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INDOCRYPT
2001
Springer

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

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Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree
In this paper, the authors 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 ∈ [100, 600], elliptic curve parameters are identified 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 solving the ECDLP on any other cryptographically interesting elliptic curve over F2N . The feasibility of the GHS attack on the specific elliptic curves is examined over F2176 , F2208 , F2272 , F2304 and F2368 , which are provided as examples in the ANSI X9.62 standard for the elliptic curve signature scheme ECDSA. Finally, several concrete instances are provided of the ECDLP over F2N , N composite, of increasing difficulty; these resist all previously known att...
Markus Maurer, Alfred Menezes, Edlyn Teske
Added 30 Jul 2010
Updated 30 Jul 2010
Type Conference
Year 2001
Where INDOCRYPT
Authors Markus Maurer, Alfred Menezes, Edlyn Teske
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