattath, O.: Quantum tokens for digital signatures. QCrypt 2017 (2016). https://doi.org/10.48550/ARXIV.1609.09047
Bouland, A., Fefferman, B., Vazirani, U.V.: Computational pseudorandomness, the wormhole growth paradox, and constraints on the ADS/CFT duality (abstract). In: Vidick, T. (ed.) 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, 12–14 January 2020, Seattle, Washington, USA. LIPIcs, vol. 151, pp. 63:1–63:2. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020). https://doi.org/10.4230/LIPIcs.ITCS.2020.63
Brakerski, Z., Canetti, R., Qian, L.: On the computational hardness needed for quantum cryptography (2022)
Brakerski, Z., Shmueli, O.: (Pseudo) random quantum states with binary phase. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 229–250. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36030-6_10
Brakerski, Z., Shmueli, O.: Scalable pseudorandom quantum states. In: Micciancio, D., Ristenpart, T. (eds.) Advances in Cryptology - CRYPTO 2020–40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, 17–21 August 2020, Proceedings, Part II. LNCS, vol. 12171, pp. 417–440. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_15
Coladangelo, A., Liu, J., Liu, Q., Zhandry, M.: Hidden cosets and applications to unclonable cryptography. In: Malkin, T., Peikert, C. (eds.) Advances in Cryptology - CRYPTO 2021–41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, 16–20 August 2021, Proceedings, Part I. LNCS, vol. 12825, pp. 556–584. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84242-0_20
Coladangelo, A., Sattath, O.: A quantum money solution to the blockchain scalability problem. Quantum 4, 297 (2020). https://doi.org/10.22331/q-2020-07-16-297
Goldreich, O.: The Foundations of Cryptography - Volume 2: Basic Applications. Cambridge University Press, Cambridge (2004). https://doi.org/10.1017/CBO9780511721656, http://www.wisdom.weizmann.ac.il/%7Eoded/foc-vol2.html
Harrow, A.W.: The church of the symmetric subspace (2013)
Ji, Z., Liu, Y., Song, F.: Pseudorandom quantum states. In: Shacham, H., Boldyreva, A. (eds.) Advances in Cryptology - CRYPTO 2018–38th Annual International Cryptology Conference, Santa Barbara, CA, USA, 19–23 August 2018, Proceedings, Part III. LNCS, vol. 10993, pp. 126–152. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_5
Kretschmer, W.: Quantum pseudorandomness and classical complexity. In: Hsieh, M. (ed.) 16th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2021, 5–8 July 2021, Virtual Conference. LIPIcs, vol. 197, pp. 2:1–2:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.TQC.2021.2
Molina, A., Vidick, T., Watrous, J.: Optimal counterfeiting attacks and generalizations for Wiesner’s quantum money. In: Iwama, K., Kawano, Y., Murao, M. (eds.) Theory of Quantum Computation, Communication, and Cryptography, TQC. LNCS, vol. 7582, pp. 45–64. Springer, Cham (2012). https://doi.org/10.1007/978-3-642-35656-8_4
Morimae, T., Yamakawa, T.: Quantum commitments and signatures without one-way functions. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology - CRYPTO 2022–42nd Annual International Cryptology Conference, CRYPTO 2022, Santa Barbara, CA, USA, 15–18 August 2022, Proceedings, Part I. LNCS, vol. 13507, pp. 269–295. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15802-5_10
Morimae, T., Yamakawa, Y.: One-wayness in quantum cryptography, October 2022
Radian, R., Sattath, O.: Semi-quantum money. In: Proceedings of the 1st ACM Conference on Advances in Financial Technologies, AFT 2019, Zurich, Switzerland, 21–23 October 2019, pp. 132–146. ACM (2019). https://doi.org/10.1145/3318041.3355462
Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of reducibility between cryptographic primitives. In: Naor, M. (ed.) TCC 2004, Cambridge, MA, USA Proceedings. LNCS, vol. 2951, pp. 1–20. Springer, Cham (2004). https://doi.org/10.1007/978-3-540-24638-1_1
Shmueli, O.: Public-key quantum money with a classical bank. In: Leonardi, S., Gupta, A. (eds.) STOC 2022: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, 20–24 June 2022, pp. 790–803. ACM (2022). https://doi.org/10.1145/3519935.3519952
Shmueli, O.: Semi-quantum tokenized signatures. Cryptology ePrint Archive, Report 2022/228 (2022). https://ia.cr/2022/228
Zhandry, M.: How to construct quantum random functions. In: 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, New Brunswick, NJ, USA, 20–23 October 2012, pp. 679–687. IEEE Computer Society (2012). https://doi.org/10.1109/FOCS.2012.37
Zhandry, M.: A note on quantum-secure PRPs (2016)
Zhandry, M.: Quantum lightning never strikes the same state twice. Or: quantum money from cryptographic assumptions. J. Cryptol. 34(1), 6 (2021)
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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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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