一类安全椭圆曲线的选取及其标量乘法的快速计算

安全椭圆曲线的选取和标量乘法的快速计算是有效实现椭圆曲线密码体制的两个主要问题.本文将二者结合起来考虑给出了一类适合普通PC机实现的安全椭圆曲线,并详细给出了选取这类曲线的具体步骤和基于"大步-小步法"思想构造了一种新的计算这类曲线上标量乘法的快速算法.这类曲线不仅选取容易而且利用本文所提出方法计算其标量乘法时能使所需椭圆曲线运算次数大大减少.此外,选用这类曲线后基域中元素不再需要专门的表示方法,各种运算能非常快地得到实现,从而能极大地提高体制的整体实现速度.

A Selection of the Secure Elliptic Curve and Fast Calculation of Scalar Multiplication

The selection of secure elliptic curves and the scalar multiplications of elliptic curves are two important problems in the practice of efficiently implementing an elliptic curve cryptosystems.In this paper,we study those two problems jointly,give a class of secure elliptic curves mainly based on the computer words,describe a detailed process of how to selecting those curves,and present a new method,which is based on the idea of "baby step giant step",of computing the scalar multiplication concerning those curves.With the new method,the amount of scalar multiplications based on those curves can be reduced greatly. Besides,when those curves are used,special representation method for the elements in the base field is no longer needed,and all the arithmetic in the field can be quickly accomplished.