摘要
在椭圆曲线公钥密码体制中,计算q元域Fq上椭圆曲线有理点的数目是至关重要的,这里q为素数p的幂.一个公认有效的计算有理点数目的Schoof算法需要用到有限域Fp2的原根.设n是一个正整数,F=Fqn为q元域K=Fq的n次扩张,α是F中的任意元,NF/K(α)是α在K上的范函数.用初等而简洁的方法,得到了α是F的原根的几个充分必要条件,并由此给出了由K的原根求Fq2的原根的一个算法.
In the elliptic curves public-key cryptic system, it is very important to count the number of rational points of elliptic curves over the finite field F_q, where q is a power of a prime p. A well-known effective algorithm-Shoof's algorithm needs a primitive element of the finite field F_(p^2) when counting the number of rational points over F_(p^2). Let n be a positive integer, K=F_q be the finite field with q elements and F=F_(q^n) be the nth extension of K. Suppose α is any element of F and N_(F/K)(α) is the norm function of α over K. In an elementary and brief method, several sufficient and necessary conditions for which α is a primitive element of F are obtained. Furthermore, an algorithm for finding primitive elements of the finite fields F_(q^2) from a primitive element of K is given.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2005年第2期134-137,共4页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(10128103)
四川省学位委员会和四川省教育厅重点学科建设基金资助项目
关键词
椭圆曲线公钥密码体制
有限域
原根
范函数
Elliptic curves public-key cryptic system
Finite fields
Primitive elements
Norm function
