Issue No. 01 - Jan. (2013 vol. 62)

ISSN: 0018-9340

pp: 193-199

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2011.198

A.H. Namin , University of Waterloo, Waterloo

A. Barsoum , University of Waterloo, Waterloo

M.A. Hasan , University of Waterloo, Waterloo

C. Negre , Universite de Perpignan, Perpignan, and Universite Montpellier 2, Montpellier

J. Adikari , University of Waterloo, Waterloo

ABSTRACT

In this paper, we propose new schemes for subquadratic arithmetic complexity multiplication in binary fields using optimal normal bases. The schemes are based on a recently proposed method known as block recombination, which efficiently computes the sum of two products of Toeplitz matrices and vectors. Specifically, here we take advantage of some structural properties of the matrices and vectors involved in the formulation of field multiplication using optimal normal bases. This yields new space and time complexity results for corresponding bit parallel multipliers.

INDEX TERMS

Complexity theory, Computer architecture, Logic gates, Symmetric matrices, Delay, Matrix decomposition, Polynomials, block recombination, Binary field, optimal normal basis, Toeplitz matrix

CITATION

A.H. Namin, A. Barsoum, M.A. Hasan, C. Negre, J. Adikari, "Improved Area-Time Tradeoffs for Field Multiplication Using Optimal Normal Bases",

*IEEE Transactions on Computers*, vol. 62, no. , pp. 193-199, Jan. 2013, doi:10.1109/TC.2011.198SEARCH