椭圆曲线密码体制的实现速度依赖于曲线上标量乘法的运算速度。
The fast implementation of elliptic curve cryptosystems relies on the efficient computation of scalar multiplication.
本文主要研究了椭圆曲线公钥密码体制中标量乘法运算的快速算法。
In this dissertation the elliptic curve cryptosystems and fast scalar multiplication algorithms are investigated.
ECC算法中基域的选择、坐标系的选择、标量乘法和域算术运算的实现。
The process of ECC includes the selection of base field and coordinates, scalar multiplication and field operation.
求逆是标量乘法中最耗时的运算，求逆运算次数的多少直接决定标量乘法的性能。
A field inversion is the most expensive operation on scalar multiplication, and the number of inversion determines the performance of scalar multiplication.
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。
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.
通过对椭圆曲线密码体制的研究，将快速实现椭圆曲线密码的问题归结为标量乘法的实现效率。
By investigating the elliptic curve cryptosystems, the problems are reduced the fast computations of scalar multiplication of the elliptic curve.
这些公钥密码算法的关键操作为大整数模幂乘操作与椭圆曲线标量乘法操作，均属于计算密集型运算。
In these public key cryptographic algorithms, the kernel operations are modular exponentiation of multi-precision integer and elliptic curve scalar multiplication, which both are computing intensive.
主要从两个方面来研究快速算法，一是研究数域系统以加快标量乘法运算，二是研究标量乘法运算的并行算法。
The methods to speed up the scalar multiplication computation are mainly discussed in two ways: one is the number system, another is parallel algorithm.
最简单的办法是我们只允许对标量数字进行乘法和除法运算。
The simplest approach is to only permit multiplication and division by scalar Numbers.
最简单的办法是我们只允许对标量数字进行乘法和除法运算。
The simplest approach is to only permit multiplication and division by scalar Numbers.
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