RSA的类循环攻击

A cycling-like attack on RSA

给出了RSA密码算法的一种类循环攻击算法.记RSA算法的公钥为(e,N),私钥为d.若存在正整数k,使得整数ek和整数dkmod(N)都较小,则基于一些已有的低解密指数攻击方法,可将RSA模数N的分解问题转化为RSA的公私钥方程的小根问题,从而可在多项式时间求解.实验数据表明,本方法可以找出RSA新的弱密钥.

A cycling-like attack on rivest, shamir and adleman （RSA） is presented. Let （e,N） be a RSA public key with corresponding private key d. If there exists a proper integer k such that both e^k and d^k mod Ф（N） are relatively small, then based on some known low private exponent attacks, the problem of factoring RSA modulus N can be changed into the problem of finding small roots of RSA key equations, which can be solved in polynomial time. Experiments show that our method can find some new weak keys of RSA.