用L^3算法分解RSA的模  

FACTORING MODULUS OF THE RSA BY USING L^3 ALGORITHM

作　　者：隆永红[1] 

机构地区：[1]湘潭大学计算机科学系

出　　处：《湘潭大学自然科学学报》1993年第3期128-132,共5页Natural Science Journal of Xiangtan University

摘　　要：本文讨论了L^3多项式因子分解算法与RSA公开钥密码体制安全性的关系,提出了一条大整数因子分解的新思路。指出:(1)RSA的模n的分解问题可以转化为一个O(logn)次本原整系数多项式的分解问题,因此存在一个多项式时间的随机算法;(2)本原整系数多项式的可约性与RSA的安全性有密切关系.本文的算法容易推广到一般大整数因子分解的情形。The relation between the security of the public key crypto-system RSA and the L^3 algorithm for factoring polynomials with rationalcoefficients has been discussed in this paper. It is pointed out that:(1) The problem of factoring the modulus n of the RSA can be transformedto the problem of factoring a primitive integer polynomial of degree0(log n).And thus,there is a probabilistic algorithm of polynomial timecomplexity to do so;(2)The probability with which the primitive integerpolynomials are irreducible has close relation to the security of the RSA andother public key crypto systems based on the difficulty of factoring verylarge integers. However,the most important thing is no doubt that anew idea of factoring very large integers has been found.Two unsolvedproblems are mentioned in the conclusion.

关 键 词：公钥密码学 数论 L^3算法 因子分解 

分 类 号：TN918.2[电子电信—通信与信息系统]