幂运算

在设计中还采用了窗口法减少模幂运算过程中所需进行的模乘运算次数，大大提高了处理速度。

The window method is used to significantly reduce the number of modular multiplications needed for completing the modular exponentiation .

综述了RSA密码算法中模幂运算的主要攻击方法及其防御措施。

First countermeasures for the exponentiation computation of RSA cryptographic algorithm were summarized .

p函数类的点乘和点幂运算

Pointwise multiplication and power on the class of d-functions

模幂运算是RSA公钥密码算法中最基本也是最耗时的运算。

Modular exponentiation is the most common fundamental and time consuming operation in RSA public-key cryptosystems .

RSA硬件的执行效率主要取决于模幂运算的实现效率。

The performance of RSA hardware implementation is mainly determined by the efficiency of modular multiplication implementation .

Montgomery算法在大数模幂运算中的改进

An Improved Design of Montgomery Algorithm for Large Modular Power Multiplication

RSA算法的核心运算是大整数模幂运算，而模幂运算是由一系列的模乘运算构成。

The large number exponentiation algorithms is the key of RSA Cryptography System , which is performed by a series of modular multiplication .

模幂运算的并行算法NSP

NSP algorithm for modular exponentiation

尤其是对RSA算法的研究，并行思想渗透到其基本算法中，这些基本算法主要包括模加、模乘、模逆和模幂运算。

Specially the research on RSA algorithm , parallel idea penetrates into its basic algorithm including modular addition , modular multiply , modular inverse and modular power .

基于RSA的公钥密码体制已被广泛运用于数字签名、身份认证等信息安全领域，其核心运算为大数模幂运算。

RSA public-key cryptosystem , whose basic key arithmetic operation is modular exponentiation , is widely used in the information security areas such as digital signature and identification authentication .

本文着重分析了RSA算法的核心-模幂运算，提出了有利于硬件实现的改进算法，并利用中国剩余定理加快了RSA的解密及数字签名的运算速度。

This paper mainly analyzes the core operation of RSA algorithm - modular power operation , proposes an ameliorative algorithm which makes for hardware realization , and improves the operation speed of RSA decryption and Digital Signature with the Chinese remainder theorem .

实验结果显示：芯片完成一次1024b的模幂运算需要约1.2M个时钟周期，而芯片规模在54K个等效门以下；

The experimental result shows that a 1024-bit modular exponentiation calculation can be performed in about 1.2 mega cycles , and less than 54K gates are needed .

本文在传统的Montgomery算法的基础上，利用快速大整数平方运算，提出了Montgomery算法的一种改进方案，有效缩短了大数模幂运算的时间，从而提高了RSA算法的加解密速度。

Based on the traditional Montgomery algorithm , this paper uses fast square of large integer multiplication and proposes an improved scheme , which remarkably reduces the time of large modular multiplication and improves the encryption and decryption rate of RSA algorithm .

在分析一般矩阵乘法运算对计算方阵高次幂运算局限性基础上，结合实例介绍了矩阵分解法、HamiltonCayley定理法等七种方阵高次幂求解方法。

In this paper , seven methods for calculating square matrix high math power are introduced with examples on the basis of limit of normal multiplication operation for square matrix high math power . These methods are matrix resolve and Hamilton-Cayley theory etc.

结果表明，采用这种组合的模幂运算算法具有十分高效的执行效率，4096位多精度整数的模幂计算大约需要1.5s，并可满足RSA的应用对密钥长度的安全需求。

The result indicates that the combined algorithm carries out an efficient calculation , the elapsed time of 4 096 bits multiple-precision integers modular exponentiation is about 1.5 s , and it will be the base of applied RSA public-key cryptography used in information security .

该文旨在介绍一种引入中国剩余定理加速私钥操作，并采用Barret模缩减方法，避开除法运算，将模幂运算转换成三个乘法运算和一个加法运算的快速模幂算法及其硬件实现方法。

This paper presents the application of the Chinese Remainder Theorem in the private key operations , and the application of Barret 's modular reduction method to avoid the long critical path of division , by transferring a single modular multiplication into three multiplications and one addition .

加法链快速模幂运算的设计

Design for Fast Implement of Modular Exponent Based on Addition Chain

快速可扩展的矩阵幂运算并行算法及其应用

Fast and scalable algorithms for matrix power computation and its application

基于大数模幂运算的公钥密码体制快速实现

Fast Implementation of Public-Key Cryptosystem with Large Number Modular Exponentiation

多精度整数高效模幂运算算法的研究

A Study on Multiple-precision Integer Efficient Modular Exponentiation Algorithm

通过一系列数学变换，将模幂运算变换成多次模乘运算。

To transform the Modular Exponentiation into multiple Modular Multiplication by a series of mathematical derivation .

研究了矩阵幂运算的逆运算，即矩阵的开方运算。

This paper studies the inverse operation of the matrix power operation , namely the root operation .

大数运算是很费时间的，尤其是大整数的模逆和模幂运算。

Big numbers operation will take time , especially modular inverse operation and modular power operation for big numbers .

在供暖收费系统的关系数据库中，当两个表连接运算的要求为元素和集合之间运算时，可以利用集合的幂运算进行简化处理，讨论了几种不同数据表结构定义方式来处理连接运算。

In heating charged relation database , while the requirement of calculation of two tables relation is that of element and set , power calculation of set can be used to simply the processing .

在线/离线签名最大的好处是降低签名开销，因为不需要做复杂的模幂运算，只要做简单的异或或者加乘运算。

The merit of online / offline signature is that it can reduce the overhead due to that the online signing do simple XOR , addition or multiplication operations and so it does not need complex modular or exponentiations .

本文给出债务关系的模糊矩阵表示，通过模糊矩阵幂运算实现了间接债务关系的基本要素-债务链，债务圈，债务量的刻画。

In this paper , the fuzzy matrix expression of debt relations is given and its power operation is used to judge the existence of the indirect debt relation . We describe and analyze debt chain , debt circle and debt quantity by using the power operations on fuzzy matrix .

快速幂乘运算的最优Window法

Optimal Window Method for Fast Exponentiation

大数模幂乘运算的VLSI实现

The VLSI Implementation for Modular Exponentiation of Large Operands

在变换过程中，RSA必需经历大数的模幂乘运算。

During the period of transforming , RSA should perform the modular exponentiation multiplication algorithm of large number .

论文提出了对传统BR算法的改进方法，能明显提高大数模幂乘运算的效率，从而大大缩短加解密的时间，提高加解密的效率。

This paper presents an improved method on the traditional BR algorithm , and it can obtain higher efficiency of the product calculation of large modulus power . Hence , it will reduce the encryption and decryption time dramatically , and will improve the efficiency of the encryption and decryption .