Progress in Cryptology — INDOCRYPT 2001

Volume 2247 of the series Lecture Notes in Computer Science pp 195-213


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

(Extended Abstract)
  • Markus MaurerAffiliated withDept. of C&O, University of Waterloo
  • , Alfred MenezesAffiliated withDept. of C&O, University of Waterloo
  • , Edlyn TeskeAffiliated withDept. of C&O, University of Waterloo

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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 F2 N, N ∈ [160, 600], we identify elliptic curve parameters such that (i)there should exist a cryptographically interesting elliptic curve E over F2 N with these parameters; and (ii)the GHS attack is more efficient for solving the ECDLP in E(F 2 N )than for any other cryptographically interesting elliptic curve over F2 N.