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Abstract: In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves whose group orders are equal to the order of the finite field. (Update)
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BibTeX entry: (Update)
N. Smart, "The discrete logarithm problem on elliptic curves of trace one", preprint, 1997. http://citeseer.ist.psu.edu/smart99discrete.html More
@article{ smart99discrete,
author = "N. P. Smart",
title = "The Discrete Logarithm Problem on Elliptic Curves of Trace One",
journal = "Journal of Cryptology: the journal of the International Association for Cryptologic Research",
volume = "12",
number = "3",
pages = "193--196",
year = "1999",
url = "citeseer.ist.psu.edu/smart99discrete.html" }
Citations (may not include all citations):257 Elliptic curve cryptosystems (context) - Koblitz - 1987
237 The Arithmetic Of Elliptic Curves (context) - Silverman - 1986
228 Use of elliptic curves in cryptography (context) - Miller - 1986
10 Elliptic curves over Fp suitable for cryptosystems (context) - Miyaji - 1993
6 Reducing elliptic curve logarithms to a finite field (context) - Menezes, Okamoto et al. - 1993
1 Hewlett-Packard Laboratories (context) - Smart, on et al. - 1994
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