Cryptology ePrint Archive: Report 2001/041

Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent

Michael Jacobson and Alfred Menezes and Andreas Stein

Abstract: We provide a concrete instance of the discrete logarithm problem on an elliptic curve over F_{2^{155}} which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index-calculus methods for hyperelliptic curves over characteristic two finite fields, and discuss the cryptographic implications of our results.

Category / Keywords: foundations / elliptic curve discrete logarithm problem, Weil descent

Date: received 17 May 2001

Contact author: ajmeneze at uwaterloo ca

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Version: 20010520:170217 (All versions of this report)

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