Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
A course in computational algebraic number theory
A survey of fast exponentiation methods
Journal of Algorithms
Elliptic curves in cryptography
Elliptic curves in cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
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
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
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
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
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based 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
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 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
A DPA countermeasure by randomized frobenius decomposition
WISA'05 Proceedings of the 6th international conference on Information Security Applications
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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In this work we analyse the GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) which uses a fast endomorphism 驴 with minimal polynomial X2 +rX +s to compute any multiple kP of a point P of order n lying on an elliptic curve.First we fill in a gap in the proof of the bound of the kernel 驴 vectors of the reduction map f : (i, j) 驴 i+驴j (mod n). In particular, we prove the GLV decomposition with explicit constant kP = k1P + k2驴(P), with max{|k1|, |k2|} 驴 驴1 +|r| + s驴n.Next we improve on this bound and give the best constant in the given examples for the quantity supk, n max{|k1|, |k2|}/驴n. Independently Park, Jeong, Kim, and Lim (PKC 2002) have given similar but slightly weaker bounds.Finally we provide the first explicit bounds for the GLV method generalised to hyperelliptic curves as described in Park, Jeong and Lim (EUROCRYPT 2002).