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Breaking symmetric cryptosystems using the offline distributed Grover-meets-Simon algorithm

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Abstract

The model of superposition queries in symmetric cryptanalysis has yielded remarkable results, such as Simon’s period-finding algorithm, which can break many constructions in polynomial time. However, due to limitations of current physical devices, quantum circuits with long depths are often noisy and difficult to realize in practice. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we propose an offline algorithm model that combines distributed Simon’s and Grover’s algorithms. This model enables us to perform key recovery attacks on different rounds Feistel structures, Even Mansour construction, and the FX construction, while minimizing the quantum query complexity. Despite being limited to classical queries and offline quantum computations, we leverage the algebraic structure of cryptosystems to achieve successful key recovery attacks.

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References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

  4. Kuwakado, H., Morii, M.: Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: IEEE International Symposium on Information Theory. IEEE (2010)

  5. Simon, Daniel R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. J. Cryptol. 10, 151–161 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kuwakado, H., Morii, M.: Security on the quantum-type even-Mansour cipher. In: Proceedings of International Symposium on Information Theory and Its Applications, Honolulu, pp. 312–316 (2012)

  8. Kaplan, M., Leurent, G., Leverrier, A., et al.: Breaking symmetric cryptosystems using quantum period finding. In: Advances in Cryptology—CRYPTO 2016, pp. 207–237. Springer, Berlin (2016)

  9. Kaplan, M.: Quantum attacks against iterated block ciphers. Mat. Vopr. Kriptogr. 7(2), 71–90 (2016)

    MathSciNet  MATH  Google Scholar 

  10. Kaplan, M., Leurent, G., Leverrier, A., et al.: Quantum differential and linear cryptanalysis. Computer Science. 71–94 (2017)

  11. Dong, X., Wang, X.: Quantum key-recovery attack on Feistel structures. Sci. China Inf. Sci. 61, 102501 (2018)

    Article  Google Scholar 

  12. Hosoyamada, A., Yu, S.: Quantum Demiric-Selçuk meet-in-the-middle attacks: applications to 6-round generic Feistel constructions. In: Security and Cryptography for Networks, pp. 386–403 (2018)

  13. Hosoyamada, A., Sasaki, Y.: Cryptanalysis against symmetric-key schemes with online classical queries and offline quantum computations. In: CT-RSA. Lecture Notes in Computer Science, vol. 10808, pp. 198–218 (2018)

  14. Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Quantum differential and linear cryptanalysis. IACR Trans. Symmetric Cryptol. 1, 71–94 (2016)

    Article  MATH  Google Scholar 

  15. Leander, G., May, A.: Grover meets Simon—quantumly attacking the FX-construction. In: Advances in Cryptology—ASIACRYPT 2017, Part II, pp. 161–178. Springer, Berlin (2017)

  16. Bonnetain, X., Naya-Plasencia, M.: Hidden shift quantum cryptanalysis and implications. In: ASIACRYPT 2018. Lecture Notes in Computer Science, vol. 11272, pp. 560–592 (2018)

  17. Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170–188 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Bonnetain, X., Hosoyamada, A., Nay-Plasencia, M., et al.: Quantum attacks without superposition queries: the offline Simon’s algorithm. (2020). https://doi.org/10.1007/978-3-030-34578-5-20

  19. Liu, W., Wang, M., Li, Z.: Quantum all-subkeys-recovery attacks on 6-round Feistel-2* structure based on multi-equations quantum claw finding. Quantum Inf. Process. 22(3), 142 (2023)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Nan, J., Hu, H., Zhang, P., Luo, Y.: Quantum attacks against BBB secure PRFs or MACs built from public random permutations. Quantum Inf. Process. 22(1), 26 (2023)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Buhrman, H., Rohrig, H.: Distributed quantum computing. In: 28th International Symposium on Mathematical Foundations of Computer Science, vol. 2003, pp. 1–20. Springer, Berlin (2003)

  22. Yimsiriwattana, A., Lomonaco, S.: Distributed quantum computing: a distributed Shor algorithm. In: Quantum Information and Computation II, vol. 5436 (2004)

  23. Beals, R., Brierley, S., Gray, O., et al.: Efficient distributed quantum computing. Proc. R. Soc. A. 469, 20120686 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Li, K., Qiu, D., Li, L., et al.: Application of distributed semi-quantum computing model in phase estimation. Inf. Process. Lett. 120, 23–29 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  25. Avron, J., Casper, O., Rozen, I.: Quantum advantage and noise reduction in distributed quantum computing. Phys. Rev. A 104, 052404 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  26. Qiu, D., Luo, L., Xiao, L.: Distributed Grover’s algorithm. arXiv: 2204.10487v3 (2022)

  27. Tan, J., Xiao, L., Qiu, D., et al.: Distributed quantum algorithm for Simon’s problem. Phys. Rev. A 106(3), 032417 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  28. Zhou, X., Qiu, D., Luo, L.: Distributed exact quantum algorithms for Bernstein-Vazirani and search problems. arXiv:2303.10670v1 (2023)

  29. Brassard, G., Hoyer, P., Mosca, M., et al.: Quantum amplitude amplification and estimation. AMS Contemp. Math. 305, 53–74 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. Lub, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Open Fund of Advanced Cryptography and System Security Key Laboratory of Sichuan Province (Grant No. SKLACSS-202103).

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Authors and Affiliations

  1. College of Cybersecurity, University of Science and Technology of China, Hefei, 230026, China

    Bao-Min Zhou & Zheng Yuan

  2. Beijing Electronic Science Technology Institute, Beijing, 100070, China

    Bao-Min Zhou

  3. China Satellite Network Group Co., Ltd, Beijing, 100086, China

    Zheng Yuan

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  1. Bao-Min Zhou
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  2. Zheng Yuan
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Correspondence to Bao-Min Zhou.

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Zhou, BM., Yuan, Z. Breaking symmetric cryptosystems using the offline distributed Grover-meets-Simon algorithm. Quantum Inf Process 22, 333 (2023). https://doi.org/10.1007/s11128-023-04089-9

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