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Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation

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2 Author(s)
Anwar Hasan ; University of Waterloo, Canada ; Christophe Negre

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.

Published in:

IEEE Transactions on Computers  (Volume:60 ,  Issue: 4 )