Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem.
除子标量乘是超椭圆曲线密码体制中的关键运算。
The scalar multiplication in elliptic curves is the basic to elliptic curve cryptosystem.
计算椭圆曲线上点的数乘是椭圆曲线密码算法的基础。
This paper presents a new fast scalar multiplication algorithm on elliptic curve cryptography.
基于椭圆曲线密码，提出了一种快速标量乘算法。
Many studies were carried out on improving scalar multiplication, and many improved algorithms were presented.
在串行的范畴内，人们对改进数乘运算的效率进行了大量的研究，并提出了不少改进算法。
The definition of work suggests a third process of vector algebra, namely, scalar multiplication of two vectors.
功的定义用到矢量代数的第三种运算，即两个矢量的标积。
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。
The process of ECC includes the selection of base field and coordinates, scalar multiplication and field operation.
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 fast implementation of elliptic curve cryptosystems relies on the efficient computation 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 finite field arithmetic, elliptic curve scalar multiplication and the related algorithms are investigated in this dissertation.
本文主要研究有限域运算算法和椭圆曲线数乘运算算法。
The main operations of elliptic curve cryptosystem are scalar multiplication and multi-scalar multiplication for a pair of integers.
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。
Basic operation rules have been established, including addition, positive scalar multiplication, cancellation law for addition and so on.
基本的运算法则已经形成，包括加法运算、数乘运算、加法的消去律等。
The center to the implementation of elliptic curve cryptosystems efficiently lies in the arithmetic of scalar multiplication and addition.
椭圆曲线密码体制高速实现的关键是点的数乘与加法。
Secondly, it analyzed ECC and how to improve the algorithm efficiency from the point of Times-dot algorithm and scalar multiplication algorithm.
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。
By investigating the elliptic curve cryptosystems, the problems are reduced the fast computations of scalar multiplication of the elliptic curve.
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。
The algorithm can greatly reduce the number of elliptic point addition, so the efficiency of scalar multiplication in elliptic curves is improved.
该算法比经典算法减少了点的加法的计算次数，从而加快了椭圆曲线上点的数乘的运算速度。
The methods to speed up the scalar multiplication computation are mainly discussed in two ways: one is the number system, another is parallel 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。
A field inversion is the most expensive operation on scalar multiplication, and the number of inversion determines the performance of scalar multiplication.
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。
Using the improved algorithm, we present the attack on elliptic curve cryptosystems with binary scalar multiplication, and verify it through software simulation.
采用改进的算法针对二进制方法点乘的椭圆曲线密码进行了符号变换故障攻击，利用仿真实验进行了验证。
Firstly, based on the signed factorial expansions,. The fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are presented.
首先，设计基于带符号阶乘展开式的椭圆曲线标量乘和多标量乘算法。
Secondly, the fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are designed based on integer splitting and precomputation technique.
其次，设计基于整数拆分与预计算相结合的椭圆曲线标量乘和多标量乘算法。
This algorithm greatly reduces times of addition operation which takes time for scalar multiplication algorithm by introducing signed and unsigned sliding window coding methods.
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。
Several key problems in the implementation of ECC based on OEF are analyzed, which includes validating the parameters, selecting base point and the algorithms for scalar multiplication.
接着研究基于最优扩域的椭圆曲线密码实现过程中的几个关键问题，包括参数的生成、基点的选取和标量乘算法。
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.
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。
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.
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。
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