中文摘要：

Boneh和Durfee运用Coppersmith的方法在d〈N^0.292。的条件下分解了RSA模数N。将RSA离散比特私钥泄漏攻击与小指数攻击相结合，在P，q平衡和P的一个中间比特块已知的情况下，将解密指数的界提高到了d〈N^0.5。最后给出了实验测试，证明文章构造的格可以运用到实际攻击中。

英文摘要：

Boneh and Durfee used Coppersmith＇ s method to factorize N using e when d 〈 N^0. 292. This paper presents a heuristic algorithm that combines the low exponent attack with the partial key exposure attack given discrete bits. It is shown that if the private exponent d used in the RSA public key cryptosystem is less than N^0.5 , the system is insecure with some bits of p known which is located in one consecutive middle block. Also provided is a clear evidence that RSA, can be cryptanalysed in practice.