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Issue No.04 - April (2011 vol.60)
pp: 602-607
M. Anwar Hasan , University of Waterloo, Canada
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 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.
INDEX TERMS
Binary field, Dickson basis, Toeplitz matrix, multiplier, parallel, sequential.
CITATION
M. Anwar Hasan, "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
REFERENCES
[1] B. Ansari and M. Anwar Hasan, "Revisiting Finite Field Multiplication Using Dickson Bases," technical report, Univ. of Waterloo, 2007.
[2] L.E. Dickson, "The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group," Annals of Math., vol. 11, pp. 161-183, 1897.
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[10] A. Reyhani-Masoleh and M.A. Hasan, "Low Complexity Sequential Normal Basis Multipliers over GF($2^m$ )," Proc. 16th IEEE Symp. Computer Arithmetic (ARITH '03), pp. 188-195, 2003.
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