Remarks on Elliptic Curve Discrete Logarithm Problems(Special Section on Cryptography and Information Security)
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概要
- 論文の詳細を見る
The MOV and FR algorithms, which are representative attacks on elliptic curve cryptosystems, reduce the elliptic curve discrete logarithm problem(ECDLP)to the discrete logarithm problem in a finite field.This paper studies these algorithms and introduces the following three results.First, we show an explicit condition under which the MOV algorithm can be applied to non-supersingular elliptic curves.Next, by comparing the effectiveness of the MOV algorithm to that of the FR algorithm, it is explicitly shown that the condition needed for the MOV algorithm to be subexponential is the same as that for the FR algorithm except for elliptic curves of trace two.Finally, a new explicit reduction algorithm is proposed for the ECDLP over elliptic curves of trace two.This algorithm differs from a simple realization of the FR algorithm.Furthermore, we show, by experimental results, that the running time of the proposed algorithm is shorter than that of the original FR algorithm.
- 社団法人電子情報通信学会の論文
- 2000-01-25
著者
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Saito T
Tokyo Denki University
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Kanayama Naoki
Department Of Information And Communication Engineering The University Of Electro-comrnunications
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Kanayama N
Waseda Univ. Tokyo Jpn
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Saito Taiichi
Telecommunications Advancement Organization Of Japan
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KANAYAMA Naoki
the Graduate School of Science and Engineering, Waseda University
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KOBAYASHI Tetsutaro
NTT Laboratories
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UCHIYAMA Shigenori
NTT Laboratories
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Kanayama Naoki
The Graduate School Of Science And Engineering Waseda University
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Kobayashi Tetsutaro
Ntt Information Sharing Platform Laboratories
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Kobayashi T
Ntt Information Sharing Platform Laboratories
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Uchiyama S
Ntt Information Sharing Platform Laboratories
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Kobayashi Takehiko
NTT Information Sharing Platform Laboratories
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