Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Quantum key-recovery attack on Feistel structures

  • 71 Accesses

  • 5 Citations

Abstract

Post-quantum cryptography has drawn considerable attention from cryptologists on a global scale. At Asiacrypt 2017, Leander and May combined Grover’s and Simon’s quantum algorithms to break the FX-based block ciphers, which were introduced by Kilian and Rogaway to strengthen DES. In this study, we investigate the Feistel constructions using Grover’s and Simon’s algorithms to generate new quantum key-recovery attacks on different rounds of Feistel constructions. Our attacks require 20.25nr−0.75n quantum queries to break an r-round Feistel construction. The time complexity of our attacks is less than that observed for quantum brute-force search by a factor of 20.75n. When compared with the best classical attacks, i.e., Dinur et al.’s attacks at CRYPTO 2015, the time complexity is reduced by a factor of 20.5n without incurring any memory cost.

This is a preview of subscription content, log in to check access.

References

  1. 1

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

  2. 2

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

  3. 3

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

  4. 4

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

  5. 5

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

  6. 6

    Moody D. The ship has sailed: the NIST post-quantum cryptography “competition” (invited talk). In: Advances in Cryptology-ASIACRYPT 2017. Berlin: Springer, 2017

  7. 7

    Boneh D, Zhandry M. Secure signatures and chosen ciphertext security in a quantum computing world. In: Advances in Cryptology -CRYPTO 2013. Berlin: Springer, 2013. 361–379

  8. 8

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

  9. 9

    Simon D R. On the power of quantum computation. SIAM J Comput, 1997, 26: 1474–1483

  10. 10

    Feistel H, Notz W A, Smith J L. Some cryptographic techniques for machine-to-machine data communications. Proc IEEE, 1975, 63: 1545–1554

  11. 11

    International Organization for Standardization (ISO). Information Technology-Security Techniques-Encryption Algorithms-Part 3: Block Ciphers. International Standard-ISO/IEC 18033–3. 2010. https://doi.org/www.iso.org/standard/54531.html

  12. 12

    Luby M G, Rackoff C. How to construct pseudorandom permutations from pseudorandom functions. SIAM J Comput, 1988, 17: 373–386

  13. 13

    Kuwakado H, Morii M. Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: Proceedings of International Symposium on Information Theory, Austin, 2010. 2682–2685

  14. 14

    Dinur I, Dunkelman O, Keller N, et al. New attacks on Feistel structures with improved memory complexities. In: Advances in Cryptology -CRYPTO 2015, Part I. Berlin: Springer, 2015. 433–454

  15. 15

    Brassard G, Hoyer P, Mosca M, et al. Quantum amplitude amplification and estimation. 2000. ArXiv:quant-ph/0005055

  16. 16

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

  17. 17

    Kilian J, Rogaway P. How to protect DES against exhaustive key search. In: Advances in Cryptology -CRYPTO 1996. Berlin: Springer, 1996. 252–267

  18. 18

    Borghoff J, Canteaut A, G¨uneysu T, et al. PRINCE — a low-latency block cipher for pervasive computing applications — extended abstract. In: Advances in Cryptology -ASIACRYPT 2012. Berlin: Springer, 2012. 208–225

  19. 19

    Albrecht M R, Driessen B, Kavun E B, et al. Block ciphers - focus on the linear layer (feat. PRIDE). In: Advances in Cryptology - CRYPTO 2014. Berlin: Springer, 2014. 57–76

Download references

Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2017YFA0303903), National Natural Science Foundation of China (Grant No. 61672019), Fundamental Research Funds of Shandong University (Grant No. 2016JC029), National Cryptography Development Fund (Grant No. MMJJ20170121), Zhejiang Province Key R&D Project (Grant No. 2017C01062), and Project Funded by China Postdoctoral Science Foundation (Grant No. 2017M620807).

Author information

Correspondence to Xiaoyun Wang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dong, X., Wang, X. Quantum key-recovery attack on Feistel structures. Sci. China Inf. Sci. 61, 102501 (2018). https://doi.org/10.1007/s11432-017-9468-y

Download citation

Keywords

  • quantum cryptanalysis
  • quantum key-recovery
  • Feistel structure
  • Simon
  • Grover