Elliptic Curve Cryptosystems Immune to Any Reduction into the Discrete Logarithm Problem

Atsuko MIYAJI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.1   pp.50-54
Publication Date: 1993/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
public-key,  discrete logarithms,  elliptic curves,  

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In 1990, Menezes, Okamoto and Vanstone proposed a method that reduces EDLP to DLP, which gave an impact on the security of cryptosystems based on EDLP. But this reducing is valid only when Weil pairing can be defined over the m-torsion group which includes the base point of EDLP. If an elliptic curve is ordinary, there exists EDLP to which we cannot apply the reducing. In this paper, we investigate the condition for which this reducing is invalid.