The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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
Elliptic curves in cryptography
Elliptic curves in cryptography
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
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
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
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Analysis of linear combination algorithms in cryptography
ACM Transactions on Algorithms (TALG)
Theoretical Computer Science
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
A note on the signed sliding window integer recoding and a left-to-right analogue
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Analysis of Fractional Window Recoding Methods and Their Application to Elliptic Curve Cryptosystems
IEEE Transactions on Computers
Implementing public-key infrastructure for sensor networks
ACM Transactions on Sensor Networks (TOSN)
Faster Multi-exponentiation through Caching: Accelerating (EC)DSA Signature Verification
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
A New Upper Bound for the Minimal Density of Joint Representations in Elliptic Curve Cryptosystems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Unbalanced digit sets and the closest choice strategy for minimal weight integer representations
Designs, Codes and Cryptography
Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
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
Exponent Recoding and Regular Exponentiation Algorithms
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
A note on signed binary window algorithm for elliptic curve cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Fast elliptic curve cryptography using minimal weight conversion of d integers
AISC '12 Proceedings of the Tenth Australasian Information Security Conference - Volume 125
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This paper extends results concerning efficient exponentiation in groups where inversion is easy (e.g. in elliptic curve cryptography). It examines the right-to-left and left-to-right signed fractional window (RL-SFW and LR-SFW) techniques and shows that both RL-SFW and LR-SFW representations have minimal weight among all signed-digit representations with digit set {±1, ±3, ..., ±m, 0}.(Fractional windows generalize earlier sliding-window techniques, providing more flexibility for exponentiation algorithms in order to make best use of the memory that is available for storing intermediate results.) Then it considers the length of representations: LR-SFW representations are an improvement over RL-SFW representations in that they tend to be shorter; further length improvements are possible by post-processing the representations.