| 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. |
| 关键词: 椭圆曲线 二次函数域 公钥密码 不定方程 |
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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) |
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| Construction of Elliptic Curves over Finite Fields with a Point of Given Order |
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WANG Kun-Peng,LI Bao
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| 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. |
| Key words: elliptic curve quadratic function field public cryptography Diophantian equation |
