On the bit security of the weak Diffie-Hellman problem = Weak Diffie-Hellman 문제의 비트 안전성

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dc.contributor.advisorHahn, Sang-Geun-
dc.contributor.advisor한상근-
dc.contributor.authorRoh, Dong-Young-
dc.contributor.author노동영-
dc.date.accessioned2011-12-14T04:41:02Z-
dc.date.available2011-12-14T04:41:02Z-
dc.date.issued2011-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=466390&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41951-
dc.description학위논문(박사) - 한국과학기술원 : 수리과학과, 2011.2, [ iii, 25 p. ]-
dc.description.abstractBoneh 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.languageeng-
dc.publisher한국과학기술원-
dc.subjectHidden number problem-
dc.subjectCryptography-
dc.subjectWeak Diffie-Hellman problem-
dc.subjectWeak Diffie-Hellman 문제-
dc.subject숨겨진 수 문제-
dc.subject암호학-
dc.titleOn the bit security of the weak Diffie-Hellman problem = Weak Diffie-Hellman 문제의 비트 안전성-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN466390/325007 -
dc.description.department한국과학기술원 : 수리과학과, -
dc.identifier.uid020047188-
dc.contributor.localauthorHahn, Sang-Geun-
dc.contributor.localauthor한상근-
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