Skip to main content
SpringerLink
Log in

ALIAS: A Modular Tool for Finding Backdoors for SAT

  • Conference paper
  • First Online:
Theory and Applications of Satisfiability Testing – SAT 2018 (SAT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10929))

Abstract

We present ALIAS, a modular tool aimed at finding backdoors for hard SAT instances. Here by a backdoor for a specific SAT solver and SAT formula we mean a set of its variables, all possible instantiations of which lead to construction of a family of subformulas with the total solving time less than that for an original formula. For a particular backdoor, the tool uses the Monte-Carlo algorithm to estimate the runtime of a solver when partitioning an original problem via said backdoor. Thus, the problem of finding a backdoor is viewed as a black-box optimization problem. The tool’s modular structure allows to employ state-of-the-art SAT solvers and black-box optimization heuristics. In practice, for a number of hard SAT instances, the tool made it possible to solve them much faster than using state-of-the-art multithreaded SAT-solvers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Irkutsk Supercomputer Center of SB RAS, http://hpc.icc.ru.

References

  1. Ansótegui, C., Sellmann, M., Tierney, K.: A gender-based genetic algorithm for the automatic configuration of algorithms. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 142–157. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04244-7_14

    Chapter  Google Scholar 

  2. Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39071-5_23

    Chapter  MATH  Google Scholar 

  3. Audemard, G., Simon, L.: Lazy clause exchange policy for parallel SAT solvers. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 197–205. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_15

    Chapter  MATH  Google Scholar 

  4. Balyo, T., Biere, A., Iser, M., Sinz, C.: SAT race 2015. Artif. Intell. 241, 45–65 (2016)

    Article  MathSciNet  Google Scholar 

  5. Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling, YalSAT entering the SAT competition 2017. In: Proceedings of SAT Competition 2017, vol. B-2017-1, pp. 14–15 (2017)

    Google Scholar 

  6. Chen, J.: Improving abcdSAT by At-Least-One recently used clause management strategy. CoRR abs/1605.01622 (2016). http://arxiv.org/abs/1605.01622

  7. Courtois, N.: Low-complexity key recovery attacks on GOST block cipher. Cryptologia 37(1), 1–10 (2013)

    Article  Google Scholar 

  8. Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional horn formulae. J. Log. Program. 1(3), 267–284 (1984)

    Article  MathSciNet  Google Scholar 

  9. Eibach, T., Pilz, E., Völkel, G.: Attacking bivium using SAT solvers. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 63–76. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79719-7_7

    Chapter  MATH  Google Scholar 

  10. Le Frioux, L., Baarir, S., Sopena, J., Kordon, F.: PaInleSS: a framework for parallel SAT solving. In: Gaspers, S., Walsh, T. (eds.) SAT 2017. LNCS, vol. 10491, pp. 233–250. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66263-3_15

    Chapter  MATH  Google Scholar 

  11. Günther, C.G.: Alternating step generators controlled by de Bruijn sequences. In: Chaum, D., Price, W.L. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 5–14. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-39118-5_2

    Chapter  Google Scholar 

  12. Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Proceedings of LION-5, pp. 507–523 (2011)

    Google Scholar 

  13. Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T.: ParamILS: an automatic algorithm configuration framework. JAIR 36, 267–306 (2009)

    MATH  Google Scholar 

  14. Hutter, F., Lindauer, M., Balint, A., Bayless, S., Hoos, H., Leyton-Brown, K.: The configurable SAT solver challenge (CSSC). Artif. Intell. 243, 1–25 (2017)

    Article  MathSciNet  Google Scholar 

  15. Kilby, P., Slaney, J.K., Thiébaux, S., Walsh, T.: Backbones and backdoors in satisfiability. AAAI 2005, 1368–1373 (2005)

    Google Scholar 

  16. Manthey, N.: Towards next generation sequential and parallel SAT solvers. Constraints 20(4), 504–505 (2015)

    Article  MathSciNet  Google Scholar 

  17. Metropolis, N., Ulam, S.: The Monte Carlo method. J. Amer. Stat. Assoc. 44(247), 335–341 (1949)

    Article  Google Scholar 

  18. Oh, C.: Between SAT and UNSAT: the fundamental difference in CDCL SAT. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 307–323. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24318-4_23

    Chapter  Google Scholar 

  19. Russell, S., Norvig, P.: Artificial Intelligence A Modern Approach, 3rd edn. Prentice Hall, Englewood Cliffs (2009)

    MATH  Google Scholar 

  20. Semenov, A., Zaikin, O.: Algorithm for finding partitionings of hard variants of Boolean satisfiability problem with application to inversion of some cryptographic functions. SpringerPlus 5(1), 1–16 (2016)

    Article  Google Scholar 

  21. Semenov, A., Zaikin, O., Otpuschennikov, I., Kochemazov, S., Ignatiev, A.: On cryptographic attacks using backdoors for SAT. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, New Orleans, Louisiana, USA, 2–7 February 2018 (2018). https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16855

  22. 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). https://doi.org/10.1007/978-3-642-02777-2_24

    Chapter  Google Scholar 

  23. Szeider, S.: Backdoor sets for DLL subsolvers. J. Autom. Reasoning 35(1), 73–88 (2005)

    MathSciNet  MATH  Google Scholar 

  24. Van Gelder, A., Spence, I.: Zero-one designs produce small hard SAT instances. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 388–397. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14186-7_37

    Chapter  MATH  Google Scholar 

  25. Wicik, R., Rachwalik, T.: Modified alternating step generators. IACR Cryptology ePrint Archive 2013, 728 (2013)

    Google Scholar 

  26. Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: IJCAI, pp. 1173–1178 (2003)

    Google Scholar 

  27. Zaikin, O., Kochemazov, S.: An improved SAT-based guess-and-determine attack on the alternating step generator. In: Nguyen, P., Zhou, J. (eds.) ISC 2017. LNCS, vol. 10599. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69659-1_2

    Chapter  Google Scholar 

Download references

Acknowledgements

We thank anonymous reviewers for their insightful comments that made it possible to significantly improve the quality of presentation.

The research was funded by Russian Science Foundation (project No. 16-11-10046). Stepan Kochemazov was additionally supported by Council for Grants of the President of the Russian Federation (stipend no. SP-1829.2016.5).

Author information

Authors and Affiliations

  1. ISDCT SB RAS, Irkutsk, Russia

    Stepan Kochemazov & Oleg Zaikin

Authors
  1. Stepan Kochemazov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oleg Zaikin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oleg Zaikin .

Editor information

Editors and Affiliations

  1. Friedrich Schiller University Jena, Jena, Germany

    Olaf Beyersdorff

  2. Microsoft Research Ltd., Cambridge, United Kingdom

    Christoph M. Wintersteiger

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kochemazov, S., Zaikin, O. (2018). ALIAS: A Modular Tool for Finding Backdoors for SAT. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94144-8_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94143-1

  • Online ISBN: 978-3-319-94144-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation