【摘要】 应用二次剩余理论,对二阶强RSA算法中Z*φ(n)的代数结构进行研究,证明Z*φ(n)中元素a取最大阶的充要条件为1gcd(a 1,n)1,以及任意元素的阶Z*φ(n)中模(n)的二次剩余个数为((n))/8,以所有二次剩余构成的群对Z*φ(n)进行分割,利用所有陪集构成一个Klein八元群,在此基础上证明Z*φ(n)可由7个二次非剩余元素生成。更多还原

【Abstract】 Based on the theory of quadratic residues,this paper considers the algebraic structure of Z*φ(n)in the two order strong RSA algorithm.It is proved that the element a of Z*φ(n)gets maximal order if and only if 1 gcd(a 1,n) 1,and the numbers of quadratic residues in the group Z*φ(n) is ((n))/8.Z*φ(n) is divided up by the group which is composed of all quadratic residues,and all cosets form a Klein eight-group.It proves that the group Z*φ(n)can be generated by seven elements of quadratic non-residues.更多还原