Skip to main content

Extending SAT Solvers to Cryptographic Problems

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-02777-2_24
  • Chapter length: 14 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-02777-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. 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)

    CrossRef  Google Scholar 

  3. Nohl, K.: Description of HiTag2 (Webpage), http://cryptolib.com/ciphers/hitag2/

  4. Raddum, H.: Cryptanalytic results on Trivium. Technical Report 2006/039, ECRYPT Stream Cipher Project (2006)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  6. McDonald, C., Charnes, C., Pieprzyk, J.: Attacking Bivium with Minisat. Technical Report 2007/040, ECRYPT Stream Cipher Project (2007)

    Google Scholar 

  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. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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. 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. 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)

    CrossRef  Google Scholar 

  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. Massacci, F., Marraro, L.: Logical cryptanalysis as a SAT-problem: Encoding and analysis. Journal of Automated Reasoning 24, 165–203 (2000)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. Sinz, C.: Visualizing SAT instances and runs of the DPLL algorithm. J. Autom. Reason. 39(2), 219–243 (2007)

    CrossRef  MATH  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Soos, M., Nohl, K., Castelluccia, C. (2009). Extending SAT Solvers to Cryptographic Problems. In: Kullmann, O. (eds) Theory and Applications of Satisfiability Testing - SAT 2009. SAT 2009. Lecture Notes in Computer Science, vol 5584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02777-2_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02777-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02776-5

  • Online ISBN: 978-3-642-02777-2

  • eBook Packages: Computer ScienceComputer Science (R0)