H - Electricity – 04 – L
Patent
H - Electricity
04
L
H04L 9/30 (2006.01) G06F 7/72 (2006.01)
Patent
CA 2310588
The present invention provides a transformation method for obtaining optimized hardware and software implementations of elliptic curve cryptographic systems, including elliptic curve encryption, decryption, and signature functions. The method is applicable to any elliptic curve group G defined over any field F. More specifically, the present invention is characterized by speeding up the elliptic curve point multiplication operation, which consists of the calculation Q = eP, where P is a member of G and e is an integer. This is achieved by transforming P = (x, y) to a point P' = (x', y') in order to compute Q' = (u, v = eP'). The point P' is not necessarily on the elliptic curve, but by performing calculation on P' and transforming the resulting Q' back into G, it may be possible to calculate Q more efficiently than utilizing a direct method. The present invention also includes a method for optimizing the calculation of cryptographic operations involving arbitrary expressions in finite field arithmetic through a transformation method that permits the use of any field F in an efficient manner. The invention includes a method for optimizing arbitrary finite calculation in any finite field. The present invention teaches a set of transformations of cryptographic calculations that allows the use of other known techniques that have only been applicable to certain limited special cases prior to this invention.
L'invention concerne un procédé de transformation permettant l'implémentation optimisée logicielle et matérielle de systèmes cryptographiques à courbes elliptiques, dont le cryptage à courbes elliptiques, le décryptage et les fonctions de signature. Le procédé s'applique à tout groupe de courbes elliptiques G défini dans tout champ F. Plus spécifiquement, le procédé de l'invention consiste à accélérer l'opération de multiplication de points sur une courbe elliptique, qui consiste à calculer Q = eP, P étant un membre de G et e étant un entier. Pour ce faire, on transforme P = (x,y) en un point P'= (x', y') de manière à calculer Q'= (u,v = eP'). Le point P' ne se trouve pas nécessairement sur la courbe elliptique, mais par le calcul sur P' et la transformation de Q' de sorte qu'il se retrouve dans G, il est possible de calculer Q plus efficacement qu'au moyen d'un procédé direct. L'invention porte également sur un procédé d'optimisation du calcul d'opérations cryptographiques impliquant les expressions arbitraires en arithmétique de champ fini par un procédé de transformation permettant l'utilisation efficace de tout champ F. L'invention concerne un procédé d'optimisation du calcul fini arbitraire dans tout champ fini. Le procédé comprend un ensemble de transformations de calculs cryptographiques permettant l'utilisation d'autres techniques connues applicables jusqu'à maintenant seulement à certains cas spéciaux limités.
Beahan John J. Jr.
Koc Cetin Kaya
Sadeghi Behzad
Gowling Lafleur Henderson Llp
Rt Technologies Inc.
Secured Information Technology Inc.
The State Of Oregon Acting By And Through The State Board Of Hig
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