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An Improved SAT-Based Guess-and-Determine Attack on the Alternating Step Generator

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Information Security (ISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10599))

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Abstract

In this paper, we propose an algorithm for constructing guess-and-determine attacks on keystream generators and apply it to the cryptanalysis of the alternating step generator (ASG) and two its modifications (MASG and MASG0). In a guess-and-determine attack, we first “guess” some part of an initial state and then apply some procedure to determine, if the guess was correct and we can use the guessed information to solve the problem, thus performing an exhaustive search over all possible assignments of bits forming a chosen part of an initial state. We propose to use in the “determine” part the algorithms for solving Boolean satisfiability problem (SAT). It allows us to consider sets of bits with nontrivial structure. For each such set it is possible to estimate the runtime of a corresponding guess-and-determine attack via the Monte-Carlo method, so we can search for a set of bits yielding the best attack via a black-box optimization algorithm augmented with several SAT-specific features. We constructed and implemented such attacks on ASG, MASG, and MASG0 to prove that the constructed runtime estimations are reliable. We show, that the constructed attacks are better than the trivial ones, which imply exhaustive search over all possible states of the control register, and present the results of experiments on cryptanalysis of ASG and MASG/MASG0 with total registers length of 72 and 96, which have not been previously published in the literature.

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References

  1. Balyo, T., Heule, M.J.H., Järvisalo, M.: SAT competition 2016: recent developments. In: Singh, S.P., Markovitch, S. (eds.) Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, California, USA, pp. 5061–5063. AAAI Press, 4–9 February 2017

    Google Scholar 

  2. Bard, G.V.: Algebraic Cryptanalysis, 1st edn. Springer, US (2009)

    Book  MATH  Google Scholar 

  3. Biere, A.: Splatz, Lingeling, Plingeling, Treengeling, YalSAT entering the SAT competition 2016. In: Balyo, T., Heule, M., Järvisalo, M. (eds.) Proceedings of SAT Competition 2016 – Solver and Benchmark Descriptions. Department of Computer Science Series of Publications B, vol. B-2016-1, pp. 44–45. University of Helsinki (2016)

    Google Scholar 

  4. 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 

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

    Article  Google Scholar 

  6. Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dubrova, E.: A list of maximum period NLFSRs. IACR Cryptology ePrint Archive 2012, 166 (2012). Informal publication

    Google Scholar 

  8. 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). doi:10.1007/978-3-540-24605-3_37

    Chapter  Google Scholar 

  9. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)

    Article  MATH  Google Scholar 

  10. 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). doi:10.1007/978-3-540-79719-7_7

    Chapter  Google Scholar 

  11. Erkök, L., Matthews, J.: High assurance programming in Cryptol. In: Sheldon, F.T., Peterson, G., Krings, A.W., Abercrombie, R.K., Mili, A. (eds.) Fifth Cyber Security and Information Intelligence Research Workshop, CSIIRW 2009, Knoxville, TN, USA, p. 60. ACM, 13–15 April 2009

    Google Scholar 

  12. Fishman, G.S.: Monte Carlo: Concepts, Algorithms, and Applications. Springer Series in Operations Research. Springer, New York (1996)

    Book  MATH  Google Scholar 

  13. Foster, I.: Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering. Addison-Wesley Longman Publishing Co., Inc., Boston (1995)

    MATH  Google Scholar 

  14. Golić, J.D., Menicocci, R.: Edit distance correlation attack on the alternating step generator. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 499–512. Springer, Heidelberg (1997). doi:10.1007/BFb0052258

    Chapter  Google Scholar 

  15. Golic, J.D., Menicocci, R.: Correlation analysis of the alternating step generator. Des. Codes Crypt. 31(1), 51–74 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. 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). doi:10.1007/3-540-39118-5_2

    Google Scholar 

  17. Hyvärinen, A.E.J.: Grid Based Propositional Satisfiability Solving. Ph.D. thesis, Aalto University (2011)

    Google Scholar 

  18. Janicic, P.: URSA: a system for uniform reduction to SAT. Logical Methods Comput. Sci. 8(3), 1–39 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Johansson, T.: Reduced complexity correlation attacks on two clock-controlled generators. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 342–356. Springer, Heidelberg (1998). doi:10.1007/3-540-49649-1_27

    Chapter  Google Scholar 

  20. 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). doi:10.1007/978-3-540-77360-3_1

    Chapter  Google Scholar 

  21. Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere et al. [4], pp. 131–153

    Google Scholar 

  22. Massacci, F., Marraro, L.: Logical cryptanalysis as a SAT problem. J. Autom. Reasoning 24(1/2), 165–203 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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

  24. 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). doi:10.1007/11814948_13

    Chapter  Google Scholar 

  25. Maximum period NLFSRs. https://people.kth.se/~dubrova/nlfsr.html

  26. Otpuschennikov, I., Semenov, A., Gribanova, I., Zaikin, O., Kochemazov, S.: Encoding cryptographic functions to SAT using TRANSALG system. In: ECAI 2016 - 22nd European Conference on Artificial Intelligence, 29 August-2 September 2016, The Hague, The Netherlands. Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 1594–1595. IOS Press (2016)

    Google Scholar 

  27. Prestwich, S.D.: CNF encodings. In: Biere et al. [4], pp. 75–97

    Google Scholar 

  28. Semenov, A.A., Zaikin, O.S.: Using Monte Carlo method for searching partitionings of hard variants of Boolean satisfiability problem. In: Malyshkin, V. (ed.) Proceedings of the 13th International Conference on Parallel Computing Technologies, 31 August - 4 September, Petrozavodsk, Russia, pp. 222–230 (2015)

    Google Scholar 

  29. 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 

  30. 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). doi:10.1007/978-3-642-02777-2_24

    Chapter  Google Scholar 

  31. Soos, M.: Grain of salt - an automated way to test stream ciphers through SAT solvers. In: Tools 2010: Proceedings of the Workshop on Tools for Cryptanalysis, pp. 131–144 (2010)

    Google Scholar 

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

    Google Scholar 

  33. 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). doi:10.1007/0-387-34805-0_16

    Chapter  Google Scholar 

  34. Zenner, E.: On the efficiency of the clock control guessing attack. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 200–212. Springer, Heidelberg (2003). doi:10.1007/3-540-36552-4_14

    Chapter  Google Scholar 

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Acknowledgments

Authors thank all anonymous reviewers for valuable comments.

The research was funded by Russian Science Foundation (project No. 16-11-10046) and by Council for Grants of the President of the Russian Federation (stipends no. SP-1184.2015.5 and SP-1829.2016.5).

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Authors and Affiliations

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

    Oleg Zaikin & Stepan Kochemazov

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  1. Oleg Zaikin
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  2. Stepan Kochemazov
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Correspondence to Oleg Zaikin .

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Editors and Affiliations

  1. Inria, Tokyo, Japan

    Phong Q. Nguyen

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

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Zaikin, O., Kochemazov, S. (2017). An Improved SAT-Based Guess-and-Determine Attack on the Alternating Step Generator. In: Nguyen, P., Zhou, J. (eds) Information Security. ISC 2017. Lecture Notes in Computer Science(), vol 10599. Springer, Cham. https://doi.org/10.1007/978-3-319-69659-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-69659-1_2

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