Advertisement

Extending SAT Solvers to Cryptographic Problems

  • Mate Soos
  • Karsten Nohl
  • Claude Castelluccia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5584)

Abstract

Cryptography ensures the confidentiality and authenticity of information but often relies on unproven assumptions. SAT solvers are a powerful tool to test the hardness of certain problems and have successfully been used to test hardness assumptions. This paper extends a SAT solver to efficiently work on cryptographic problems. The paper further illustrates how SAT solvers process cryptographic functions using automatically generated visualizations, introduces techniques for simplifying the solving process by modifying cipher representations, and demonstrates the feasibility of the approach by solving three stream ciphers.

To optimize a SAT solver for cryptographic problems, we extended the solver’s input language to support the XOR operation that is common in cryptography. To better understand the inner workings of the adapted solver and to identify bottlenecks, we visualize its execution. Finally, to improve the solving time significantly, we remove these bottlenecks by altering the function representation and by pre-parsing the resulting system of equations.

The main contribution of this paper is a new approach to solving cryptographic problems by adapting both the problem description and the solver synchronously instead of tweaking just one of them. Using these techniques, we were able to solve a well-researched stream cipher 26 times faster than was previously possible.

Keywords

Search Tree Gaussian Elimination Conjunctive Normal Form Stream Cipher Linear Feedback Shift Register 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bard, G.V.: Algorithms for the solution of polynomial and linear systems of equations over finite fields, with an application to the cryptanalysis of KeeLoq. Technical report, University of Maryland Dissertation (April 2008)Google Scholar
  2. 2.
    Garcia, F.D., et al.: Dismantling MIFARE Classic. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 97–114. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Nohl, K.: Description of HiTag2 (Webpage), http://cryptolib.com/ciphers/hitag2/
  4. 4.
    Raddum, H.: Cryptanalytic results on Trivium. Technical Report 2006/039, ECRYPT Stream Cipher Project (2006)Google Scholar
  5. 5.
    De Cannière, C.: Trivium: A stream cipher construction inspired by block cipher design principles. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds.) ISC 2006. LNCS, vol. 4176, pp. 171–186. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    McDonald, C., Charnes, C., Pieprzyk, J.: Attacking Bivium with Minisat. Technical Report 2007/040, ECRYPT Stream Cipher Project (2007)Google Scholar
  7. 7.
    Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. In: Proc. of Intl. Workshop on Bounded Model Checking. ENTCS, vol. 89 (2003)Google Scholar
  8. 8.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Marques, J.P., Karem, S., Sakallah, A.: Conflict analysis in search algorithms for propositional satisfiability. In: Proc. of the IEEE Intl. Conf. on Tools with Artificial Intelligence (1996)Google Scholar
  10. 10.
    Malik, S., Zhao, Y., Madigan, C.F., Zhang, L., Moskewicz, M.W.: Chaff: Engineering an efficient SAT solver. In: Design Automation Conference, pp. 530–535 (2001)Google Scholar
  11. 11.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Faugère, J.C.: A new efficient algorithm for computing Gröbner bases without reduction to zero (F5). In: ISSAC 2002, pp. 75–83. ACM Press, New York (2002)Google Scholar
  13. 13.
    Massacci, F., Marraro, L.: Logical cryptanalysis as a SAT-problem: Encoding and analysis. Journal of Automated Reasoning 24, 165–203 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Courtois, N.T.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176–194. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Li, C.M.: Equivalency reasoning to solve a class of hard SAT problems. Information Processing Letters 75(1-2), 75–81 (1999)Google Scholar
  16. 16.
    Sinz, C.: Visualizing SAT instances and runs of the DPLL algorithm. J. Autom. Reason. 39(2), 219–243 (2007)CrossRefzbMATHGoogle Scholar
  17. 17.
    Courtois, N.T., Nohl, K., O’Neil, S.: Algebraic attacks on the Crypto-1 stream cipher in Mifare Classic and Oyster cards. Technical Report 2008/166, Cryptology ePrint Archive (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mate Soos
    • 1
  • Karsten Nohl
    • 2
  • Claude Castelluccia
    • 1
  1. 1.INRIA Rhône-AlpesFrance
  2. 2.University of VirginiaUSA

Personalised recommendations