Construction of elliptic curves over finite fields with a point of given order

被引：0
|
作者：
Wang, Kun-Peng [1 ]
Li, Bao [1 ]
机构：
[1] State Key Laboratory of Information Security, Graduate University, Chinese Academy of Sciences
来源：
Ruan Jian Xue Bao/Journal of Software | 2007年 / 18卷 / 07期
关键词：
Diophantian equation; Elliptic curve; Public cryptography; Quadratic function field;
D O I：
10.1360/jos181774
中图分类号：
学科分类号：
摘要：
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)εGF (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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页码：1774 / 1777
页数：3
相关论文
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