, w dec dans les instances du problème RSL avec les paramètres considérés dans
, Ces résultats ont été obtenus avec Magma et l'utilisation d'un processeur Intel Core i5, cadencé à 1.6 GHz à un seul coeur et avec 8 Go de RAM. Dans notre implémentation nous vérifions que les mots de poids w dec révèlent bien l'espace F généré comme étant le secret
, Éviter l'attaque
, Bien que notre attaque casse les paramètres proposés dans [Gab+17b] nous allons ici montrer qu'il existe en principe un ensemble de paramètres l'évitant. Commençons tout d'abord par rappeler qu'il existe
, Nombre attendu de solutions au problème du décodage générique en métrique rang pour m
,
, Exposant asymptotique ? P range de la complexité de l'algorithme de Prange en base 2 pour q " 2 et R " 1{2 en fonction de ? " w{n, p.79
Exposant asymptotique ? P range de la complexité de l'algorithme de Prange en base 2 pour q " 2 et w{n " ?´en fonction de R, p.80 ,
, Algorithme de Wagner de profondeur a " 2 appliqué au décodage, p.84
, Exposant asymptotique ? W agner en base 2 de la complexité de l'algorithme de Wagner pour trouver une solution du problème de décodage avec q " 2 et R " 0.7 en fonction de ? " w{n fixé
, Exposants asymptotiques ? W agner et ? W agnerLisse de la complexité de l'algorithme en base 2 des algorithmes de Wagner non lissé et lissé pour trouver une solution du problème de décodage avec q " 2 et R " 0.7 en fonction de ? " w{n fixé
, Exposants asymptotiques ? P range et ? Dumer de la complexité de l'algorithme de Prange et Dumer pour R " 1{2 en fonction de ? " w{n fixé
Exposants asymptotiques ? P range et ? Dumer de la complexité de l'algorithme de Prange et Dumer pour w{n " ?´en fonction de R, p.91 ,
) écrit par découpage en deux et (2) utilisant les représentations ,
, Dumer et BJMM pour R " 1{2 en fonction de ? " w{n fixé, Exposants asymptotiques ? P range , ? Dumer et ? BJM M de la complexité des algorithmes de Prange
, Exposants asymptotiques ? P range , ? Dumer et ? BJM M de la complexité des algorithmes de Prange, Dumer et BJMM pour w{n " ?´en fonction de R. 96
, Exposants asymptotiques de la complexité de l'algorithme de Prange pour R " 1{2 en fonction de ? pour q " 2 et q " 3
, Exposant asymptotique de la complexité de l'algorithme de Prange pour R " 1{5 en fonction de ? ? " w{n et avec q " 3
, Exposant asymptotique l'algorithme de Prange pour q " 3 et w{n " ?`en fonction de R
, Distributions pq 2 ps, tqq s et pq unif 2 ps, tqq s avec les distributions internes D t U choisies comme Lappt´3 2 m max cible ptq, 6, maxp0, k U`t´n {2q, tq pour les paramètres n, 2000.
, Une figure représentant J , I et I 1 en fonction de la forme d'un mot de code dans V 1
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