Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key 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
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
On Modular Decomposition of Integers
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
Information Processing Letters
New families of hyperelliptic curves with efficient gallant-lambert-vanstone method
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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Since Miller and Koblitz applied elliptic curves to cryptographic system in 1985[3,6], a lot of researchers have been interested in this field and various speedup techniques for the scalar multiplication have been developed. Recently, Gallant et al. published a method that accelerates the scalar multiplication and is applicable to a larger class of curves[4]. In the process of their method, they assumed the existence of a special pair of two short linearly independent vectors. Once a pair of such vectors exists, their decomposition method improves the efficiency of the scalar multiplication roughly about 50%. In this paper, we state and prove a necessary condition for the existence of a pair of desired vectors and we also present an algorithm to find them.