An Method of Factoring Large Integers

被引：0

作者：

Shaohua Zhang Gongliang Chen Zhongping Qin Xinrong Yan (Wuhan Maritime Communications Research Institute

CSIC. School of Information Security Engineering of Shanghai Jiaotong University College of Software in Huazhong University of Science and Technology)

机构：

来源：

信息安全与通信保密 | 2005年 / 07期

关键词：

factoring large integers polynomial-time algorithm RSA cryptosystem RSA modulus safe prime;

D O I：

暂无

中图分类号：

TN918 [通信保密与通信安全];

学科分类号：

0839 ; 1402 ;

摘要：

<正>In this paper, we prove the following result: Let a and bbe large integers, satisfying that (a, b)=1. If Diophantine equation ax+by=z has solutions: |X0|=O(log2ab) |y0|=O(log2ab) |Z0|=O(log2ab) then there is a polynomial-time algorithm that factors a large integern = ab , which runs in O(log2 6 n) time. Based on the proposed algorithm, we can factor easily n=1600000000000000229500000000000003170601. In fact, we have n=20000000000000002559 ×80000000000000001239, where 20000000000000002559 and 80000000000000001239 are all safe primes. Our result also shows that some safe primes are not safe.

引用

页码：108 / 109

页数：2