Advertisement

Analysis of Impossible, Integral and Zero-Correlation Attacks on Type-II Generalized Feistel Networks Using the Matrix Method

  • Céline Blondeau
  • Marine Minier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9054)

Abstract

While recent publications have shown strong relations between impossible differential and zero-correlation distinguishers as well as between zero-correlation and integral distinguishers, we analyze in this paper some relations between the underlying key-recovery attacks against Type-II Feistel networks. The results of this paper are build on the relation presented at ACNS 2014. In particular, using a matrix representation of the round function, we show that we can not only find impossible, integral and multidimensional zero-correlation distinguishers but also find the key-words involved in the underlined key-recovery attacks. Based on this representation, for matrix-method-derived strongly-related zero-correlation and impossible distinguishers, we show that the key-words involved in the zero-correlation attack is a subset of the key-words involved in the impossible differential attack. Other relations between the key-words involved in zero-correlation, impossible and integral attacks are also extracted. Also we show that in this context the data complexity of the multidimensional zero-correlation attack is larger than that of the other two attacks.

Keywords

Block ciphers Feistel like ciphers Impossible differential Zero-correlation Integral Key-recovery attacks Matrix method 

Notes

Acknowledgment

The authors would like to thank the anonymous referees for their helpful comments. We also wish to thank the Aalto Science Institute (AScI) for funding the research visit of Marine Minier at Aalto University.

References

  1. 1.
    Berger, T.P., Minier, M., Thomas, G.: Extended generalized Feistel networks using matrix representation. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 289–305. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  2. 2.
    Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 12. Springer, Heidelberg (1999) Google Scholar
  3. 3.
    Blondeau, C., Bogdanov, A., Wang, M.: On the (in)equivalence of impossible differential and zero-correlation distinguishers for Feistel- and Skipjack-type ciphers. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 271–288. Springer, Heidelberg (2014) Google Scholar
  4. 4.
    Blondeau, C., Gérard, B., Tillich, J.-P.: Accurate estimates of the data complexity and success probability for various cryptanalyses. Des. Codes Crypt. 59(1–3), 3–34 (2011)CrossRefzbMATHGoogle Scholar
  5. 5.
    Blondeau, C., Minier, M.: Relations between impossible, integral and zero-correlation key-recovery attacks (extended version). Cryptology ePrint Archive, Report 2015/141 (2015). http://eprint.iacr.org/
  6. 6.
    Blondeau, C., Nyberg, K.: New links between differential and linear cryptanalysis. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 388–404. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  7. 7.
    Blondeau, C., Nyberg, K.: Links between truncated differential and multidimensional linear properties of block ciphers and underlying attack complexities. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 165–182. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  8. 8.
    Bogdanov, A., Geng, H., Wang, M., Wen, L., Collard, B.: Zero-correlation linear cryptanalysis with FFT and improved attacks on ISO standards Camellia and CLEFIA. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 306–323. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  9. 9.
    Bogdanov, A., Leander, G., Nyberg, K., Wang, M.: Integral and multidimensional linear distinguishers with correlation zero. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 244–261. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  10. 10.
    Bogdanov, A., Rijmen, V.: Zero-correlation linear cryptanalysis of block ciphers. IACR Cryptology, p. 123 (2011) ePrint Archive 2011Google Scholar
  11. 11.
    Bogdanov, A., Wang, M.: Zero correlation linear cryptanalysis with reduced data complexity. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 29–48. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  12. 12.
    Bouillaguet, C., Dunkelman, O., Fouque, P.-A., Leurent, G.: New insights on impossible differential cryptanalysis. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 243–259. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  13. 13.
    Boura, C., Minier, M., Naya-Plasencia, M., Suder, V.: Improved impossible differential attacks against round-reduced LBlock. Cryptology ePrint Archive, Report 2014/279 (2014). http://eprint.iacr.org/
  14. 14.
    Boura, C., Naya-Plasencia, M., Suder, V.: Scrutinizing and improving impossible differential attacks: applications to CLEFIA, Camellia, LBlock and Simon. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 179–199. Springer, Heidelberg (2014) Google Scholar
  15. 15.
    Chen, J., Wang, M., Preneel, B.: Impossible differential cryptanalysis of the lightweight block ciphers TEA, XTEA and HIGHT. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 117–137. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  16. 16.
    Daemen, J., Knudsen, L.R., Rijmen, V.: The block cipher SQUARE. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997) CrossRefGoogle Scholar
  17. 17.
    Ferguson, N., Kelsey, J., Lucks, S., Schneier, B., Stay, M., Wagner, D., Whiting, D.L.: Improved cryptanalysis of Rijndael. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  18. 18.
    Karakoç, F., Demirci, H., Harmancı, A.E.: Impossible differential cryptanalysis of reduced-round LBlock. In: Askoxylakis, I., Pöhls, H.C., Posegga, J. (eds.) WISTP 2012. LNCS, vol. 7322, pp. 179–188. Springer, Heidelberg (2012) Google Scholar
  19. 19.
    Kim, J.-S., Hong, S.H., Sung, J., Lee, S.-J., Lim, J.-I., Sung, S.H.: Impossible differential cryptanalysis for block cipher structures. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 82–96. Springer, Heidelberg (2003) CrossRefGoogle Scholar
  20. 20.
    Knudsen, L.: DEAL-a 128-bit block cipher. complexity, vol. 258, no. 2 (1998)Google Scholar
  21. 21.
    Knudsen, L.R., Wagner, D.: Integral Cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  22. 22.
    Lu, J., Wei, Y., Kim, J., Pasalic, E.: The higher-order meet-in-the-middle attack and its application to the Camellia block cipher. Theor. Comput. Sci. 527, 102–122 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Luo, Y., Lai, X., Wu, Z., Gong, G.: A unified method for finding impossible differentials of block cipher structures. Inf. Sci. 263, 211–220 (2014)CrossRefGoogle Scholar
  24. 24.
    Sasaki, Y., Wang, L.: Comprehensive study of integral analysis on 22-round LBlock. In: Kwon, T., Lee, M.-K., Kwon, D. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 156–169. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  25. 25.
    Sasaki, Y., Wang, L.: Meet-in-the-middle technique for integral attacks against Feistel ciphers. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 234–251. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  26. 26.
    Soleimany, H., Nyberg, K.: Zero-correlation linear cryptanalysis of reduced-round LBlock. Des. Codes Crypt. 73(2), 683–698 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Suzaki, T., Minematsu, K.: Improving the generalized Feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  28. 28.
    Voutier, P.M.: A new approximation to the normal distribution quantile function (2010). ArXiv e-prints, February 2010Google Scholar
  29. 29.
    Wang, Q., Liu, Z., Varici, K., Sasaki, Y., Rijmen, V., Todo, Y.: Cryptanalysis of Reduced-round SIMON32 and SIMON48. Cryptology ePrint Archive, Report 2014/761 (2014). http://eprint.iacr.org/
  30. 30.
    Wen, L., Wang, M., Bogdanov, A.: Multidimensional zero-correlation linear cryptanalysis of E2. In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT. LNCS, vol. 8469, pp. 147–164. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  31. 31.
    Wen, L., Wang, M., Bogdanov, A., Chena, H.: Multidimensional zero-correlation attacks on lightweight block cipher HIGHT: improved cryptanalysis of an ISO standard. Inf. Process. Lett. 114(6), 322–330 (2014)CrossRefzbMATHGoogle Scholar
  32. 32.
    Wu, W., Zhang, L.: LBlock: a lightweight block cipher. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 327–344. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  33. 33.
    Zhang, W., Su, B., Wu, W., Feng, D., Wu, C.: Extending higher-order integral: an efficient unified algorithm of constructing integral distinguishers for block ciphers. In: Bao, F., Samarati, P., Zhou, J. (eds.) ACNS 2012. LNCS, vol. 7341, pp. 117–134. Springer, Heidelberg (2012) CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.Department of Computer Science, School of ScienceAalto UniversityEspooFinland
  2. 2.Université de Lyon, INRIA, INSA-Lyon, CITIVilleurbanneFrance

Personalised recommendations