利用有限简单连分数的最佳逼近原理破译公钥密码RSA及其实现

攻击RSA密码体制最有效的方式就是计算出它的解密指数,即找出其密钥.介绍一种新的攻击方法:当RSA密码体制使用低加密指数时,利用有限简单连分数的最佳有理逼近原理,依次计算出它的渐近分数,逐一加以试用,直到找到其最佳收敛子,从而将模数分解并计算出它的解密指数,即密钥.使用这种方法可以准确地计算出解密指数,减少解密时间,加快解密过程.

RSA Public Key Cryptosystems Deciphered by Principle of Optimal Approach of Limited Simple Continued Fraction and Its Application

The most obvious way of attacking RSA public key cryptosystems is to compute the index of de- cryption, namely to find out its key of decryption. A new attack method was introduced in this paper. When RSA cryptosystem uses low index of decryption, the principle of optimal approach of continued fraction could be used to compute the approaching fraction which would be utilized on trial till optimal convergent was found. Then modulus would be decomposed and the index of decryption would be worked out. This method can accurately calculate its decryption index, reduce the time of decrypfing text and increase the process of decoding.