RSA公钥算法的新探讨及改进  

The Discussion about the Improvement of RSA Algorithm

作　　者：武亚宁[1] 

机构地区：[1]南京理工大学计算机科学与技术学院,江苏南京210094

出　　处：《信息安全与技术》2012年第9期27-28,51,共3页

摘　　要：众所周知,RSA是唯一一个能够同时实现数据加密、数字签名、秘钥交换的算法。其过程可简述为选取两个大的质数乘积n=p*q(非公开),然后选择一个和准(n)互质的整数e(其中1<e<准(n)),求其关于欧拉函数准(n)=(p-1)(q-1)=准(p)*准(q)的逆元d,进而得到公钥对与私钥对(e,n)和(d,n)。假如n是三个或更多素数的乘积会怎样?该算法是否依然成立?本文旨在探讨n取更多素数乘积时所得到的结论以及根据这些结论所能对RSA作出的改进。As we all know, RSA is the only Algorithm that can be used in Data Encryption, Digital Signature and Key Distribution collectively. The process of RSA can be briefly summarized into 3 stages. First, select an integer n that is the result of 2 prime numbers＇ product （n=p＊q, private）. Then, select an integer e that is relatively prime to ~ （n） （l〈e〈~ （n）, ,~ （n） is the Euler＇s totient function）. Next, calculate d that is e＇s multiplicative inverse about ^（n）. Thus, we get the public key {e, n} and private key {d, n}. Consider if n is the result of the product of 3 or more integers. Is the Algorithm still work？ In this essay, I am attempt to discuss some conclusions under the condition that n is the result of the product of more integers and suggest some possible improvements based on those conclusions.

关 键 词：RSA 改进 公钥算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]