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DOI:
Journal of Software:2007.18(7):1774-1777

构造有限域上具有给定阶点的椭圆曲线
王鲲鹏,李宝
(中山大学,信息科学与技术学院,广东,广州,510275)
Construction of Elliptic Curves over Finite Fields with a Point of Given Order
WANG Kun-Peng,LI Bao
()
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Received:June 13, 2005    Revised:April 26, 2006
> 中文摘要: 考虑有限域上椭圆曲线的构造.设q是一个奇素数的方幂,l是一个素数.证明了,如果GF(q)[x]上的方程U2-D(x)V2=ε(x-a)l有本原解,其中,D(x)∈GF(q)[x]是一个首1三次无平方因子的多项式,则椭圆曲线y2=D(x)上的点(a,b)的阶是l.由此,给出了一种构造具有给定阶点的椭圆曲线的算法.
Abstract:The elliptic curves over a finite field with q elements are constructed. Let l be a prime, it is proved in this paper that if the equation U2-D(x)V2=ε(x-a)l defined over GF(q)[x] has a primitive solution over GF(q)[x], where D(x)∈GF(q)[x] is a monic squarefree degree three polynomial, then the elliptic curve y2=D(x) has a point (a,b) with order l. This result provides an algorithm on constructing elliptic curves with a point of the prescribed order.
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基金项目:Supported by the National Natural Science Foundation of China under Grant No.60673073 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2006AA01Z427 (国家高技术研究发展计划(863)); the Presidential Foundation of Graduate University of the Chinese Academy of Sciences under Grant No.Y1039 (中国科学院研究生院院长基金) Supported by the National Natural Science Foundation of China under Grant No.60673073 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2006AA01Z427 (国家高技术研究发展计划(863)); the Presidential Foundation of Graduate University of the Chinese Academy of Sciences under Grant No.Y1039 (中国科学院研究生院院长基金)
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王鲲鹏,李宝.构造有限域上具有给定阶点的椭圆曲线.软件学报,2007,18(7):1774-1777

WANG Kun-Peng,LI Bao.Construction of Elliptic Curves over Finite Fields with a Point of Given Order.Journal of Software,2007,18(7):1774-1777