Realizing the Menezes-Okamoto-Vanstone (MOV) Reduction Efficiently for Ordinary Elliptic Curves

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概要

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• The problem we consider in this paper is whether the Menezes-Okamoto-Vanstone (MOV) reduction for attacking elliptic curve cryptosystems can be realized for genera elliptic curves. In realizing the MOV reduction, the base field F_q is extended so that the reduction to the discrete logarithm problem in a finite field is possible. Recent results by Balasubramanian and Koblitz suggest that, if l ⫮q-1, such a minimum extension degree is the minimum k such that l∖q^k -1, which is equivalent to the condition under which the Frey-Ruck (FR) reduction can be applied, where l is the order of the group in the elliptic curve discrete logarithm problem. Our point is that the problem of finding an l-torsion point required in evaluating the Weil pairing should be considered as well from an algorithmic point of view. In this paper, we actually propose a method which leads to a solution of the problem. In addition, our contribution allows us to draw the conclusion that the MOV reduction is indeed as powerful as the FR reduction under l ⩘q -1 not only from the viewpoint of the minimum extension degrees but also from that of the effectiveness of algorithms.

• 社団法人電子情報通信学会の論文
• 2000-04-25

著者

• Zheng Y

  Univ. North Carolina Charlotte Nc Usa

• Zheng Yuliang

  Department Of Software And Information Systems

• Shikata Junji

  Graduate School Of Environment And Information Sciences Yokohama National University

• IMAI Hideki

  The author is with Institute of Industrial Sience, the University of Tokyo

• Imai H

  Research Center For Information Security (rcis) National Institute Of Advanced Industrial Science An

• Imai Hideki

  3rd Department Institute Of Industrial Science The University Of Tokyo

• Shikata J

  The Graduate School Of Environment And Information Sciences Yokohama National University

• Shikata Junji

  The Authors Are With The Institute Of Industrial Science The University Of Tokyo

• ZHENG Yuliang

  The author is with the School of Network Computing, Monash University

• SUZUKI Joe

  The authors are with the Graduate School of Science, Osaka University

• Suzuki Joe

  The Authors Are With The Department Of Mathematics Graduate School Of Science Osaka University

• Suzuki Joe

  The Authors Are With The Graduate School Of Science Osaka University

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