The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
고리 위의 초이례적인 타원 곡선 Z/nZ ;(n=Πi = 1k piei)는 소수 필드 위에 변칙적인 타원 곡선을 확장하여 정의됩니다. F피. 그들은 가지고 있다 n 링 위의 포인트 Z/nZ and pi 포인트 Fpi 모두에게 pi. 우리는 변칙 타원 곡선에 대한 이산 로그 문제를 해결하는 Satoh-Araki-Smart 알고리즘과 Ruck 알고리즘을 일반화합니다. 우리는 "초이례적인 타원 곡선에 대한 이산 로그 문제"가 다음과 같이 해결될 수 있음을 증명합니다. 결정 론적 인 소인수를 모르는 다항식 시간 n.
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Noboru KUNIHIRO, Kenji KOYAMA, "Two Discrete Log Algorithms for Super-Anomalous Elliptic Curves and Their Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 1, pp. 10-16, January 2000, doi: .
Abstract: Super-anomalous elliptic curves over a ring Z/nZ ;(n=Πi=1k piei) are defined by extending anomalous elliptic curves over a prime filed Fp. They have n points over a ring Z/nZ and pi points over Fpi for all pi. We generalize Satoh-Araki-Smart algorithm and Ruck algorithm, which solve a discrete logarithm problem over anomalous elliptic curves. We prove that a "discrete logarithm problem over super-anomalous elliptic curves" can be solved in deterministic polynomial time without knowing prime factors of n.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_1_10/_p
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@ARTICLE{e83-a_1_10,
author={Noboru KUNIHIRO, Kenji KOYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Two Discrete Log Algorithms for Super-Anomalous Elliptic Curves and Their Applications},
year={2000},
volume={E83-A},
number={1},
pages={10-16},
abstract={Super-anomalous elliptic curves over a ring Z/nZ ;(n=Πi=1k piei) are defined by extending anomalous elliptic curves over a prime filed Fp. They have n points over a ring Z/nZ and pi points over Fpi for all pi. We generalize Satoh-Araki-Smart algorithm and Ruck algorithm, which solve a discrete logarithm problem over anomalous elliptic curves. We prove that a "discrete logarithm problem over super-anomalous elliptic curves" can be solved in deterministic polynomial time without knowing prime factors of n.},
keywords={},
doi={},
ISSN={},
month={January},}
부
TY - JOUR
TI - Two Discrete Log Algorithms for Super-Anomalous Elliptic Curves and Their Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 10
EP - 16
AU - Noboru KUNIHIRO
AU - Kenji KOYAMA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2000
AB - Super-anomalous elliptic curves over a ring Z/nZ ;(n=Πi=1k piei) are defined by extending anomalous elliptic curves over a prime filed Fp. They have n points over a ring Z/nZ and pi points over Fpi for all pi. We generalize Satoh-Araki-Smart algorithm and Ruck algorithm, which solve a discrete logarithm problem over anomalous elliptic curves. We prove that a "discrete logarithm problem over super-anomalous elliptic curves" can be solved in deterministic polynomial time without knowing prime factors of n.
ER -