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1. WO2000039668 - A METHOD FOR ACCELERATING CRYPTOGRAPHIC OPERATIONS ON ELLIPTIC CURVES

Publication Number WO/2000/039668
Publication Date 06.07.2000
International Application No. PCT/CA1999/001222
International Filing Date 23.12.1999
Chapter 2 Demand Filed 14.07.2000
IPC
G06F 7/72 2006.01
GPHYSICS
06COMPUTING; CALCULATING OR COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations
72using residue arithmetic
CPC
G06F 7/725
GPHYSICS
06COMPUTING; CALCULATING; COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations ; , e.g. using difunction pulse trains, STEELE computers, phase computers
72using residue arithmetic
724Finite field arithmetic
725over elliptic curves
Applicants
  • CERTICOM CORP. [CA/CA]; 4th floor 5520 Explorer Drive Mississauga, Ontario L4W 5L1, CA (AllExceptUS)
  • GALLANT, Robert [CA/CA]; CA (UsOnly)
  • LAMBERT, Robert, J. [CA/CA]; CA (UsOnly)
  • VANSTONE, Scott, A. [CA/CA]; CA (UsOnly)
Inventors
  • GALLANT, Robert; CA
  • LAMBERT, Robert, J.; CA
  • VANSTONE, Scott, A.; CA
Agents
  • ORANGE, John, R., S. ; Orange & Chari Suite 4900, P.O. Box 190 66 Wellington Street West, Toronto Dominion Bank Tower, Toronto-Dominion Centre Toronto, Ontario M5K 1H6, CA
Priority Data
2,257,00824.12.1998CA
Publication Language English (EN)
Filing Language English (EN)
Designated States
Title
(EN) A METHOD FOR ACCELERATING CRYPTOGRAPHIC OPERATIONS ON ELLIPTIC CURVES
(FR) PROCEDE D'ACCELERATION DES OPERATIONS CRYPTOGRAPHIQUES SUR DES COURBES ELLIPTIQUES
Abstract
(EN)
This invention provides a method for accelerating multiplication of an elliptic curve point Q(x,y) by a scalar k, the method comprising the steps of selecting an elliptic curve over a finite field Fq where q is a prime power such that there exists an endomorphism $g(c), where $g(c)(Q) = $g(l).Q for all points Q(x,y) on the elliptic curve; and using smaller representations ki of the scalar k in combination with the mapping $g(c) to compute the scalar multiple of the elliptic curve point Q.
(FR)
Cette invention concerne un procédé d'accélération de la multiplication d'un point de courbe elliptique Q(x,y) par une k scalaire, le procédé comprenant les étapes consistant à sélectionner une courbe elliptique sur un champ fini Fq dans lequel q représente une puissance de nombre premier de manière qu'il existe un endomorphisme $g(c), dans lequel $g(c)(Q) = $g(l).Q pour tous les points Q(x,y) sur la courbe elliptique, et à utiliser des représentations ki plus petites de k scalaire en combinaison avec la cartographie $g(c) pour calculer le multiple scalaire du point Q de la courbe elliptique.
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