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Modular Multiplication in GF(pk) Using Lagrange Representation

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Progress in Cryptology — INDOCRYPT 2002 (INDOCRYPT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2551))

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Abstract

In this paper we present a new hardware modular multiplication algorithm over the finite extension fieldsGF(p k) where p >2k. We use an alternate polynomial representation of the field elements and a Lagrange like interpolation technique. We describe our algorithm in terms of matrix operations and point out some properties of the matrices that can be used to improve the hardware design. The proposed algorithm is highly parallelizable and seems well suited for hardware implementation of elliptic curve cryptosystems.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique de Robotique et de Microélectronique de Montpellier, LIRMM - CNRS UMR 5506, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Jean-Claude Bajard, Laurent Imbert & Christophe Négre

Authors
  1. Jean-Claude Bajard
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  2. Laurent Imbert
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  3. Christophe Négre
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Editor information

Editors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alfred Menezes

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, 700108, Kolkata, India

    Palash Sarkar

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Bajard, JC., Imbert, L., Négre, C. (2002). Modular Multiplication in GF(pk) Using Lagrange Representation. In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology — INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_22

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  • DOI: https://doi.org/10.1007/3-540-36231-2_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00263-5

  • Online ISBN: 978-3-540-36231-9

  • eBook Packages: Springer Book Archive

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