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Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions

Part of the Lecture Notes in Computer Science book series (LNSC,volume 11035)

Abstract

This paper shows that quantum computers can significantly speed-up a type of meet-in-the-middle attacks initiated by Demiric and Selçuk (DS-MITM attacks), which is currently one of the most powerful cryptanalytic approaches in the classical setting against symmetric-key schemes. The quantum DS-MITM attacks are demonstrated against 6 rounds of the generic Feistel construction supporting an n-bit key and an n-bit block, which was attacked by Guo et al. in the classical setting with data, time, and memory complexities of \(O(2^{3n/4})\). The complexities of our quantum attacks depend on the adversary’s model. When the adversary has an access to quantum computers for offline computations but online queries are made in a classical manner, the attack complexities become \(\tilde{O}(2^{n/2})\), which significantly improves the classical attack. The attack is then extended to the case that the adversary can make superposition queries. The attack is based on 3-round distinguishers with Simon’s algorithm and then appends 3 rounds for key recovery. This can be solved by applying the combination of Simon’s and Grover’s algorithms recently proposed by Leander and May.

Keywords

  • Post-quantum cryptography
  • Demiric-Selçuk meet-in-the-middle attack
  • Feistel construction
  • Grover’s algorithm
  • Claw finding algorithm
  • Q1 model

Due to space limitations, some details and proofs are left to the full paper [HS17].

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Fig. 1.

Notes

  1. 1.

    Dong and Wang [DW17] independently pointed out the combination of the 3-round distinguisher [KM10] and key recovery attack [LM17].

  2. 2.

    Since any Q1 attack can be trivially converted to a Q2 attack by regarding quantum oracles as classical oracles, we can construct a Q2 attack with \(\max (T, D, M, N)\,=\,N^{1/2} \ll N^{3/4}\) from the best Q1 attack. However, such a Q2 attack requires time \(T=N\) in the case that only \(O(\log N)\) qubits are available.

References

  1. Ambainis, A.: Quantum walk algorithm for element distinctness. In: Proceedings of the 45th Symposium on Foundations of Computer Science (FOCS 2004), Rome, Italy, 17–19 October 2004, pp. 22–31 (2004)

    Google Scholar 

  2. Banegas, G., Bernstein, D.J.: Low-communication parallel quantum multi-target preimage search. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 325–335. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_16

    CrossRef  Google Scholar 

  3. Beals, R., et al.: Efficient distributed quantum computing. Proc. R. Soc. A 469(2153), 20120686 (2013)

    MathSciNet  CrossRef  Google Scholar 

  4. Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschr. Phys. 46(4–5), 493–505 (1998)

    CrossRef  Google Scholar 

  5. Bernstein, D.J.: Cost analysis of hash collisions: Will quantum computers make SHARCS obsolete? In: Special-Purpose Hardware for Attacking Cryptographic Systems, SHARCS 2009, p. 105 (2009)

    Google Scholar 

  6. Brassard, G., Høyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Contemp. Math. 305, 53–74 (2002)

    MathSciNet  CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

  8. Bonnetain, X.: Quantum key-recovery on full AEZ. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 394–406. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_20

    CrossRef  Google Scholar 

  9. Dinur, I., Dunkelman, O., Keller, N., Shamir, A.: New attacks on Feistel structures with improved memory complexities. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 433–454. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_21

    CrossRef  Google Scholar 

  10. Derbez, P., Fouque, P.-A., Jean, J.: Improved key recovery attacks on reduced-round AES in the single-key setting. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 371–387. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_23

    CrossRef  MATH  Google Scholar 

  11. Derbez, P., Perrin, L.: Meet-in-the-middle attacks and structural analysis of round-reduced PRINCE. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 190–216. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48116-5_10

    CrossRef  Google Scholar 

  12. Demirci, H., Selçuk, A.A.: A meet-in-the-middle attack on 8-round AES. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 116–126. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71039-4_7

    CrossRef  Google Scholar 

  13. Dong, X., Wang, X.: Quantum key-recovery attack on Feistel structures. IACR Cryptology ePrint Archive, 2017:1199 (2017)

    Google Scholar 

  14. Guo, J., Jean, J., Nikolić, I., Sasaki, Y.: Meet-in-the-middle attacks on generic Feistel constructions. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 458–477. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_24

    CrossRef  Google Scholar 

  15. Guo, J., Jean, J., Nikolic, I., Sasaki, Y.: Meet-in-the-middle attacks on classes of contracting and expanding Feistel constructions. IACR Trans. Symmetric Cryptol. 2016(2), 307–337 (2016)

    Google Scholar 

  16. Grover, L.K., Rudolph, T.: How significant are the known collision and element distinctness quantum algorithms? Quantum Inf. Comput. 4(3), 201–206 (2004)

    MathSciNet  MATH  Google Scholar 

  17. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, 22–24 May 1996, pp. 212–219 (1996)

    Google Scholar 

  18. Hosoyamada, A., Sasaki, Y.: Quantum Demiric-Selçuk meet-in-the-middle attacks: applications to 6-round generic Feistel constructions. IACR Cryptology ePrint Archive, 2017:1229 (2017)

    Google Scholar 

  19. Hosoyamada, A., Sasaki, Y.: Cryptanalysis against symmetric-key schemes with online classical queries and offline quantum computations. In: Smart, N.P. (ed.) CT-RSA 2018. LNCS, vol. 10808, pp. 198–218. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76953-0_11

    CrossRef  Google Scholar 

  20. Isobe, T., Shibutani, K.: All subkeys recovery attack on block ciphers: extending meet-in-the-middle approach. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 202–221. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35999-6_14

    CrossRef  MATH  Google Scholar 

  21. Isobe, T., Shibutani, K.: Generic key recovery attack on Feistel scheme. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8269, pp. 464–485. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42033-7_24

    CrossRef  Google Scholar 

  22. Kaplan, M.: Quantum attacks against iterated block ciphers. CoRR abs/1410.1434 (2014)

    Google Scholar 

  23. Kaplan, M., Leurent, G., Leverrier, A.,  Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 207–237. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_8

    CrossRef  Google Scholar 

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

    MATH  Google Scholar 

  25. Kuwakado, H., Morii, M.: Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: Proceedings of the IEEE International Symposium on Information Theory, ISIT 2010, Austin, Texas, USA, 13–18 June 2010, pp. 2682–2685 (2010)

    Google Scholar 

  26. Kuwakado, H., Morii, M.: Security on the quantum-type Even-Mansour cipher. In: Proceedings of the International Symposium on Information Theory and its Applications, ISITA 2012, Honolulu, HI, USA, 28–31 October 2012, pp. 312–316 (2012)

    Google Scholar 

  27. Knudsen, L.R.: The security of Feistel ciphers with six rounds or less. J. Cryptol. 15(3), 207–222 (2002)

    MathSciNet  CrossRef  Google Scholar 

  28. Leander, G., May, A.: Grover meets Simon – quantumly attacking the FX-construction. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 161–178. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_6

    CrossRef  Google Scholar 

  29. McKay, K.A., Bassham, L., Turan, M.S., Mouha, N.: NISTIR 8114 report on lightweight cryptography. Technical report, U.S. Department of Commerce, National Institute of Standards and Technology (2017)

    Google Scholar 

  30. Mennink, B., Szepieniec, A.: XOR of PRPs in a quantum world. In: Lange, T., Takagi, T. (eds.) PQCrypto 2017. LNCS, vol. 10346, pp. 367–383. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59879-6_21

    CrossRef  Google Scholar 

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

    MathSciNet  CrossRef  Google Scholar 

  32. Tani, S.: Claw finding algorithms using quantum walk. Theor. Comput. Sci. 410(50), 5285–5297 (2009)

    MathSciNet  CrossRef  Google Scholar 

  33. Zhang, S.: Promised and distributed quantum search. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 430–439. Springer, Heidelberg (2005). https://doi.org/10.1007/11533719_44

    CrossRef  Google Scholar 

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Correspondence to Akinori Hosoyamada .

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Hosoyamada, A., Sasaki, Y. (2018). Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-98113-0_21

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