DC Field | Value | Language |
---|---|---|

dc.contributor.advisor | Hahn, Sang-Geun | - |

dc.contributor.advisor | 한상근 | - |

dc.contributor.author | Roh, Dong-Young | - |

dc.contributor.author | 노동영 | - |

dc.date.accessioned | 2011-12-14T04:41:02Z | - |

dc.date.available | 2011-12-14T04:41:02Z | - |

dc.date.issued | 2011 | - |

dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=466390&flag=dissertation | - |

dc.identifier.uri | http://hdl.handle.net/10203/41951 | - |

dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2011.2, [ iii, 25 p. ] | - |

dc.description.abstract | Boneh and Venkatesan proposed a problem called the \textit{hidden number problem} and they gave a polynomial time algorithm to solve it. And they showed that one can compute $g^{xy}$ from $g^{x}$ and $g^{y}$ if one has an oracle which computes roughly $\sqrt{\log p}$ most significant bits of $g^{xy}$ from given $g^{x}$ and $g^{y}$ in $\mathbb F_{p}$ by using an algorithm for solving the hidden number problem. Later, Shparlinski showed that one can compute $g^{x^{2}}$ if one can compute roughly $\sqrt{\log p}$ most significant bits of $g^{x^{2}}$ from given $g^{x}$. In this paper we extend these results by using some improvements on the hidden number problem and the bound of exponential sums. We show that for given $g, g^{\alpha}, \ldots, g^{\alpha^{l}} \in \mathbb F_{\it p}^{*}$, computing about $\sqrt{\log p}$ most significant bits of $g^{\frac{1}{\alpha}}$ is as hard as computing $g^{\frac{1}{\alpha}}$ itself, provided that the multiplicative order of $g$ is prime and not too small. Furthermore, we show that we can do it when $g$ has even much smaller multiplicative order in some special cases. | eng |

dc.language | eng | - |

dc.publisher | 한국과학기술원 | - |

dc.subject | Hidden number problem | - |

dc.subject | Cryptography | - |

dc.subject | Weak Diffie-Hellman problem | - |

dc.subject | Weak Diffie-Hellman 문제 | - |

dc.subject | 숨겨진 수 문제 | - |

dc.subject | 암호학 | - |

dc.title | On the bit security of the weak Diffie-Hellman problem = Weak Diffie-Hellman 문제의 비트 안전성 | - |

dc.type | Thesis(Ph.D) | - |

dc.identifier.CNRN | 466390/325007 | - |

dc.description.department | 한국과학기술원 : 수리과학과, | - |

dc.identifier.uid | 020047188 | - |

dc.contributor.localauthor | Hahn, Sang-Geun | - |

dc.contributor.localauthor | 한상근 | - |

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- MA-Theses_Ph.D.(박사논문)

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