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Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith’s Methods

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Computing and Combinatorics (COCOON 2016)

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Abstract

We analyze the security of the Elliptic Curve Linear Congruential Generator (EC-LCG). We show that this generator is insecure if sufficiently many bits are output at each iteration. In 2007, Gutierrez and Ibeas showed that this generator is insecure given a certain amount of most significant bits of some consecutive values of the sequence. Using the Coppersmith’s methods, we are able to improve their security bounds.

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Acknowledgments

The author was supported in part by the French ANR JCJC ROMAnTIC project (ANR-12-JS02-0004) and by the Simons foundation Pole PRMAIS. I would like to thank anonymous referees for their helpful comments.

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Authors and Affiliations

  1. ENS, CNRS, INRIA, PSL, Paris, France

    Thierry Mefenza

  2. Department of Mathematics, University of Yaounde 1, Yaoundé, Cameroon

    Thierry Mefenza

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  1. Thierry Mefenza
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Correspondence to Thierry Mefenza .

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Editors and Affiliations

  1. Virginia Commonwealth Univ , Richmond, Virginia, USA

    Thang N. Dinh

  2. University of Florida , Gainesville, Alabama, USA

    My T. Thai

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Mefenza, T. (2016). Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith’s Methods. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_24

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  • DOI: https://doi.org/10.1007/978-3-319-42634-1_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42633-4

  • Online ISBN: 978-3-319-42634-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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