Elliptic curve point counting타원곡선의 위수 계산

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dc.contributor.advisorHahn, Sang-Geun-
dc.contributor.advisor한상근-
dc.contributor.authorKim, Hae-Young-
dc.contributor.author김해영-
dc.date.accessioned2011-12-14T04:39:31Z-
dc.date.available2011-12-14T04:39:31Z-
dc.date.issued2002-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=177223&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41854-
dc.description학위논문(박사) - 한국과학기술원 : 수학전공, 2002.8, [ [ii], 38 p. ; ]-
dc.description.abstractIn this thesis we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on Satoh-Skjernaa-Taguchi algorithm, and uses a Gaussian Normal Basis (GNB) of small type t≤4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p=2 and 160< N<600) have such bases. They can be lifted from $\F_{p^N}$ to $\Z_{p^N}$ in a natural way. From the specific properties of GNBs, efficient multiplication and the Frobenius substitutions are available. Thus a fast norm computation algorithm is derived, which runs in $O(N^{2μ logN)$ with $O(N^2)$ space, where the time complexity of multiplying two n-bit objects is $O(n^μ)$. As a result, for all small characteristic p, we reduced the time complexity of the SST-algorithm from $O(N^{2μ+ 0.5})$ to $O(N^{2μ + \frac{1}{μ + 1}})$ and the space complexity still fits in $O(N^2)$.eng
dc.languageeng-
dc.publisher한국과학기술원-
dc.subject타원곡선-
dc.subject위수 계산-
dc.subjectGaussian normal basis-
dc.subjectelliptic curve-
dc.subjectorder counting-
dc.titleElliptic curve point counting-
dc.title.alternative타원곡선의 위수 계산-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN177223/325007-
dc.description.department한국과학기술원 : 수학전공, -
dc.identifier.uid000995108-
dc.contributor.localauthorHahn, Sang-Geun-
dc.contributor.localauthor한상근-
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