Method for multiplying divisor classes by a scalar

Details Method for multiplying divisor classes by a scalar Method for multiplying divisor classes by a scalar

G - Physics

06

F

G06F 7/72 (2006.01)

Patent

CA 2389157

The invention relates to a method for the multiplication of divisor classes with a scalar (m), whereby the scalar (m) is a whole number and the divisor class is an element of the Jacobian variety of a hyperelliptic curve (C) on a finite body (F2n) (d.isin.JC(F2n), C: v2+uv=u5+u2+1). The inventive method is based on Frobenius endomorphism, whereby a very short .tau.-adic expansion is obtained enabling rapid calculation of multiplication.

La présente invention concerne un procédé de multiplication de classes de diviseurs avec un scalaire (m), dans lequel le scalaire (m) est un nombre entier et la classe de diviseurs est un élément de la variété jacobienne d'une courbe hyperélliptique (C) sur un corps infini (F¿2??n¿) (d.isin.J¿C?(F¿2??n¿), C: v?2¿+uv=u?5¿+u?2¿+1). Le procédé de l'invention repose sur l'endomorphisme de Frobénius, ce qui permet d'obtenir une très courte expansion .tau. qui permet un calcul rapide de la multiplication.

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