A Method of Generating Secure Elliptic Curves
Kai Wu · 2006
Elliptic curve cryptography is a very efficient basic technology for public key infrastructures,but there is a paucity of efficient means for generating suitable elliptic curves.This paper presents a method for generating elliptic curves of known order over finite fields.It is well known that if the prime p=6k+1,k∈Z,this prime can be factored into W~2+4V~2,W,V∈Z.Based on this,the paper proved that the order of the elliptic curve E:y~2=x_2+1 over finite fields F_p with j-invarant being 1728 is p+1±2W(when W=4L+1,L∈Z,#E(F_p)=p+1+2W;when W=4L-1,L E Z,#E(Fe)=p+1-2W).Furthermore,the constructing method of elliptic curves is propsed.