### 摘要

The study of paper "Cryptanalysis of RSA with Private Key d less than N^{0.292}' [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July 2000, supported that when d < N^{0.292}, the RSA system can be cracked by using the LLL algorithm. In this paper, we find ways to utilize the LLL algorithm to break the RSA system even when the value of d is large. According to the proposed cryptanalysis, if d satisfies |λ - d| < N ^{0.25}, the RSA system will be possible to be resolved computationally.

原文 | English |
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頁（從 - 到） | 516-525 |

頁數 | 10 |

期刊 | Applied Mathematics and Computation |

卷 | 169 |

發行號 | 1 |

DOIs | |

出版狀態 | Published - 1 十月 2005 |

## 指紋 深入研究「Cryptanalysis of large RSA exponent by using the LLL algorithm」主題。共同形成了獨特的指紋。

## 引用此

Chen, C. Y., Ku, C-Y., & Yen, D. C. (2005). Cryptanalysis of large RSA exponent by using the LLL algorithm.

*Applied Mathematics and Computation*,*169*(1), 516-525. https://doi.org/10.1016/j.amc.2004.10.082