适于构建密码体制的椭圆曲线上的快速点加算法研究

Research of Rational Point Addition on Elliptic Curves Suitable for Cryptosystem

椭圆曲线上有理点的加法是椭圆曲线密码体制的关键运算，它执行的速度直接影响到整个密码体制执行的速度，文章对于适于建立密码体制的一类椭圆曲线进行了相应的仿射代换和其运算的映射变换，对其性质进行了阐述和分析。研究设计了椭圆曲线上的快速的有理点的相加算法。

The rational point addition on Elliptic Curves is the key operation of the Elliptic curve cryptosystem.The speed of the rational point addition on Elliptic Curves will immediacy effect the speed of the Elliptic curves cryptosystem.For this reason,the paper makes the correlation counterchange on the elliptic curve that suitable for constructing the cryptosystem and the operation on it.It expatiates and analyzes the character of this kind of elliptic curves,Researches and Designs the fast arithmetic of rational point addition on Elliptic Curves.