Discussion on Mantissa-multi-phase particle swarm optimization applied to large integer factorization problem

doi:10.3778/j.issn.1002-8331.2010.25.031

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (25): 105-108.DOI: 10.3778/j.issn.1002-8331.2010.25.031

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Discussion on Mantissa-multi-phase particle swarm optimization applied to large integer factorization problem

ZHANG Shu-mei¹，SONG Wei-tang¹，SONG Wan-li²

1.Nanjing Communications Institute of Technology，Nanjing 211188，China
2.Hohai University，Nanjing 211188，China

Received:2010-04-20 Revised:2010-06-09 Online:2010-09-01 Published:2010-09-01
Contact: ZHANG Shu-mei

一种用于大整数因数分解的多相位粒子群算法

张淑梅¹，宋维堂¹，宋万里²

1.南京交通职业技术学院，南京 211188
2.河海大学，南京 211188

通讯作者: 张淑梅

Abstract

Abstract: If the two factors p and q of N（a large integer） satisfy the constraint of p=x_p×D+y_pq=x_q×D+y_qand D>y_p×y_q，then N can be easily factorized.Therefore，the Mantissa-Multi-Phase Particle Swarm Optimization（MMPPSO） applied to large Integer Factorization Problem（IFP） is proposed on the basis of the constraint and some related theorems.Data experiment shows that MMPPSO is excellent in solving IFP.Meanwhile，it is suggested that the cryptosystem relied on large IFP of N be tested on the above constrained conditions，so as to guarantee the safety of encryption key and the system.

Key words: RSA, strong prime numbers, Integer Factorization Problem（IFP）, Particle Swarm Optimization（PSO）

摘要： 如果大整数N的两个因数p与q满足p=x_p×D+y_p，q=x_q×D+y_q，D>y_p×y_q约束，那么该大整数N将有可能被轻易分解。因此，根据该约束及相关定理，提出了一种用于求解大整数因数分解问题（IFP）的尾数多相位粒子群搜索算法，MMPPSO。数值实验证明，MMPPSO算法对IFP具有良好的求解能力。同时，建议依赖于大整数N分解问题的密码系统做上述约束条件测试，从而保证密钥和系统的安全性。

关键词: RSA, 强素数, 大整数因数分解问题（IFP）, 粒子群优化算法（PSO）

CLC Number:

TP393

ZHANG Shu-mei¹，SONG Wei-tang¹，SONG Wan-li². Discussion on Mantissa-multi-phase particle swarm optimization applied to large integer factorization problem[J]. Computer Engineering and Applications, 2010, 46(25): 105-108.

张淑梅¹，宋维堂¹，宋万里². 一种用于大整数因数分解的多相位粒子群算法[J]. 计算机工程与应用, 2010, 46(25): 105-108.

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Discussion on Mantissa-multi-phase particle swarm optimization applied to large integer factorization problem

一种用于大整数因数分解的多相位粒子群算法

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