Issue No. 04 - April (2011 vol. 60)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2010.132
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.
Binary field, Dickson basis, Toeplitz matrix, multiplier, parallel, sequential.
C. Negre and M. A. Hasan, "Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation," in IEEE Transactions on Computers, vol. 60, no. , pp. 602-607, 2010.