DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Hahn, Sang-Geun | - |
dc.contributor.advisor | 한상근 | - |
dc.contributor.author | Kim, Hae-Young | - |
dc.contributor.author | 김해영 | - |
dc.date.accessioned | 2011-12-14T04:39:31Z | - |
dc.date.available | 2011-12-14T04:39:31Z | - |
dc.date.issued | 2002 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=177223&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41854 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학전공, 2002.8, [ [ii], 38 p. ; ] | - |
dc.description.abstract | In 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.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 타원곡선 | - |
dc.subject | 위수 계산 | - |
dc.subject | Gaussian normal basis | - |
dc.subject | elliptic curve | - |
dc.subject | order counting | - |
dc.title | Elliptic curve point counting | - |
dc.title.alternative | 타원곡선의 위수 계산 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 177223/325007 | - |
dc.description.department | 한국과학기술원 : 수학전공, | - |
dc.identifier.uid | 000995108 | - |
dc.contributor.localauthor | Hahn, Sang-Geun | - |
dc.contributor.localauthor | 한상근 | - |
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