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Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation

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Book cover Arithmetic of Finite Fields (WAIFI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5130))

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Abstract

We study Dickson bases for binary field representation. Such a representation seems interesting when no optimal normal basis exists for the field. We express the product of two elements as Toeplitz or Hankel matrix vector product. This provides a parallel multiplier which is subquadratic in space and logarithmic in time.

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References

  1. Ansari, B., Anwar Hasan, M.: Revisiting finite field multiplication using dickson bases. Technical report, University of Waterloo, Ontario, Canada (2007)

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, Canada

    M. Anwar Hasan

  2. Team DALI/ELIAUS, University of Perpignan, France

    Christophe Negre

Authors
  1. M. Anwar Hasan
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  2. Christophe Negre
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Editor information

Joachim von zur Gathen José Luis Imaña Çetin Kaya Koç

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© 2008 Springer-Verlag Berlin Heidelberg

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Hasan, M.A., Negre, C. (2008). Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation. In: von zur Gathen, J., Imaña, J.L., Koç, Ç.K. (eds) Arithmetic of Finite Fields. WAIFI 2008. Lecture Notes in Computer Science, vol 5130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69499-1_8

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  • DOI: https://doi.org/10.1007/978-3-540-69499-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69498-4

  • Online ISBN: 978-3-540-69499-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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