Computer Science ›› 2015, Vol. 42 ›› Issue (1): 79-81.doi: 10.11896/j.issn.1002-137X.2015.01.018

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Hardware Implementation of Scalar Multiplication on Elliptic Curves over GF(2m)

WU Gui-ming, ZHENG Fang, XIE Xiang-hui, WU Dong and YAN Xin-kai   

  • Online:2018-11-14 Published:2018-11-14

Abstract: A three-stage non-pipelined normal base multiplier was implemented based on an algorithm for GF(2m) multiplication using Gaussian normal base proposed by Reyhani-Masoleh.On basis of the Gaussian normal base multiplier,we presented a high-performance hardware implementation for the López-Dahab algorithm of scalar multiplication over GF(2m).The Reyhani-Masoleh algorithm can reduce the computation complexity of the multiplication through exploiting the symmetry of the multiplication matrix,and the memory requirement of the López-Dahab algorithm can be reduced by using projective coordinate.Our architecture can benefit from the combination of the two algorithms,making its performance be equivalent to the best architecture to date.

Key words: Normal base multiplier,Scalar multiplication,Elliptic curve,Finite field arithmetic

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