与RSA不动点有关的一个渐近表示(Ⅱ)

An Approximate Expression Related with the RSA Fixed Points(Ⅱ)

用T(p,q,e,α)表示RSA公钥加密系统RSA(p,q,e)的α阶不动点的个数,当满足x2>2x1,y2>2y1,y1>x2,x1→∞(或x2>2x1,y2>2y1,x1>y2,y1→∞)

Let T（p ,q ,e α）denote the number of α-order fixed points of RSA （p ,q ,e ）. If x2〉2x1 ,y2〉2y1 ,y1〉x2,x1→∞（or x2〉2x1,y2〉2y1,x1〉y2,y1→∞）, then 1/｜A｜｜B｜∑ρ∈A∑q∈B T（p,q,e,α）=c7^2/c1^2（1＋0（1））, where e^α-1=k∏i=1 ri^vi,e=h∏j=1 sj^vj,A={p;p is prime,（e,p-1）=1 ,x1〈p≤x2｜,B={q;q is prime, （e,q-1）=1 ,y1〈q≤y2},c1 and c7 are constants only concerning with e ,α.