Skip to main content
Springer Nature Link
Log in

Quantum related-key differential cryptanalysis

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum computation models have profoundly impacted cryptanalysis. Differential cryptanalysis is one of the most fundamental methods in cryptanalysis of block ciphers, and one of the variations of this attack is related-key differential cryptanalysis. In this paper, quantum related-key differential cryptanalysis is implemented in two main stages of classical version. We employ Bernstein–Vazirani algorithm to find related-key differential characteristics in the first stage. Building on this basis, the second stage combines quantum maximum algorithm and quantum counting algorithm to recover correct key pair by quantum random access memory model. Compared to classical related-key differential cryptanalysis, the first stage achieves exponential acceleration, while the second stage accelerates at O(K), where \(K^2\) represents the number of candidate key pairs.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Algorithm 2
Fig. 2
Fig. 3
Fig. 4
Algorithm 3
Algorithm 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Notes

  1. Common block ciphers include Feistel structure, SPN structure, Lai-Massey structure.

  2. The qRACM, which stores classical data, is easier to implement and less powerful than quantum random access quantum memory (qRAQM) model, where storage is a quantum superposition state.

  3. The exact number of iterations required is \(22.5K+1.4lg^2(K^2)\) in [30].

References

  1. Mosca, M.: Cybersecurity in an era with quantum computers: will we be ready? IEEE Secur. Privacy 16(5), 38–41 (2018)

    Article  Google Scholar 

  2. Haonan, Y., Baonan, W.: Progress in quantum computing cryptography attacks. Chin. J. Comput. 43(9), 1691–1707 (2020)

    Google Scholar 

  3. Monz, T., Nigg, D., Martinez, E.A., Brandl, M.F., Schindler, P., Rines, R., Wang, S.X., Chuang, I.L., Blatt, R.: Realization of a scalable shor algorithm. Science 351(6277), 1068–1070 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  4. Liu, X., Song, H., Wang, H., Jiang, D., An, J.: Survey on improvement and application of grover algorithm. Comput. Sci. 48(10), 315–323 (2021)

  5. Ulitzsch, V.Q., Seifert, J.-P.: Breaking the quadratic barrier: quantum cryptanalysis of milenage, telecommunications’ cryptographic backbone. In: International Conference on Post-Quantum Cryptography, pp. 476–504 (2023). Springer

  6. Schrottenloher, A.: Quantum algorithms for cryptanalysis and quantum-safe symmetric cryptography. Ph.D. thesis, Sorbonne université (2021)

  7. Simon, D.: On the power of quantum computation. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 116–123 (1994). IEEE

  8. Bonnetain, X., Schrottenloher, A., Sibleyras, F.: Beyond quadratic speedups in quantum attacks on symmetric schemes. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 315–344 (2022). Springer

  9. Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. ACM SIGACT News 28(2), 14–19 (1997)

    Article  Google Scholar 

  10. Hosoyamada, A., Sasaki, Y.: Quantum demiric-selçuk meet-in-the-middle attacks: Applications to 6-round generic feistel constructions. In: Catalano, D., De Prisco, R. (eds.) Secur. Cryptogr. Netw., pp. 386–403. Springer, Cham (2018)

    Chapter  Google Scholar 

  11. Frixons, P., Naya-Plasencia, M., Schrottenloher, A.: Quantum boomerang attacks and some applications. In: AlTawy, R., Hülsing, A. (eds.) Sel. Areas Cryptogr., pp. 332–352. Springer, Cham (2022)

    Chapter  Google Scholar 

  12. Erlacher, J., Mendel, F., Eichlseder, M.: Bounds for the security of ascon against differential and linear cryptanalysis. IACR Trans. Symmetric Cryptol., pp. 64–87 (2022)

  13. Biham, E., Shamir, A.: Differential cryptanalysis of des-like cryptosystems. J. Cryptol. 4, 3–72 (1991)

    Article  MathSciNet  Google Scholar 

  14. Jakimoski, G., Desmedt, Y.: Related-key differential cryptanalysis of 192-bit key aes variants. In: International Workshop on Selected Areas in Cryptography, pp. 208–221 (2003). Springer

  15. ElSheikh, M., Youssef, A.M.: Related-key differential cryptanalysis of full round craft. In: International Conference on Security, Privacy, and Applied Cryptography Engineering, pp. 50–66 (2019). Springer

  16. Teh, J.S., Biryukov, A.: Differential cryptanalysis of warp. J. Inf. Secur. Appl. 70, 103316 (2022)

    Google Scholar 

  17. Li, H., Yang, L.: Quantum differential cryptanalysis to the block ciphers. In: Applications and Techniques in Information Security: 6th International Conference, ATIS 2015, Beijing, China, November 4–6, 2015, Proceedings 6, pp. 44–51 (2015). Springer

  18. Xie, H., Yang, L.: Using Bernstein–Vazirani algorithm to attack block ciphers. Des. Codes Crypt. 87, 1161–1182 (2019)

    Article  MathSciNet  Google Scholar 

  19. Zhou, Q., Lu, S., Zhang, Z., Sun, J.: Quantum differential cryptanalysis. Quantum Inf. Process. 14, 2101–2109 (2015)

    Article  ADS  Google Scholar 

  20. Jojan, P., Soni, K.K., Rasool, A.: Classical and quantum based differential cryptanalysis methods. In: 2021 12th International Conference on Computing Communication and Networking Technologies (ICCCNT), pp. 1–7 (2021). IEEE

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

    Article  Google Scholar 

  22. Li, H., Yang, L.: A quantum algorithm to approximate the linear structures of Boolean functions. Math. Struct. Comput. Sci. 28(1), 1–13 (2018)

    Article  MathSciNet  Google Scholar 

  23. Hosoyamada, A., Sasaki, Y.: Finding hash collisions with quantum computers by using differential trails with smaller probability than birthday bound. In: Advances in Cryptology—EUROCRYPT 2020: 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings, Part II 30, pp. 249–279 (2020). Springer

  24. Dou, S., Mao, M., Li, Y., Qiu, D.: Quantum rebound attack to dm structure based on aria algorithm. J. Phys.: Conf. Ser., vol. 2078, p. 012003 (2021). IOP Publishing

  25. Zou, H., Zou, J., Luo, Y.: New results on quantum boomerang attacks. Quantum Inf. Process. 22(4), 171 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  26. Albrecht, M.R., Shen, Y.: Quantum augmented dual attack. arXiv preprint arXiv:2205.13983 (2022)

  27. Aaronson, S., Rall, P.: Quantum approximate counting, simplified. In: Symposium on Simplicity in Algorithms, pp. 24–32 (2020). SIAM

  28. Brassard, G., Høyer, P., Tapp, A.: Quantum counting. In: Automata, Languages and Programming: 25th International Colloquium, ICALP’98 Aalborg, Denmark, July 13–17, 1998 Proceedings 25, pp. 820–831 (1998). Springer

  29. Diao, Z., Huang, C., Wang, K.: Quantum counting: algorithm and error distribution. Acta Appl. Math. 118, 147–159 (2012)

    Article  MathSciNet  Google Scholar 

  30. Durr, C., Hoyer, P.: A quantum algorithm for finding the minimum. arXiv preprint arXiv:quant-ph/9607014 (1996)

  31. Chen, Y., Wei, S., Gao, X., Wang, C., Tang, Y., Wu, J., Guo, H.: A low failure rate quantum algorithm for searching maximum or minimum. Quantum Inf. Process. 19, 1–28 (2020)

    Article  MathSciNet  Google Scholar 

  32. Xie, H., Yang, L.: A quantum related-key attack based on the Bernstein–Vazirani algorithm. Quantum Inf. Process. 19, 1–20 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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

  34. Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Advances in Cryptology—CRYPTO 2016: 36th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 14–18, 2016, Proceedings, Part II 36, pp. 207–237 (2016). Springer

  35. Denisenko, D.: Quantum differential cryptanalysis. J. Comput. Virol. Hack. Tech., pp. 1–8 (2022)

  36. Bonnetain, X., Hosoyamada, A., Naya-Plasencia, M., Sasaki, Y., Schrottenloher, A.: Quantum attacks without superposition queries: the offline Simon’s algorithm. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 552–583 (2019). Springer

Download references

Acknowledgements

The authors thank the editors and the reviewers for their useful comments. This work was supported by the National Natural Science Foundation of China (No.51979048).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Harbin Engineering University, Harbin, 150001, China

    Hongyu Wu & Xiaoning Feng

Authors
  1. Hongyu Wu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xiaoning Feng
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Xiaoning Feng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, H., Feng, X. Quantum related-key differential cryptanalysis. Quantum Inf Process 23, 269 (2024). https://doi.org/10.1007/s11128-024-04472-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-024-04472-0

Keywords