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Introducing a New Variant of Fast Algebraic Attacks and Minimizing Their Successive Data Complexity

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Progress in Cryptology – Mycrypt 2005 (Mycrypt 2005)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3715))

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Abstract

Algebraic attacks have established themselves as a powerful method for the cryptanalysis of LFSR-based keystream generators (e.g., E 0 used in Bluetooth). The attack is based on solving an overdetermined system of low-degree equations R t =0, where R t is an expression in the state of the LFSRs at clock t and one or several successive keystream bits z t ,...,z t + δ .

In fast algebraic attacks, new equations of a lower degree are constructed in a precomputation step. This is done by computing appropriate linear combinations of T successive initial equations R t =0. The successive data complexity of the attack is the number T of successive equations.

We propose a new variant of fast algebraic attacks where the same approach is employed to eliminate some unknowns, making a divide-and-conquer attack possible. In some cases, our variant is applicable whereas the first one is not.

Both variants can have a high successive data complexity (e.g., T≥ 8.822.188 for E 0). We describe how to keep it to a minimum and introduce suitable efficient algorithms for the precomputation step.

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Mannheim, 68131, Mannheim, Germany

    Frederik Armknecht

  2. IRMAR, University of Rennes, Campus de Beaulieu, 35042, Rennes, France

    Gwénolé Ars

Authors
  1. Frederik Armknecht
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  2. Gwénolé Ars
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Editor information

Editors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, 4001, Brisbane, Queensland, Australia

    Ed Dawson

  2. EPFL, CH-1015, Lausanne, Switzerland

    Serge Vaudenay

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Armknecht, F., Ars, G. (2005). Introducing a New Variant of Fast Algebraic Attacks and Minimizing Their Successive Data Complexity. In: Dawson, E., Vaudenay, S. (eds) Progress in Cryptology – Mycrypt 2005. Mycrypt 2005. Lecture Notes in Computer Science, vol 3715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554868_3

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  • DOI: https://doi.org/10.1007/11554868_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28938-8

  • Online ISBN: 978-3-540-32066-1

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