Abstract: This paper analyzes the elliptic curves over prime field GF(p), while p is greater than 3. It discusses an algorithm to generate an elliptic curve with a prime order. On basis of this, the problems for generating an elliptic curve with an order which equals to the product of two prime numbers are studied. A secure elliptic curve generating algorithm over GF(p) is proposed. It gives some examples for producing an elliptic curve and all the points on this elliptic curve under these two circumstances. Simulation experimental results show this algorithm is effective and feasible.

Key words: elliptic curve group, order, base point

摘要： 研究素数域GF(p)(p>3)上的椭圆曲线，讨论阶为素数的椭圆曲线的产生算法，在此基础上，分析阶为2个素数之积的椭圆曲线产生问题，并提出一种GF(p)上安全椭圆曲线的产生算法，给出椭圆曲线及其全体有理点的随机产生实例。仿真实验结果表明，该算法是有效可行的。

关键词: 椭圆曲线群, 阶, 基点

CLC Number: 

• TP309