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Software Implementation of Arithmetic in

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Arithmetic of Finite Fields (WAIFI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4547))

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Abstract

Fast arithmetic for characteristic three finite fields is desirable in pairing-based cryptography because there is a suitable family of elliptic curves over having embedding degree 6. In this paper we present some structure results for Gaussian normal bases of , and use the results to devise faster multiplication algorithms. We carefully compare multiplication in using polynomial bases and Gaussian normal bases. Finally, we compare the speed of encryption and decryption for the Boneh-Franklin and Sakai-Kasahara identity-based encryption schemes at the 128-bit security level, in the case where supersingular elliptic curves with embedding degrees 2, 4 and 6 are employed.

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Author information

Authors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Toronto,  

    Omran Ahmadi

  2. Dept. of Mathematics and Statistics, Auburn University,  

    Darrel Hankerson

  3. Dept. of Combinatorics & Optimization, University of Waterloo,  

    Alfred Menezes

Authors
  1. Omran Ahmadi
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  2. Darrel Hankerson
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  3. Alfred Menezes
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Editor information

Claude Carlet Berk Sunar

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© 2007 Springer-Verlag Berlin Heidelberg

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Ahmadi, O., Hankerson, D., Menezes, A. (2007). Software Implementation of Arithmetic in . In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_8

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  • DOI: https://doi.org/10.1007/978-3-540-73074-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73073-6

  • Online ISBN: 978-3-540-73074-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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