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Quantum differential cryptanalysis

Abstract

The work is devoted to the study quantum versions of the differential cryptanalysis based on using a combination of the quantum minimum/maximum search algorithm and the quantum counting algorithm. We have estimated the complexity and the required resources for applying the quantum differential and quantum linear cryptanalysis to searching round keys of block ciphers. It is shown that the implementation of the quantum linear method requires less logical qubits than for the implementation of the quantum differential method. The acceleration of calculations due to “quantum parallelism” in the quantum differential cryptanalysis, based on a combination of Grover’s quantum algorithms and quantum counting algorithm, is apparently absent, because the using of quantum counting as “subprogram” in the Grover algorithm eliminates quantum acceleration, as far as \( O (\sqrt{K}) \cdot O (\sqrt{K}) \approx O (K) \).

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References

  1. 1.

    Biham E., Shamir A.: Differential cryptanalysis of the data encrypt standard. ISBN 978-1-4613-9314-6 (1993)

  2. 2.

    Matsui M.: Linear cryptanalysis method for DES cipher. In: Workshop on the Theory and Application of of Cryptographic Technique, pp. 386–397 (1994)

  3. 3.

    Xie, H., Yang, L.: Using Bernstein-Vazirani algorithm to attack block ciphers. Des. Codes Cryptogr. 87, 1161–1182 (2019). https://doi.org/10.1007/s10623-018-0510-5

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Li, H.-W., Yang, L.: A quantum algorithm to approximate the linear structures of Boolean functions. Math. Struct. Comput. Sci. 1, 1–13 (2014). https://doi.org/10.1017/S0960129516000013

    MathSciNet  Article  Google Scholar 

  5. 5.

    Li, H.-W., Yang, L.: Quantum differential cryptanalysis to the block ciphers. Int. Conf. Appl. Tech. Inf. Secur. (2015). https://doi.org/10.1017/978-3-662-48683-2_5

    Article  Google Scholar 

  6. 6.

    Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Quantum differential and linear cryptanalysis. IACR Trans. Symmetric Cryptol. 1, 71–94 (2016). https://doi.org/10.13154/tosc.v2016.i1.71-94

    Article  MATH  Google Scholar 

  7. 7.

    Zhou, Q., Lu, S., Zhang, A., Sun, J.: Quantum differential cryptanalysis. Quantum Inf. Process. 14, 2101–2109 (2015). https://doi.org/10.1007/s11128-015-0983-3

    Article  MATH  Google Scholar 

  8. 8.

    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)

    Article  Google Scholar 

  9. 9.

    Brassard, G., Hoyer, P., Tapp, A.: Quantum counting. Automata Lang. Program. 1443, 820–831 (1998). https://doi.org/10.1007/BFb0055105

    Article  Google Scholar 

  10. 10.

    Denisenko, D.V.: Application of the quantum counting to estimation the weights of Boolean functions in Quipper. J. Exp. Theor. Phys. 130, 643–648 (2020). https://doi.org/10.1134/S1063776120040032

    Article  Google Scholar 

  11. 11.

    Durr, C., Hoyer, P.: A quantum algorithm for finding the minimum. Phys. Rev. Lett. https://arxiv.org/abs/quant-ph/9607014 (1996)

  12. 12.

    Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press. http://csis.pace.edu/ctappert/cs837-18spring/QC-textbook.pdf (2010)

  13. 13.

    Denisenko, D.V.: Quantum circuits for S-box implementation without ancilla qubits. J. Exp. Theor. Phys. 128(6), 847–855 (2019). https://doi.org/10.1134/S1063776119050108

    Article  Google Scholar 

  14. 14.

    Denisenko, D.V., Nikitenkova, M.V.: Optimization of S-boxes GOST R 34.12–2015 “Magma” quantum circuits without ancilla qubits. Matematicheskie Voprosy Kriptografii 11, 43–52 (2020). https://doi.org/10.4213/mvk312

  15. 15.

    Bernstein E., Vazirani, U.: Quantum complexity theory. In: Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pp. 11–20. https://doi.org/10.1145/167088.167097 (1993)

  16. 16.

    Benenti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information (2004). https://doi.org/10.1142/5528

    Article  Google Scholar 

  17. 17.

    Denisenko, D.V., Nikitenkova, M.V.: Application of Grover’s quantum algorithm for SDES key searching. J. Exp. Theor. Phys. 128, 25–44 (2019). https://doi.org/10.1134/S1063776118120142

  18. 18.

    Roetteler, M., Steinwandt, R.: A note on quantum related-key attacks. Inf. Process. Lett. 115, 40–44 (2015). https://doi.org/10.1016/j.ipl.2014.08.009

    Article  MATH  Google Scholar 

  19. 19.

    Cuccaro, S.A., Draper, T.G., Kutin, S.A., Moulton, D.P.: A new quantum ripple-carry addition circuit. https://arxiv.org/abs/quant-ph/0410184 (2004)

  20. 20.

    Draper, T.G., Kutin, S.A., Rains, E.M., Svore, K.M.: A logarithmic-depth quantum carry-lookahead adder, Quantum information and computation, vol. 6. https://arxiv.org/abs/quant-ph/0406142 (2004)

  21. 21.

    Kaye, P.: Reversible addition circuit using one ancillary bit with application to quantum computing. https://arxiv.org/abs/quant-ph/0408173 (2004)

  22. 22.

    Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. AMS Contemporary Mathematics Series, vol. 305, ISBN 9780821821404. https://doi.org/10.1090/conm/305/05215 (2000)

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Correspondence to Denis Denisenko.

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Denisenko, D. Quantum differential cryptanalysis. J Comput Virol Hack Tech (2021). https://doi.org/10.1007/s11416-021-00395-x

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Keywords

  • Symmetric cryptography
  • Quantum attacks
  • Differential cryptanalysis
  • Block ciphers
  • Grover’s algorithm
  • Quantum counting