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.
除子标量乘是超椭圆曲线密码体制中的关键运算。
Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.
传统的标量计算方法不适应在向量计算机上并行运算。
Usual scalar calculation method can not be well used to make parallel operation on a vector computer.
椭圆曲线密码体制最主要的运算就是椭圆曲线上的标量乘和多标量乘，在各种密码协议中起到了核心作用。
The main operations of elliptic curve cryptosystem are scalar multiplication and multi-scalar multiplication for a pair of integers.
此算法通过引入有符号和无符号滑动窗口编码方法，大大减少了标量乘算法中费时的加法运算次数。
This algorithm greatly reduces times of addition operation which takes time for scalar multiplication algorithm by introducing signed and unsigned sliding window coding methods.
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.
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.
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.
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.
其次文章详细论述了ECC的相关知识及从倍点乘算法和标量乘运算两方面来提高该算法的运算效率。
Secondly, it analyzed ECC and how to improve the algorithm efficiency from the point of Times-dot algorithm and scalar multiplication algorithm.
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.
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.
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.
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