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Pseudorandom Strings from Pseudorandom Quantum States

Authors Prabhanjan Ananth , Yao-Ting Lin, Henry Yuen

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Prabhanjan Ananth
  • Department of Computer Science, University of California Santa Barbara, CA, USA
Yao-Ting Lin
  • Department of Computer Science, University of California Santa Barbara, CA, USA
Henry Yuen
  • Department of Computer Science, Columbia University, New York, NY, USA

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Prabhanjan Ananth, Yao-Ting Lin, and Henry Yuen. Pseudorandom Strings from Pseudorandom Quantum States. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.6

Abstract

We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states that are computationally indistinguishable from Haar random states. PRSGs have found applications in quantum gravity, quantum machine learning, quantum complexity theory, and quantum cryptography. Pseudorandom generators, on the other hand, a pseudorandomness notion in the classical world, is ubiquitous to theoretical computer science. While some separation results were known between PRSGs, for some parameter regimes, and PRGs, their relationship has not been completely understood. In this work, we show that a natural variant of pseudorandom generators called quantum pseudorandom generators (QPRGs) can be based on the existence of logarithmic output length PRSGs. Our result along with the previous separations gives a better picture regarding the relationship between the two notions. We also study the relationship between other notions, namely, pseudorandom function-like state generators and pseudorandom functions. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.

Subject Classification

ACM Subject Classification
  • Security and privacy → Mathematical foundations of cryptography
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum Cryptography

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References

  1. Prabhanjan Ananth, Aditya Gulati, Luowen Qian, and Henry Yuen. Pseudorandom (function-like) quantum state generators: New definitions and applications. In Theory of Cryptography Conference, pages 237-265. Springer, 2022. Google Scholar
  2. Prabhanjan Ananth, Luowen Qian, and Henry Yuen. Cryptography from pseudorandom quantum states. In CRYPTO, 2022. Google Scholar
  3. Benny Applebaum, Yuval Ishai, and Eyal Kushilevitz. Computationally private randomizing polynomials and their applications. computational complexity, 15(2):115-162, 2006. Google Scholar
  4. James Bartusek, Andrea Coladangelo, Dakshita Khurana, and Fermi Ma. One-way functions imply secure computation in a quantum world. In Tal Malkin and Chris Peikert, editors, Advances in Cryptology - CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16-20, 2021, Proceedings, Part I, volume 12825 of Lecture Notes in Computer Science, pages 467-496. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-84242-0_17.
  5. Amit Behera, Zvika Brakerski, Or Sattath, and Omri Shmueli. Pseudorandomness with proof of destruction and applications. Cryptology ePrint Archive, Paper 2023/543, 2023. URL: https://eprint.iacr.org/2023/543.
  6. Adam Bouland, Bill Fefferman, Soumik Ghosh, Umesh Vazirani, and Zixin Zhou. Quantum pseudoentanglement. arXiv preprint, 2022. URL: https://arxiv.org/abs/2211.00747.
  7. Adam Bouland, Bill Fefferman, and Umesh V. Vazirani. Computational pseudorandomness, the wormhole growth paradox, and constraints on the ads/cft duality (abstract). In Thomas Vidick, editor, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, January 12-14, 2020, Seattle, Washington, USA, volume 151 of LIPIcs, pages 63:1-63:2. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.63.
  8. Zvika Brakerski and Omri Shmueli. Scalable pseudorandom quantum states. In Daniele Micciancio and Thomas Ristenpart, editors, Advances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, August 17-21, 2020, Proceedings, Part II, volume 12171 of Lecture Notes in Computer Science, pages 417-440. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-56880-1_15.
  9. Zvika Brakerski and Henry Yuen. Quantum garbled circuits. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, pages 804-817, 2022. Google Scholar
  10. Persi Diaconis and David Freedman. A dozen de Finetti-style results in search of a theory. Annales de l'I.H.P. Probabilités et statistiques, 23(S2):397-423, 1987. URL: http://www.numdam.org/item/AIHPB_1987__23_S2_397_0/.
  11. Yevgeniy Dodis, Russell Impagliazzo, Ragesh Jaiswal, and Valentine Kabanets. Security amplification for interactive cryptographic primitives. In Theory of Cryptography: 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, March 15-17, 2009. Proceedings 6, pages 128-145. Springer, 2009. Google Scholar
  12. Dmitry Gavinsky. Quantum money with classical verification. In 2012 IEEE 27th Conference on Computational Complexity, pages 42-52. IEEE, 2012. Google Scholar
  13. Oded Goldreich. A note on computational indistinguishability. Information Processing Letters, 34(6):277-281, 1990. URL: https://doi.org/10.1016/0020-0190(90)90010-U.
  14. Oded Goldreich, Shafi Goldwasser, and Silvio Micali. How to construct random functions. Journal of the ACM (JACM), 33(4):792-807, 1986. Google Scholar
  15. Alex B. Grilo, Huijia Lin, Fang Song, and Vinod Vaikuntanathan. Oblivious transfer is in miniqcrypt. In Anne Canteaut and François-Xavier Standaert, editors, Advances in Cryptology - EUROCRYPT 2021 - 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, October 17-21, 2021, Proceedings, Part II, volume 12697 of Lecture Notes in Computer Science, pages 531-561. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-77886-6_18.
  16. Sam Gunn, Nathan Ju, Fermi Ma, and Mark Zhandry. Commitments to quantum states. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 1579-1588, 2023. Google Scholar
  17. Hsin-Yuan Huang, Michael Broughton, Jordan Cotler, Sitan Chen, Jerry Li, Masoud Mohseni, Hartmut Neven, Ryan Babbush, Richard Kueng, John Preskill, et al. Quantum advantage in learning from experiments. Science, 376(6598):1182-1186, 2022. Google Scholar
  18. Russell Impagliazzo and Avi Wigderson. P= bpp if e requires exponential circuits: Derandomizing the xor lemma. In Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pages 220-229, 1997. Google Scholar
  19. Zhengfeng Ji, Yi-Kai Liu, and Fang Song. Pseudorandom quantum states. In Hovav Shacham and Alexandra Boldyreva, editors, Advances in Cryptology - CRYPTO 2018 - 38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2018, Proceedings, Part III, volume 10993 of Lecture Notes in Computer Science, pages 126-152. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-96878-0_5.
  20. William Kretschmer. Quantum pseudorandomness and classical complexity. In Min-Hsiu Hsieh, editor, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2021, July 5-8, 2021, Virtual Conference, volume 197 of LIPIcs, pages 2:1-2:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.TQC.2021.2.
  21. Yanyi Liu and Rafael Pass. On one-way functions and kolmogorov complexity. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 1243-1254. IEEE, 2020. Google Scholar
  22. Ueli Maurer and Stefano Tessaro. Computational indistinguishability amplification: Tight product theorems for system composition. In Shai Halevi, editor, Advances in Cryptology - CRYPTO 2009, volume 5677 of Lecture Notes in Computer Science, pages 350-368. Springer-Verlag, August 2009. Google Scholar
  23. Ueli Maurer and Stefano Tessaro. A hardcore lemma for computational indistinguishability: Security amplification for arbitrarily weak prgs with optimal stretch. In Daniele Micciancio, editor, Theory of Cryptography - TCC 2010, volume 5978 of Lecture Notes in Computer Science, pages 237-254. Springer-Verlag, February 2010. Google Scholar
  24. Elizabeth S Meckes. The random matrix theory of the classical compact groups, volume 218. Cambridge University Press, 2019. Google Scholar
  25. Tomoyuki Morimae and Takashi Yamakawa. Quantum commitments and signatures without one-way functions, 2021. URL: https://doi.org/10.48550/ARXIV.2112.06369.
  26. Mervin E. Muller. A note on a method for generating points uniformly on n-dimensional spheres. Commun. ACM, 2(4):19-20, April 1959. URL: https://doi.org/10.1145/377939.377946.
  27. Moni Naor. Bit commitment using pseudorandomness. Journal of Cryptology, 4(2):151-158, January 1991. URL: https://doi.org/10.1007/BF00196774.
  28. Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010. URL: https://doi.org/10.1017/CBO9780511976667.
  29. Noam Nisan and Avi Wigderson. Hardness vs randomness. Journal of computer and System Sciences, 49(2):149-167, 1994. Google Scholar
  30. Ryan ODonnell and David Witmer. Goldreich’s prg: evidence for near-optimal polynomial stretch. In 2014 IEEE 29th Conference on Computational Complexity (CCC), pages 1-12. IEEE, 2014. Google Scholar
  31. Alexander A Razborov and Steven Rudich. Natural proofs. In Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, pages 204-213, 1994. Google Scholar
  32. S Kh Sirazhdinov and M Mamatov. On convergence in the mean for densities. Theory of Probability & Its Applications, 7(4):424-428, 1962. Google Scholar
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