A survey of fast exponentiation methods
Journal of Algorithms
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Introduction to Coding Theory
The Hardness of the Hidden Subset Sum Problem and Its Cryptographic Implications
CRYPTO '99 Proceedings of the 19th 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
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th 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
Efficient representations on koblitz curves with resistance to side channel attacks
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Short memory scalar multiplication on koblitz curves
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Advances in alternative non-adjacent form representations
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
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Techniques for fast exponentiation (multiplication) in various groups have been extensively studied for use in cryptographic primitives. Specifically, the coding of the exponent (multiplier) plays an important role in the performances of the algorithms used. The crucial optimization relies in general on minimizing the Hamming weight of the exponent (multiplier). This can be performed optimally with nonadjacent representations. This paper introduces a compact encoding of non-adjacent representations that allows to skip the exponent recoding step. Furthermore, a straightforward technique for picking random numbers that alreadysatisfythe non-adjacence propertyis proposed. Several examples of application are given, in particular in the context of scalar multiplication on elliptic curves.