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Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation

Anwar Hasan 1 Christophe Negre 2
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
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.
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Anwar Hasan, Christophe Negre. Low Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2011, 60 (4), pp.602-607. ⟨hal-00813621⟩

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