GF(p)上安全椭圆曲线产生算法  

Secure Elliptic Curve Generating Algorithm over GF(p)

作　　者：侯爱琴[1] 辛小龙[2] 杨世勇[3] 

机构地区：[1]西北大学信息科学与技术学院,西安710069 [2]西北大学数学系,西安710069 [3]西安电子科技大学ISN国家重点实验室,西安710071

出　　处：《计算机工程》2009年第23期138-140,共3页Computer Engineering

基　　金：陕西省自然科学基金资助项目(2007A19);陕西省科技攻关计划基金资助项目(2005K04G10)

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。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.

关 键 词：椭圆曲线群 阶 基点 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]