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Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation
April 2011 (vol. 60 no. 4)
pp. 602-607
M. Anwar Hasan, University of Waterloo, Canada
Christophe Negre, University of Perpignan, France
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 field elements as Toeplitz or Hankel matrix-vector products. This provides a parallel multiplier which is subquadratic in space and logarithmic in time. Using the matrix-vector formulation of the field multiplication, we also present sequential multiplier structures with linear space complexity.

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Index Terms:
Binary field, Dickson basis, Toeplitz matrix, multiplier, parallel, sequential.
Citation:
M. Anwar Hasan, Christophe Negre, "Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation," IEEE Transactions on Computers, vol. 60, no. 4, pp. 602-607, April 2011, doi:10.1109/TC.2010.132
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