计算机科学 ›› 2015, Vol. 42 ›› Issue (1): 79-81.doi: 10.11896/j.issn.1002-137X.2015.01.018

• 2013年全国理论计算机科学学术年会 • 上一篇    下一篇

GF(2m)上椭圆曲线标量乘的硬件结构实现

邬贵明,郑方,谢向辉,吴东,严忻恺   

  1. 数学工程与先进计算国家重点实验室 无锡214125,数学工程与先进计算国家重点实验室 无锡214125,数学工程与先进计算国家重点实验室 无锡214125,数学工程与先进计算国家重点实验室 无锡214125,数学工程与先进计算国家重点实验室 无锡214125
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受中国博士后科学基金(2013M532179),国家高技术研究发展计划(2013AA010105)资助

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

摘要: 基于Reyhani-Masoleh提出的GF(2m)高斯正规基乘法实现了三拍非流水的正规基乘法器,并基于该乘法器实现了一种高性能López-Dahab标量乘硬件结构。Reyhani-Masoleh算法利用乘法矩阵的对称性降低了乘法的复杂度;而López-Dahab标量乘算法由于采用投影坐标,计算速度快且可以有效降低存储需求。基于Reyhani-Masoleh乘法器的López-Dahab标量乘结构可以有效利用两种算法的优势,可以达到目前最好的标量乘硬件结构的性能。

关键词: 正规基乘法器,标量乘,椭圆曲线,有限域算术

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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