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Problems on Gaussian Normal Basis Multiplication for Elliptic Curve Cryptosystem

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Genetic and Evolutionary Computing (GEC 2015)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 388))

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  • International Conference on Genetic and Evolutionary Computing

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Abstract

Several standards such as IEEE Standard 1363-2000 and FIPS 186-2 employ Gaussian normal basis (GNB). Gaussian normal basis is a special class of normal basis. Gaussian normal basis can solve the problem that multiplication in normal basis is an very difficult and complicated operation. Two equations have been proposed in the literature to transfer GNB to polynomial basis for easy multiplication. However, we find that GNB is not correctly transformed to polynomial basis for some m values over \(GF(2^{m})\). We will show the problems and expect some feedback about this problem from other researchers.

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Author information

Authors and Affiliations

  1. Chien Hsin University of Science and Technology, Taoyuan City, 32097, Taiwan

    C. W. Chiou, Y.-S. Sun, C.-M. Lee & Y.-L. Chiu

  2. Feng Chia University, Taichung City, 407, Taiwan

    J.-M. Lin

  3. Lunghwa University of Science and Technology, Taoyuan City, 33306, Taiwan

    C.-Y. Lee

Authors
  1. C. W. Chiou
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  2. Y.-S. Sun
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  3. C.-M. Lee
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  4. Y.-L. Chiu
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  5. J.-M. Lin
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  6. C.-Y. Lee
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Corresponding author

Correspondence to C. W. Chiou .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, University of Miyazaki, Miyazaki, Japan

    Thi Thi Zin

  2. School of Computer Science and Tech..., Harbin Institute of Technology, Shenzhen Graduate School , Shenzhen, China

    Jerry Chun-Wei Lin

  3. College of Information Science and Engg, Fujian University of Technology, Fuzhou, China

    Jeng-Shyang Pan

  4. Faculty of Engineering, University of Miyazaki, Miyazaki, Japan

    Pyke Tin

  5. Faculty of Engineering, University of Miyazaki, Miyazaki, Japan

    Mitsuhiro Yokota

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Chiou, C.W., Sun, YS., Lee, CM., Chiu, YL., Lin, JM., Lee, CY. (2016). Problems on Gaussian Normal Basis Multiplication for Elliptic Curve Cryptosystem. In: Zin, T., Lin, JW., Pan, JS., Tin, P., Yokota, M. (eds) Genetic and Evolutionary Computing. GEC 2015. Advances in Intelligent Systems and Computing, vol 388. Springer, Cham. https://doi.org/10.1007/978-3-319-23207-2_20

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  • DOI: https://doi.org/10.1007/978-3-319-23207-2_20

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-23207-2

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