摘要
分析了素数域GF(Fp)(p>3)上形如y2=x3+ax+b安全椭圆曲线的构造方法.依据椭圆曲线阶与迹的关系,提出一种快速构造安全椭圆曲线的新方法.首先选择判别式Δ≠0的椭圆曲线和具有大素因子的阶,然后由素数p与迹的关系找出基点,最后由基点计算出点群.方法类似于复乘(CM)方法,但又不计算类不变量,而是通过查表的方式直接找出基点.数字例子验证了方法的正确性和有效性.与已有研究结果相比,方法具有明显的优势.
The construction method of secure elliptic curve, its shape such as y^2 = x^3 ＋ ax ＋ b, is analyzed over prime field GF（Fp） （p〉3）. By the relationship of elliptic curve order and track, a new method of quickly generating secure elliptic curve is proposed. After the elliptic curve of the discriminant △≠0 and the order with large prime factors are selected; this paper calculates the point group using the relationship of order and track. The method is similar to complex multiplication （CM）, but do not call the SEA algorithm to determine the order; and therefore is able to more quickly construct secure elliptic curve. The numerical examples verify the correctness and validity of the method. Compared with the existing research results, the method has obvious advantages.
出处
《武汉大学学报（工学版）》
CAS
CSCD
北大核心
2014年第2期286-288,共3页
Engineering Journal of Wuhan University
基金
甘肃省高等学校研究生导师科研基金项目(编号:1113-02)
关键词
椭圆曲线
阶
迹
有限域
基点
素数域
elliptic curve
order
trace
finite field
base points
prime field
