EP 1038371 A1 20000927 - TRANSFORMATION METHODS FOR OPTIMIZING ELLIPTIC CURVE CRYPTOGRAPHIC COMPUTATIONS
Title (en)
TRANSFORMATION METHODS FOR OPTIMIZING ELLIPTIC CURVE CRYPTOGRAPHIC COMPUTATIONS
Title (de)
UNWANDLUNGSVERFAHREN ZUR OPTIMIERUNG VON KRYPTOGRAPHISCHEN BERECHNUNGEN ÜBER ELLIPTISCHE KURVEN
Title (fr)
PROCEDES DE TRANSFORMATION POUR L'OPTIMISATION DE CALCULS DE COURBES ELLIPTIQUES
Publication
Application
Priority
- US 9825824 W 19981204
- US 6931497 P 19971205
Abstract (en)
[origin: WO9930458A1] 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.
IPC 1-7
IPC 8 full level
G06F 7/72 (2006.01); G09C 1/00 (2006.01); H04L 9/30 (2006.01)
CPC (source: EP)
G06F 7/724 (2013.01); G06F 7/725 (2013.01); G06F 7/728 (2013.01); H04L 9/3073 (2013.01); Y04S 40/20 (2013.01)
Designated contracting state (EPC)
AT CH DE DK ES FI FR GB IT LI LU SE
DOCDB simple family (publication)
WO 9930458 A1 19990617; AU 2198399 A 19990628; AU 758621 B2 20030327; BR 9815161 A 20001010; CA 2310588 A1 19990617; CN 1280726 A 20010117; EP 1038371 A1 20000927; EP 1038371 A4 20020130; JP 2001526416 A 20011218
DOCDB simple family (application)
US 9825824 W 19981204; AU 2198399 A 19981204; BR 9815161 A 19981204; CA 2310588 A 19981204; CN 98811822 A 19981204; EP 98965973 A 19981204; JP 2000524894 A 19981204