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Efficient Multi-bit Shifting Algorithm in Multiplicative Inversion Problems

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3481))

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Abstract

This paper proposes an efficient inversion algorithm for Galois field GF(2n) by using a modified multi-bit shifting method. It is well known that the efficiency of arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm, which modifies a multi-bit shifting based on the Montgomery algorithm, is studied. Trinomials and AOPs (all-one polynomials) are tested to calculate the inverse. It is shown that the suggested inversion algorithm reduces the computation time 1 ~ 26% of the forgoing multi-bit shifting algorithm. The modified algorithm can be applied in various applications and is easy to implement.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Inha University, Incheon, 402-751, Korea

    Injoo Jang & Hyeong Seon Yoo

Authors
  1. Injoo Jang
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  2. Hyeong Seon Yoo
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, P.O. Box, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, P.O. Box, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Jang, I., Yoo, H.S. (2005). Efficient Multi-bit Shifting Algorithm in Multiplicative Inversion Problems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424826_11

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  • DOI: https://doi.org/10.1007/11424826_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25861-2

  • Online ISBN: 978-3-540-32044-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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