TY - JOUR
T1 - New families of hyperelliptic curves with efficient gallant-lambert- vanstone method
AU - Takashima, Katsuyuki
PY - 2005
Y1 - 2005
N2 - The Gallant-Lambert-Vanstone method [14] (GLV method for short) is a scalar multiplication method for elliptic curve cryptography (ECC). In WAP WTLS[47], SEC 2[42], ANSI X9.62[1] and X9.63[2], several domain parameters for applications of the GLV method are described. Curves with those parameters have efficiently-computable endomorphisms. Recently the GLV method for hyperelliptic curve (HEC) Jacobians has also been studied. In this paper, we discuss applications of the GLV method to curves with real multiplication (RM). It is the first time to use RM in cryptography. We describe the general algorithm for using such RM, and we show that some genus 2 curves with RM have enough effciency to be used in the GLV method as in the previous CM case.
AB - The Gallant-Lambert-Vanstone method [14] (GLV method for short) is a scalar multiplication method for elliptic curve cryptography (ECC). In WAP WTLS[47], SEC 2[42], ANSI X9.62[1] and X9.63[2], several domain parameters for applications of the GLV method are described. Curves with those parameters have efficiently-computable endomorphisms. Recently the GLV method for hyperelliptic curve (HEC) Jacobians has also been studied. In this paper, we discuss applications of the GLV method to curves with real multiplication (RM). It is the first time to use RM in cryptography. We describe the general algorithm for using such RM, and we show that some genus 2 curves with RM have enough effciency to be used in the GLV method as in the previous CM case.
KW - Elliptic Curve Cryptography
KW - GLV Method
KW - Hyperelliptic Curve Cryptography
KW - Public Key Cryptography
KW - Scalar Multiplication
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U2 - 10.1007/11496618_21
DO - 10.1007/11496618_21
M3 - Conference article
AN - SCOPUS:24944542732
SN - 0302-9743
VL - 3506
SP - 279
EP - 295
JO - LECTURE NOTES IN COMPUTER SCIENCE
JF - LECTURE NOTES IN COMPUTER SCIENCE
T2 - 7th International Conference on Information Security and Cryptology - ICISC 2004
Y2 - 2 December 2004 through 3 December 2004
ER -