On the asymptotic effectiveness of Weil descent attacks

Abstract

In this paper we investigate the asymptotic effectiveness of the Gaudry–Hess–Smart Weil descent attack and its generalization to the discrete logarithm problem for elliptic curves over characteristic-two finite fields. In particular we obtain nontrivial lower and upper bounds on the smallest possible genus to which it can lead.

Keywords

• elliptic curve discrete logarithm problem
• weil descent attacks