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Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
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Handbook of Applied Cryptography
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Introduction to Coding Theory
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CRYPTO '85 Advances in Cryptology
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CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
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DSD '02 Proceedings of the Euromicro Symposium on Digital Systems Design
Improved techniques for fast exponentiation
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New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Double Point Compression with Applications to Speeding Up Random Point Multiplication
IEEE Transactions on Computers
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
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This paper introduces a new radix-2 representation with the same average weight as the {\rm width}{\hbox{-}}w nonadjacent form (w{\hbox{-}}{\rm NAF}). In both w{\hbox{-}}{\rm NAF} and the proposed representations, each nonzero digit is an odd integer with absolute value less than M. However, for w{\hbox{-}}{\rm NAF}, M is of the form 2^{w-1}, while, for the proposed representation, it can be any positive integer. Therefore, using the proposed integer representation, we can use the available memory efficiently, which is attractive for devices with limited memory. Another advantage of the proposed representation over w{\hbox{-}}{\rm NAF} is that it can be obtained by scanning the bits from left-to-right. This property is also useful for memory-constrained devices because it can reduce both the time and space complexity of fast point multiplication techniques.