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.

引用

页码：1774 / 1777

页数：3

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