Skip to main content
SpringerLink
Log in

Quantum all-subkeys-recovery attacks on 6-round Feistel-2* structure based on multi-equations quantum claw finding

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Exploiting quantum mechanisms, quantum attacks have the potential ability to break the cipher structure. Recently, Ito et al. proposed a quantum attack on Feistel-2* structure (Ito et al.’s attack) based on the Q2 model. However, it is not realistic since the quantum oracle needs to be accessed by the adversary, and the data complexity is high. To solve this problem, a quantum all-subkeys-recovery (ASR) attack based on multi-equations quantum claw-finding is proposed, which takes a more realistic model, the Q1 model, as the scenario, and only requires 3 plain-ciphertext pairs to quickly crack the 6-round Feistel-2* structure. First, we proposed a multi-equations quantum claw-finding algorithm to solve the claw problem of finding multiple equations. In addition, Grover’s algorithm is used to speedup the rest subkeys recovery. Compared with Ito et al.’s attack, the data complexity of our attack is reduced from \(O(2^n)\) to O(1), while the time complexity and memory complexity are also significantly reduced.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in this published article [and its supplementary information files].

References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  2. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of STOC’96, pp. 212-219 (1996)

  3. Long, G.: Grover algorithm with zero theoretical failure rate. Phys. Rev. A 64(2), 022307 (2001)

    Article  ADS  Google Scholar 

  4. Toyama, F., van Dijk, W., Nogami, Y.: Quantum search with certainty based on modified grover algorithms: optimum choice of parameters. Quantum Inf. Process. 12(5), 1897–1914 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Gregor, L., Alexander, M.: Grover meets simon-quantumly attacking the fxconstruction. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 161-178 (2017)

  6. Hidenori, K., Masakatu, M.: Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: 2010 IEEE International Symposium on Information Theory, IEEE, pp. 2682-2685 (2010)

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Hidenori, K., Masakatu, M.: Security on the quantum-type even-mansour cipher. In: 2012 International Symposium on Information Theory and its Applications, IEEE, pp. 312-316 (2012)

  9. Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw, M., Katz, J. (eds.) Advances in Cryptology-CRYPTO 2016. Springer, Berlin (2016)

    Google Scholar 

  10. Santoli, T., Schaffner, C.: Using simon’s algorithm to attack symmetric-key cryptographic primitives. Quantum Inf. Comput. 17, 65–78 (2017)

    MathSciNet  Google Scholar 

  11. Shi, T., Chen, H., Guan, J.: Collision attacks against AEZ-PRF for authenticated encryption AEZ. China Commun. 15(2), 46–53 (2018)

    Article  Google Scholar 

  12. Xu, Y., Liu, W., Yu, W.: Quantum forgery attacks on COPA, AES-COPA and marble authenticated encryption algorithms. Quantum Inf. Process. 20(4), 1–21 (2021)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. Xavier, B., María, N.-P., André, S.: On quantum slide attacks. In: Kenneth G. Paterson and Douglas Stebila eds., Selected Areas in Cryptography-SAC, pp. 492-519 (2020)

  14. Dong, X., Wang, X.: Quantum key-recovery attack on feistel structures. Sci. China Inf. Sci. 61(10), 1–7 (2018)

    Article  Google Scholar 

  15. Dong, X., Li, Z., Wang, X.: Quantum cryptanalysis on some generalized feistel schemes. Sci. China Inf. Sci. 62(2), 22501 (2019)

    Article  MathSciNet  Google Scholar 

  16. Dong, X., Dong, B., Wang, X.: Quantum attacks on some feistel block ciphers. Des. Codes Crypt. 88(6), 1–25 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hosoyamada, A., Sasaki, Y.: Quantum Demiric-Seluk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions. In: International Conference on Security and Cryptography for Networks, pp. 386-403 (2018)

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

    Article  MATH  Google Scholar 

  19. Feistel, H.: Cryptography and computer privacy. Sci. Am. 228(5), 15–23 (1973)

    Article  ADS  Google Scholar 

  20. Coppersmith, D.: The data encryption standard (des) and its strength against attacks. IBM J. Res. Dev. 38(3), 243–250 (1994)

    Article  MATH  Google Scholar 

  21. Aoki, K., Ichikawa, T., Kanda, M.e.a.: Camellia: A 128-Bit Block Cipher Suitable for Multiple Platforms - Design andAnalysis. In: Stinson D.R., Tavares S. (eds) Selected Areas in Cryptography. SAC 2000. Lecture Notes in Computer Science, vol. 2012. pp. 39-56 (2001)

  22. Adams, C.: The cast-128 encryption algorithm. RFC 81(4), 864–894 (1997)

    Google Scholar 

  23. Yang, D., Qi, W., Tian, T.: All-subkeys-recovery attacks on a variation of feistel-2 block ciphers. IET Inf. Secur. 11(5), 230–234 (2017)

    Article  Google Scholar 

  24. Ito, G., Hosoyamada, A., Matsumoto, R., Sasaki, Y., Iwata, T.: Quantum chosen-ciphertext attacks against Feistel ciphers. In: Matsui, M. (ed.) Topics in Cryptology-CT-RSA 2019. Springer, Berlin (2019)

    Google Scholar 

  25. Isobe, T., Shibutani, K.: Generic key recovery attack on Feistel scheme. In: Sako, K., Sarkar, P. (eds.) Advances in Cryptology - ASIACRYPT 2013. Springer, Berlin (2013)

    MATH  Google Scholar 

  26. Andris, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37(1), 210–239 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhang, S.: Promised and distributed quantum search. In: Wang, L. (ed.) Computing and Combinatorics. COCOON 2005. Springer, Berlin (2005)

    Google Scholar 

  28. Grover, L.K.: A framework for fast quantum mechanical algorithms. In: Proceedings of STOC’98, pp.53-62 (1998)

  29. Yang, G., Zhu, B., Suder, V., Aagaard, M.D., Gong, G.: The simeck family of lightweight block ciphers. Lecture Notes Artificial Intelligence, pp 307–329 (2015)

  30. Kolbl, S., Roy, A.: A brief comparison of Simon and Simeck. In: Lightweight Cryptography for Security and Privacy: 5th International Workshop, LightSec 2016, Aksaray, Turkey, September 21-22, 2016, Revised Selected Papers 5 (pp. 69-88). Springer International Publishing

  31. Brandon, L., Hai, P., Rainer, S.: Reducing the cost of implementing the advanced encryption standard as a quantum circuit. IEEE Trans. Quantum Eng. 1, 2500112 (2020)

    Google Scholar 

  32. Wang, Z., Wei, S., Long, G.: A quantum circuit design of AES requiring fewer quantum qubits and gate operations. Front. Phys. 17(4), 41501 (2022)

    Article  ADS  Google Scholar 

  33. Wang, Z., Wei, S., Long, G.L., Hanzo, L.: Variational quantum attacks threaten advanced encryption standard based symmetric cryptography. Sci. China Inform. Sci. 65(10), 200503 (2022)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (62071240) the Innovation Program for Quantum Science and Technology (2021ZD0302902), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Author information

Authors and Affiliations

  1. Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Wenjie Liu

  2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Wenjie Liu, Mengting Wang & Zixian Li

Authors
  1. Wenjie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mengting Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zixian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenjie Liu.

Ethics declarations

Conflict of interest

Authors have no conflict of interest to declare.

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

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, 142 (2023). https://doi.org/10.1007/s11128-023-03877-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03877-7

Keywords

Search

Navigation