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.
分布式乘法计算协议是应用很广泛的基础密码协议。
Distributed multiplication computation protocols are widely used as basic cryptographic protocols.
设计了一种新的分组密码算法，该算法利用矩阵乘法的扩散作用与专门设计的一种矩阵运算的混乱作用实现对信息的加密。
A new block cipher is designed where the diffusion of matrix multiplication is combined with the confusion of specially designed matrix operation to encrypt information.
蒙哥马利算法是在RSA密码系统中广泛应用的模乘法算法。
Montgomery algorithm is the most popular method for modular multiplication in RSA systems.
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.
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.
分布式乘法计算是安全多方计算中的重要部分，也是设计门限密码体制的基本协议。
Distributed multiplication computation is an important part of secure multi-party computation and a basic protocol of threshold cryptography.
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.
椭圆曲线密码体制中，最耗时的运算是倍点运算也就是椭圆曲线上的点与一个整数的乘法运算。
The operation consume most time is multiplication of a point on the elliptic curve with an integer in the system, which was called multiple point operation.
分布式乘法计算是构造门限密码体制的基本模块，同时也是安全多方计算领域的重要研究内容。
They are basic modules to construct threshold cryptosystems, and also important components of secure multiparty computation.
由于求解该离散对数的难度与求解乘法群上的离散对数的难度相同，所以在椭圆曲线上可构造出相对安全的密码系统。
Because computing the discrete logarithm more difficulty than the discrete logarithm over multiplication group, so it is possible to construct quite safe cryptosystem.
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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