Advances in Applied Mathematics
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Redundant Integer Representations and Fast Exponentiation
Designs, Codes and Cryptography - Special issue dedicated to Gustavus J. Simmons
Mathematics of Computation
A survey of fast exponentiation methods
Journal of Algorithms
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
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
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
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
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
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
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application 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
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
An Improved Algorithm for uP + vQ on a Family of Elliptic Curves
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 17 - Volume 18
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Skew Frobenius Map and Efficient Scalar Multiplication for Pairing---Based Cryptography
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
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
Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
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
Efficient techniques for high-speed elliptic curve cryptography
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Efficient software implementation of binary field arithmetic using vector instruction sets
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and Cryptography
Designing a code generator for pairing based cryptographic functions
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Scalar multiplication on koblitz curves using double bases
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
SPA-resistant simultaneous scalar multiplication
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Efficiently computable endomorphisms for hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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 method for efficient parallel computation of Tate pairing
International Journal of Grid and Utility Computing
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
A DPA countermeasure by randomized frobenius decomposition
WISA'05 Proceedings of the 6th international conference on Information Security Applications
Accelerated verification of ECDSA signatures
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Efficient precomputation schemes of kP+lQ
Information Processing Letters
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Efficient java implementation of elliptic curve cryptography for J2ME-Enabled mobile devices
WISTP'12 Proceedings of the 6th IFIP WG 11.2 international conference on Information Security Theory and Practice: security, privacy and trust in computing systems and ambient intelligent ecosystems
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
An 8-bit AVR-Based Elliptic Curve Cryptographic RISC Processor for the Internet of Things
MICROW '12 Proceedings of the 2012 45th Annual IEEE/ACM International Symposium on Microarchitecture Workshops
Batch verification suitable for efficiently verifying a limited number of signatures
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
NEON implementation of an attribute-based encryption scheme
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
High-Performance scalar multiplication using 8-dimensional GLV/GLS decomposition
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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The fundamental operation in elliptic curve cryptographic schemes is the multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves than previous such methods. For this special class of curves, a speedup of up to 50% can be expected over the best general methods for point multiplication.