Extending the GLS endomorphism to speed up GHS Weil descent using Magma - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Finite Fields and Their Applications Année : 2021

Extending the GLS endomorphism to speed up GHS Weil descent using Magma

Résumé

Let $q = 2^n$, and let $E / \mathbb{F}_{q^{\ell}}$ be a generalized Galbraith--Lin--Scott (GLS) binary curve, with $\ell \ge 2$ and $(\ell, n) = 1$. We show that the GLS endomorphism on $E / \mathbb{F}_{q^{\ell}}$ induces an efficient endomorphism on the Jacobian $J_H(\mathbb{F}_q)$ of the genus-$g$ hyperelliptic curve $H$ corresponding to the image of the GHS Weil-descent attack applied to $E/\mathbb{F}_{q^\ell}$, and that this endomorphism yields a factor-$n$ speedup when using standard index-calculus procedures for solving the Discrete Logarithm Problem (DLP) on $J_H(\mathbb{F}_q)$. Our analysis is backed up by the explicit computation of a discrete logarithm defined on a prime-order subgroup of a GLS elliptic curve over the field $\mathbb{F}_{2^{5\cdot 31}}$. A Magma implementation of our algorithm finds the aforementioned discrete logarithm in about $1,035$ CPU-days.
Fichier principal
Vignette du fichier
manuscript.pdf (275.94 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03233803 , version 1 (17-06-2021)

Identifiants

Citer

Jesús-Javier Chi-Domínguez, Francisco Rodríguez-Henríquez, Benjamin Smith. Extending the GLS endomorphism to speed up GHS Weil descent using Magma. Finite Fields and Their Applications, In press, 75, ⟨10.1016/j.ffa.2021.101891⟩. ⟨hal-03233803⟩
67 Consultations
115 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More