Application of montgomery modular multiplication in three factoring algorithm 模乘在3种分解算法中的应用
Modular exponentiation and modular multiplication are the basic algorithms for implementing the public key algorithms such as rsa, etc . however the time-consuming modulo exponentiation computation, which has always been the bottle-neck of rsa, restricts its wider application 大数模幂乘运算是实现rsa等公钥密码的基本运算,该算法存在的问题是在实现时耗时太多,这也是制约其广泛应用的瓶颈。
A method called montgomery modular multiplication is the most significant way of fast modular multiplication . the montgomery method and its improvements are studied and the performances are analyzed in this thesis 对于加快模乘法速度的方法,本文重点分析peterl.montgomery提出的及其改进算法,介绍和比较了montgomery模乘算法实现上的分类,找出了较为优越的应用于通用处理器上的montgomery模乘算法。
A method called montgomery modular multiplication is the most significant way of fast modular multiplication . the montgomery method and its improvements are studied and the performances are analyzed in this thesis 对于加快模乘法速度的方法,本文重点分析peterl.montgomery提出的及其改进算法,介绍和比较了montgomery模乘算法实现上的分类,找出了较为优越的应用于通用处理器上的montgomery模乘算法。
This thesis, focused on the large integer modular computations, studies the two ways to reduce the time consumed by modular exponentiation---algorithms for fast modular multiplication and algorithms for computing powers with the least numbers of modular multiplication 本文对数据加密体制用到的大整数模运算进行研究。我们的工作分为两个部分:一部分是对大整数快速模运算算法的分析、研究;另一部分是大整数快速模运算算法的实现。
This thesis, focused on the large integer modular computations, studies the two ways to reduce the time consumed by modular exponentiation---algorithms for fast modular multiplication and algorithms for computing powers with the least numbers of modular multiplication 本文对数据加密体制用到的大整数模运算进行研究。我们的工作分为两个部分:一部分是对大整数快速模运算算法的分析、研究;另一部分是大整数快速模运算算法的实现。
Fast implementation of the rsa public key algorithms is one of direction of current public key algorithm . the research of this paper has using value, improving the processing of encryption and decryption by fast implementation of modular exponentiation and modular multiplication algorithm rsa算法的快速实现是现代密码学研究的方向之一,本文研究表明通过改进公钥密码体制中的模幂乘算法,可以进一步提高rsa的效率,具有一定的实用价值。
Montgomery multiplication algorithm is optimized for large-bit modular multiplication and vlsi implementation . it is combined with the r-l right to left binary method to achieve speed improvement . special efforts are focused on the problems with long-bit modular arithmetic 介绍了采用蒙哥马利模乘法算法和指数的从右到左的二进制方法,并根据大整数模乘法运算和vlsi实现的要求进行改进的rsa处理器,在提供高速rsa处理能力的同时,可抵抗某些定时分析攻击和功耗分析攻击。
The latter pay special attention to the software implementation environments, including the technical details such as programming interface, data structures and 32-bits visual c + + inline assembler . a sorftware packet is designed and implemented at last, which can perform the modular multiplication with equal 2048-bits long of modulu and operands within approximately 5.239ms and the modular exponentiation with equal 2048-bits long of modulu, exponent and base within approximately 4290.559ms 经测试,在intelceleron400mhz,ram64mb的pc机上,进行一次乘数与被乘数的最大位数均为2048位长的模乘运算所需平均时间约为5.239ms,在进行一次底数和指数的最大位数均为2048位长的模指数运算所需的平均时间约为4290.559ms。
The author mainly realized the method of generating the large random numbers and judging the prime number using lehmann means, then three pairs of secure key with different lengths ( 256 bits, 512 bits, 1024 bits ) was generated to meet the demand of different security grade . in encryption module, modular multiplication arithmetic of large number was realized adopting addition chaining . in decryption module, extended euclid was used to get inverse, and the chinese remainder theorem was used to realize decryption, which increased the speed of decryption greatly 作者主要实现了大随机数的生成、采用整除小素数和勒曼测试法判定素数,可以生成三种不同长度的密钥对(256位、512位、1024位)来满足不同的加密安全等级的需求;加密模块中,选用了二进制序列的乘法方法,实现了大数模幂乘运算;解密模块中,引用了扩展的欧几里德法求逆元,并采用中国剩余定理实现解密过程,大大提高了解密速度。