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International Conference on Computational Science and Its Applications

ICCSA 2003: Computational Science and Its Applications — ICCSA 2003 pp 947–956Cite as

Computational Algorithm and Architecture for AB2 Multiplication in Finite Fields

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2667))

Abstract

In this paper, we present an effective algorithm and a simple hardware structure for the implementation of AB 2 multiplication using irreducible all one polynomial (AOP) in finite field GF(2m). We argue with a problem that conventional algorithms using irreducible AOP are operated in extended basis, then we propose an effective algorithm and an architecture which are operated in the polynomial basis. The proposed algorithm is substantially considered relationships between operands based on inner-product computation. Based on the algorithm, we propose an architecture in which its results can be immediately used for other operations. Specially, the algorithm and architecture are useful conception for modular exponentiation since exponentiation is computed by repetition of AB 2 multiplication.

This research was supported by University IT Research Center Project.

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Author information

Authors and Affiliations

  1. Department of Computer Engineeing, Kyungpook National University, Daegu, 702-701, Korea

    Jun-Cheol Jeon & Kee-Young Yoo

Authors
  1. Jun-Cheol Jeon
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  2. Kee-Young Yoo
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

  5. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  6. The Queen’s University of Belfast, School of Computer Science, Belfast BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

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© 2003 Springer-Verlag Berlin Heidelberg

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Jeon, JC., Yoo, KY. (2003). Computational Algorithm and Architecture for AB2 Multiplication in Finite Fields. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_100

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  • DOI: https://doi.org/10.1007/3-540-44839-X_100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40155-1

  • Online ISBN: 978-3-540-44839-6

  • eBook Packages: Springer Book Archive

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