Advertisement

Constraint Programming Models for Chosen Key Differential Cryptanalysis

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9892)

Abstract

In this paper, we introduce Constraint Programming (CP) models to solve a cryptanalytic problem: the chosen key differential attack against the standard block cipher AES. The problem is solved in two steps: In Step 1, bytes are abstracted by binary values; In Step 2, byte values are searched. We introduce two CP models for Step 1: Model 1 is derived from AES rules in a straightforward way; Model 2 contains new constraints that remove invalid solutions filtered out in Step 2. We also introduce a CP model for Step 2. We evaluate scale-up properties of two classical CP solvers (Gecode and Choco) and a hybrid SAT/CP solver (Chuffed). We show that Model 2 is much more efficient than Model 1, and that Chuffed is faster than Choco which is faster than Gecode on the hardest instances of this problem. Furthermore, we prove that a solution claimed to be optimal in two recent cryptanalysis papers is not optimal by providing a better solution.

Notes

Acknowledgements

Many thanks to Jean-Guillaume Fages, for sending us Choco 4 before the official public release, and to Yves Deville, Pierre Schaus and François-Xavier Standaert for enriching discussions on this work.

Supplementary material

References

  1. 1.
    Biham, E.: New types of cryptanalytic attacks using related keys. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 398–409. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential cryptanalysis of feal and N-Hash. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 1–16. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  3. 3.
    Biryukov, A., Nikolić, I.: Automatic search for related-key differential characteristics in byte-oriented block ciphers: application to AES, Camellia, Khazad and others. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 322–344. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Chu, G., Stuckey, P.J.: Chuffed solver description (2014). http://www.minizinc.org/challenge2014/description_chuffed.txt
  5. 5.
    Daemen, J., Rijmen, V.: The Design of Rijndael. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  6. 6.
    De, D., Kumarasubramanian, A., Venkatesan, R.: Inversion attacks on secure hash functions using sat solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 377–382. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Fages, J.-G.: On the use of graphs within constraint-programming. Constraints 20(4), 498–499 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    FIPS 197. Advanced Encryption Standard. Federal Information Processing Standards Publication 197. U.S. Department of Commerce/N.I.S.T (2001)Google Scholar
  9. 9.
    Fouque, P.-A., Jean, J., Peyrin, T.: Structural evaluation of AES and chosen-key distinguisher of 9-round AES-128. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 183–203. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Team, G.: Gecode: Generic constraint development environment (2006). http://www.gecode.org
  11. 11.
    Karpman, P., Peyrin, T., Stevens, M.: Practical free-start collision attacks on 76-step SHA-1. IACR Cryptology ePrint Archive 2015:530 (2015)Google Scholar
  12. 12.
    Legendre, F., Dequen, G., Krajecki, M.: Encoding hash functions as a sat problem. In: IEEE 24th International Conference on Tools with Artificial Intelligence, ICTAI 2012, Athens, Greece, 7–9 November 2012, pp. 916–921. IEEE (2012)Google Scholar
  13. 13.
    Michel, L.D., Van Hentenryck, P.: Constraint satisfaction over bit-vectors. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 527–543. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Minier, M., Solnon, C., Reboul, J.: Solving a Symmetric Key Cryptographic Problem with Constraint Programming. In: ModRef 2014, Workshop of the CP 2014 Conference, September 2014, Lyon, France, July 2014Google Scholar
  15. 15.
    Mironov, I., Zhang, L.: Applications of SAT solvers to cryptanalysis of hash functions. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 102–115. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Morawiecki, P., Srebrny, M.: A sat-based preimage analysis of reduced keccak hash functions. Inf. Process. Lett. 113(10–11), 392–397 (2013)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and linear cryptanalysis using mixed-integer linear programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012)Google Scholar
  18. 18.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.R.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Prudhomme, C., Fages, J.-G.: An introduction to choco 3.0: an open source java constraint programming library. In: CP Workshop on CP Solvers: Modeling, Applications, Integration, and Standardization (2013)Google Scholar
  20. 20.
    Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Sun, S., Hu, L., Wang, M., Yang, Q., Qiao, K., Ma, X., Song, L., Shan, J.: Extending the applicability of the mixed-integer programming technique in automatic differential cryptanalysis. In: López, J., Mitchell, C.J. (eds.) ISC 2015. LNCS, vol. 9290, pp. 141–157. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  22. 22.
    Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014)Google Scholar
  23. 23.
    Wang, X., Yu, H.: How to break MD5 and other hash functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  24. 24.
    Wang, X., Yu, H., Yin, Y.L.: Efficient collision search attacks on SHA-0. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 1–16. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • David Gerault
    • 4
  • Marine Minier
    • 1
    • 2
  • Christine Solnon
    • 1
    • 3
  1. 1.Université de Lyon, INSA-LyonVilleurbanneFrance
  2. 2.CITI, INRIAVilleurbanneFrance
  3. 3.LIRIS, CNRS UMR5205VilleurbanneFrance
  4. 4.LIMOSClermont-ferrandFrance

Personalised recommendations