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Evolutionary Computation Techniques for Constructing SAT-Based Attacks in Algebraic Cryptanalysis

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Book cover Applications of Evolutionary Computation (EvoApplications 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11454))

Abstract

In this paper we present the results on applying evolutionary computation techniques to construction of several cryptographic attacks. In particular, SAT-based guess-and-determine attacks studied in the context of algebraic cryptanalysis. Each of these attacks is built upon some set of Boolean variables, thus it can be specified by a Boolean vector. We use two general evolutionary strategies to find an optimal vector: (1+1)-EA and GA. Based on these strategies parallel algorithms (based on modern SAT-solvers) for solving the problem of minimization of a special pseudo-Boolean function are implemented. This function is a fitness function used to evaluate the runtime of a guess-and-determine attack. We compare the efficiency of (1+1)-EA and GA with the algorithm from the Tabu search class, that was earlier used to solve related problems. Our GA-based solution showed the best results on a number of test instances, namely, cryptanalysis problems of several stream ciphers (cryptographic keystream generators).

The study was funded by a grant from the Russian Science Foundation (project No. 18-71-00150).

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References

  1. Bard, G.V.: Algebraic Cryptanalysis. Springer, New York (2009). https://doi.org/10.1007/978-0-387-88757-9

    Book  MATH  Google Scholar 

  2. 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), 554 (2016)

    Article  Google Scholar 

  3. Semenov, A., Zaikin, O., Otpuschennikov, I., Kochemazov, S., Ignatiev, A.: On cryptographic attacks using backdoors for SAT. In: Proceedings of AAAI 2018, pp. 6641–6648 (2018)

    Google Scholar 

  4. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, pp. 151–158. ACM (1971)

    Google Scholar 

  5. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (2009)

    Google Scholar 

  6. Anderson, R.: A5 (was: hacking digital phones). Newsgroup Communication (1994). http://yarchive.net/phone/gsmcipher.html

  7. Gendrullis, T., Novotný, M., Rupp, A.: A real-world attack breaking A5/1 within hours. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 266–282. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85053-3_17

    Chapter  Google Scholar 

  8. Courtois, N.T., Bard, G.V.: Algebraic cryptanalysis of the data encryption standard. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 152–169. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77272-9_10

    Chapter  Google Scholar 

  9. Courtois, N.T., Gawinecki, J.A., Song, G.: Contradiction immunity and guess-then-determine attacks on GOST. Tatra Mountains Math. Publ. 53, 65–79 (2012)

    Article  MathSciNet  Google Scholar 

  10. Semenov, A., Zaikin, O., Bespalov, D., Posypkin, M.: Parallel logical cryptanalysis of the generator A5/1 in BNB-grid system. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 473–483. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23178-0_43

    Chapter  MATH  Google Scholar 

  11. Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Frontiers in Artificial Intelligence and Applications, vol. 85, pp. 131–153 (2009)

    Google Scholar 

  12. Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discrete Appl. Math. 123(1–3), 155–225 (2002)

    Article  MathSciNet  Google Scholar 

  13. King, J.C.: Symbolic execution and program testing. Commun. ACM 19(7), 385–394 (1976)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  15. Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovac, Hamburg (1997)

    MATH  Google Scholar 

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

    Google Scholar 

  17. Menezes, A.J., Vanstone, S.A., Oorschot, P.C.V.: Handbook of Applied Cryptography, 1st edn. CRC Press Inc., Boca Raton (1996)

    Book  Google Scholar 

  18. Nohl, K.: Attacking Phone Privacy, pp. 1–6. Black Hat, Las Vegas (2010)

    Google Scholar 

  19. 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). https://doi.org/10.1007/11836810_13

    Chapter  Google Scholar 

  20. Raddum, H.: Cryptanalytic Results on Trivium. eSTREAM, ECRYPT Stream Cipher Project, Report 2006/039 (2006)

    Google Scholar 

  21. Maximov, A., Biryukov, A.: Two trivial attacks on Trivium. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 36–55. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77360-3_3

    Chapter  Google Scholar 

  22. 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 

  23. Eibach, T., Völkel, G., Pilz, E.: Optimising Gröbner bases on Bivium. Math. Comput. Sci. 3(2), 159–172 (2010)

    Article  MathSciNet  Google Scholar 

  24. 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 

  25. Huang, Z., Lin, D.: Attacking Bivium and Trivium with the characteristic set method. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 77–91. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21969-6_5

    Chapter  Google Scholar 

  26. Castro Lechtaler, A., Cipriano, M., García, E., Liporace, J., Maiorano, A., Malvacio, E.: Model design for a reduced variant of a Trivium type stream cipher. J. Comput. Sci. Technol. 14(01), 55–58 (2014)

    Google Scholar 

  27. Teo, S.G., Wong, K.K.H., Bartlett, H., Simpson, L., Dawson, E.: Algebraic analysis of Trivium-like ciphers. In: Australasian Information Security Conference (ACSW-AISC 2014), vol. 149, pp. 77–81. Australian Computer Society (2014)

    Google Scholar 

  28. 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 

  29. Khazaei, S., Fischer, S., Meier, W.: Reduced complexity attacks on the alternating step generator. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 1–16. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77360-3_1

    Chapter  Google Scholar 

  30. Zeng, K., Yang, C.H., Rao, T.R.N.: On the Linear Consistency Test (LCT) in cryptanalysis with applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 164–174. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_16

    Chapter  Google Scholar 

  31. 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, pp. 21–38. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69659-1_2

    Chapter  Google Scholar 

  32. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Boston (1997)

    Book  Google Scholar 

  33. Yasumoto, T., Okuwaga, T.: ROKK 1.0.1. In: Belov, A., Diepold, D., Heule, M., Järvisalo, M. (eds.) SAT Competition 2014, p. 70 (2014)

    Google Scholar 

  34. Otpuschennikov, I., Semenov, A., Gribanova, I., Zaikin, O., Kochemazov, S.: Encoding cryptographic functions to SAT using TRANSALG system. In: ECAI 2016. FAIA, vol. 285, pp. 1594–1595 (2016)

    Google Scholar 

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Acknowledgements

The authors would like to thank Daniil Chivilikhin, Maxim Buzdalov and anonymous reviewers for useful comments.

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Authors and Affiliations

  1. ITMO University, St. Petersburg, Russia

    Artem Pavlenko & Vladimir Ulyantsev

  2. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander Semenov

Authors
  1. Artem Pavlenko
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  2. Alexander Semenov
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  3. Vladimir Ulyantsev
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Corresponding author

Correspondence to Artem Pavlenko .

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Editors and Affiliations

  1. University of Mainz, Mainz, Germany

    Paul Kaufmann

  2. University of Granada, Granada, Spain

    Pedro A. Castillo

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Pavlenko, A., Semenov, A., Ulyantsev, V. (2019). Evolutionary Computation Techniques for Constructing SAT-Based Attacks in Algebraic Cryptanalysis. In: Kaufmann, P., Castillo, P. (eds) Applications of Evolutionary Computation. EvoApplications 2019. Lecture Notes in Computer Science(), vol 11454. Springer, Cham. https://doi.org/10.1007/978-3-030-16692-2_16

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  • DOI: https://doi.org/10.1007/978-3-030-16692-2_16

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