nous avons aussi présenté l'opération de halving, soit la division par deux d'un point d'ordre impair de la courbe. Nous avons terminé par la présentation des approches les plus connues en matière de multiplication scalaire de point de courbe elliptique : Double-and-add, Halve-and-add et Double/halveand-add ,
Nous avons appliqué ces opérations aux algorithmes réguliers d'exponentiation modulaire résistants face à l'attaque Simple Power Analysis suivants : l'échelle binaire de Montgomery et les deux algorithmes Regular left-to-right 2 ? -ary exponentiation et Regular right-to-left 2 ? -ary exponentiation proposés par Joye et Tunstall dans [31]. L'application de ces opérations combinées à ces algorithmes se traduit par des gains de complexité de 4% pour l'approche Regular right-to-left 2 ? -ary exponentiation, 8% pour son homologue Regular left-to-right 2 ? -ary exponentiation et de 13% pour l'échelle binaire de Montgomery, dans le cas d'une exponentiation RSA de taille 2048 bits. Ces algorithmes améliorés ont fait l'objet d'implantations logicielles qui apportent des gains en performance de 4 % dans le cas Regular right-to-left 2 ? -ary exponentiation , jusqu'à plus de 8 % dans le cas Regular left-to-right 2 ? -ary exponentiation, et jusqu'à 15 % dans le cas de l'échelle binaire de Montgomery, pour des exponentiations de taille 4096 bits Au chapitre 5, nous avons étudié l'impact d'opérations combinées de type sur corps binaire F 2 m aux additions et doublements de points de courbe elliptique sur corps binaire et avons appliqué ensuite ces opérations de points sur les algorithmes de multiplication scalaire suivants : Double-and-add, Halve-and-add et Double/halve-and-add, Nous avons présenté la complexité de ces opérations combinées dans les cas de deux approches différentes pour la multiplication de polynômes en caractéristique deux, l'approche classique que nous avons désignée CombMul utilisant le jeu Bibliographie [1] Performance Application Programming Interface (PAPI) ,
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