Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Speeding up the Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
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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.