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IEEE Transactions on Computers
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EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
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Designs, Codes and Cryptography
Computer Arithmetic: Principles, Architecture and Design
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IEEE Transactions on Computers
Digit-Set Conversions: Generalizations and Applications
IEEE Transactions on Computers
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
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ASAP '00 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Optimised Squaring of Long Integers Using Precomputed Partial Products
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
An analysis of exponentiation based on formal languages
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
New left-to-right minimal weight signed-digit radix-r representation
Computers and Electrical Engineering
Unbalanced digit sets and the closest choice strategy for minimal weight integer representations
Designs, Codes and Cryptography
New left-to-right radix-r signed-digit recoding algorithm for pairing-based cryptosystems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A loopless gray code for minimal signed-binary representations
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A note on signed binary window algorithm for elliptic curve cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
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Abstract--This paper considers the problem of recoding a number to minimize the number of nonzero digits in its representation, that is, to minimize the weight of the representation. A general sliding window scheme is described that extends minimal binary sliding window conversion to arbitrary radix and to encompass signed digit sets. This new conversion expresses a number of known recoding techniques as special cases. Proof that this scheme achieves minimal weight for a given digit set is provided and results concerning the theoretical average and worst-case weight are derived.