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International Conference on Information and Communications Security

ICICS 2002: Information and Communications Security pp 217–230Cite as

Fast Elliptic Curve Multiplications with SIMD Operations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2513))

Abstract

The Single Instruction, Multiple Data (SIMD) architecture enables to compute in parallel on a single processor. The SIMD operations are implemented on some processors such as Pentium 3/4, Athlon, SPARC, and even on smart cards. This paper proposes efficient algorithms for assembling an elliptic curve addition (ECADD), doubling (ECDBL), and k-iterated ECDBL (k-ECDBL) with SIMD operations. Using the singed binary chain, we can compute a scalar multiplication about 10%faster than the previously fastest algorithm by Aoki et al. Combined with the sliding window method or the width-w NAF window method, we also achieve about 10% faster parallelized scalar multiplication algorithms with SIMD operations. For the implementation on smart cards, we propose two fast parallelized scalar multiplication algorithms with SIMD resistant against side channel attacks.

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Author information

Authors and Affiliations

  1. FUJITSU LABORATORIES Ltd., 4-1-1, Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan

    Tetsuya Izu

  2. Fachbereich Informatik, Technische Universität Darmstadt, Alexanderstr.10, D-64283, Darmstadt, Germany

    Tsuyoshi Takagi

Authors
  1. Tetsuya Izu
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  2. Tsuyoshi Takagi
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Editor information

Editors and Affiliations

  1. Labs for Information Technology, 21 Heng Mui Keng Terrace, Singapore, 119613

    Robert Deng , Feng Bao  & Jianying Zhou ,  & 

  2. Engineering Research Center for Information Security Technology, Chinese Academy of Sciences, P.O. Box 8718, Beijing, 100080, China

    Sihan Qing

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© 2002 Springer-Verlag Berlin Heidelberg

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Izu, T., Takagi, T. (2002). Fast Elliptic Curve Multiplications with SIMD Operations. In: Deng, R., Bao, F., Zhou, J., Qing, S. (eds) Information and Communications Security. ICICS 2002. Lecture Notes in Computer Science, vol 2513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36159-6_19

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  • DOI: https://doi.org/10.1007/3-540-36159-6_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00164-5

  • Online ISBN: 978-3-540-36159-6

  • eBook Packages: Springer Book Archive

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