Elliptic curve point counting = 타원곡선의 위수 계산

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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 $O(N^2)$.
Advisors
Hahn, Sang-Geunresearcher한상근researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2002
Identifier
177223/325007 / 000995108
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2002.8, [ [ii], 38 p. ; ]

Keywords

타원곡선; 위수 계산; Gaussian normal basis; elliptic curve; order counting

URI
http://hdl.handle.net/10203/41854
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=177223&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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