Accelerated finite field operations on an elliptic curve

Details Accelerated finite field operations on an elliptic curve Accelerated finite field operations on an elliptic curve

G - Physics

06

F

G06F 7/72 (2006.01)

Patent

CA 2324621

A method for multiplication of a point P on elliptic curve E by a value k in order to derive a point kP comprises the steps of representing the number k as vector of binary digits stored in a register and forming a sequence of point pairs (P1, P2) wherein the point pairs differed most by P and wherein the successive series of point pairs are selected either by computing (2mP,(2m+1)P) from (mP,(m+1)P) or ((2m+1)P,(2m+2)P) from (mP,(m+1)P). The computations may be performed without using the .gamma.-coordinate of the points during the computation while allowing the .gamma.-coordinate to be extracted at the end of the computations, thus, avoiding the use of inversion operations during the computation and therefore, speeding up the cryptographic processor functions. A method is also disclosed for accelerating signature verification between two parties.

L'invention se rapporte à un procédé de multiplication d'un point P sur une courbe elliptique E par une valeur k dans le but de dériver un point kP. Ce procédé consiste à représenter le nombre k comme un vecteur de chiffres binaires dans un registre et à former une séquence de paires de points (P1, P2) qui diffèrent le plus de P et qui sont telles que les séries successives de paires de points sont sélectionnées au moyen du calcul de (2mP,(2m+1)P) à partir de (mP,(m+1)P) ou ((2m+1)P,(2m+2)P) à partir de (mP,(m+1)P). On peut effectuer ces calculs sans se servir de la coordonnée-y des points pendant le calcul tout en permettant l'extraction de la coordonnée-y à la fin des calculs, ce qui permet d'éviter des opérations d'inversion et par conséquent d'accélérer les fonctions cryptographiques de l'unité de traitement. L'invention se rapporte également à un procédé d'accélération de la vérification de signatures entre deux parties.

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