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Quelques Aspects de l'Arithmétique by Diao-O

Quelques Aspects de l'Arithmétique

by Diao-O
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Book cover type: Paperback
  • ISBN13: 9786131508998
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 156
  • Original Price: GBP 40.0
  • Language: French
  • Edition: N/A
  • Item Weight: 236 grams
  • BISAC Subject(s): Geometry / General

Dans ce livre, on s'intéresse à des briques utiles à la cryptographie asymétrique et principalement au problème du logarithme discre, tout en obtenant des algorithmes résistants aux attaques par canaux auxiliaires. Dans une première partie, nous décrivons une implémentation soigneuse de différentes variantes des couplages de Weil et de Tate sur des jacobiennes de courbes de genre 2. Nous faisons une comparaison avec les couplages sur les courbes elliptiques. Une deuxième partie est dévolue à la recherche de modèles efficaces pour les courbes elliptiques et les surfaces de Kummer non-ordinaires en caractéristique 2. Pour le genre 1, nous obtenons que le modèle d'Edwards binaire se déduit du modèle d'Edwards classique en caractéristique zéro. Pour le genre 2, nous utilisons des techniques de "déformation" qui consistent à considérer une famille de jacobiennes sur un anneau des séries formelles, telle que la fibre générique soit ordinaire et la fibre spéciale soit la jacobienne considérée. Il s'agit alors de montrer que la loi de groupe sur la fibre générique s'étend à tout le modèle. Nous comparons les lois de composition ainsi obtenues avec celles déjà connues.

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