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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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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

Authors
  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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