Elliptic curve discrete logarithm and lifting problem = 타원곡선 이산로그와 올림 문제

No subexponential time algorithm is known yet for the Elliptic Curve Discrete Logarithm Problem(ECDLP) except the cases of singular curves, supersingular curves and anomalous curves. In this paper, we introduce the lifting problem and show that it implies the ECDLP and integer factorization problem(IFP) and we note that finding a point in $E_1(Q)$, the kernel of the reduction map, also implies the ECDLP and the IFP since it solves the lifting problem. Moreover, we analyze the difficulty of the lifting problem by estimating the minimum of the canonical heights on the kernel of the reduction map.
Advisors
Hahn, Sang-Geunresearcher한상근researcher
Publisher
한국과학기술원
Issue Date
2000
Identifier
157756/325007 / 000955104
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2000.2, [ [ii], [33] p. ]

Keywords

Discrete logarithm; Factorization; 타원곡선; 이산로그; 소인수 분해; Elliptic curve

URI
http://hdl.handle.net/10203/41821
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=157756&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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