RSA推广循环攻击实效性与弱模问题的研究与分析  

Investigation and analysis of the weakness and efficiency of generalized cycling attacks on RSA modulus

作　　者：姜正涛[1] 怀进鹏[2,3] 王育民[4] 

机构地区：[1]中国传媒大学计算机学院,北京100024 [2]北京航空航天大学计算机学院,北京100083 [3]北京航空航天大学软件开发环境国家重点实验室,北京100083 [4]西安电子科技大学ISN国家重点实验室,陕西西安710071

出　　处：《通信学报》2009年第6期70-74,共5页Journal on Communications

基　　金：国家"211工程"资助项目;中国博士后科学基金资助项目(20060400035);国家自然科学基金资助项目(90412011);国家杰出青年科学基金资助项目(60525209);国家重点基础研究发展计划("973"计划)基金资助项目(2003AA144150)~~

摘　　要：研究了一类RSA安全模数攻击方法的有效性,通过分析指出由于某些攻击方法成功概率可忽略,不能作为选择强安全RSA模数的理由,针对攻击方法的分析总结了当前安全RSA模数的含义,从实际安全角提高参数选择的效率。另外,对RSA模数2个素因子之差d=|p-q|不能太小的结果做了进一步研究,可以认为d为dl,m=ql-pm(l,m∈Z+)比较小时的一种特殊情况,由分析可以看出在选择RSA模数时需注意不要因特意选择比较大的d而忽略了2个素数关系的随机性,防止存在2者某种特殊的函数关系,提高安全性。The efficiency of attacking methods on secure RSA modulus was investigated. It was pointed out by analysis that since the success probability of some attack methods was neglectable, these methods could not be regarded as the reason for choosing strongly secure RSA modulus. In consideration of the analysis of attack methods, the signification of secure RSA modulus was summarized, which enhanced the efficiency of selecting secure parameters in practice. The result that the difference between two RSA primes d=｜p-q｜ must not be too small was further investigated, and the d might be seen as a special case when dt,m=q^l-p^m （l,m ∈ Z^＋） was small. From the analysis, it could be figured out that the randomness of the relation between the two primes should not be neglected during selecting RSA modulus. To improve the security, it should be avoided to have some specially functional relations between the two primes when choosing a larger d.

关 键 词：RSA 模数安全 循环攻击 攻击有效性 实际安全 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]