Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

Abstract

We analyze the Gaudry-Hess-Smart (GHS) Weil descent attack on the elliptic curve discrete logarithm problem (ECDLP) for elliptic curves defined over characteristic two finite fields of composite extension degree. For each such field F2N, N ? [160, 600], we identify elliptic curve parameters such that (i) there should exist a cryptographically interesting elliptic curve E over F2N with these parameters; and (ii) the GHS attack is more efficient for solving the ECDLP in E(F2N) than for any other cryptographically interesting elliptic curve over F2N.