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Optimal Lefttoright Binary SignedDigit Recoding
, 2000
"... This paper describes new methods for producing optimal binary signeddigit representations. This can be useful in the fast computation of exponentiations. Contrary to existing algorithms, the digits are scanned from left to right (i.e., from the most significant position to the least significant ..."
Abstract

Cited by 34 (3 self)
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This paper describes new methods for producing optimal binary signeddigit representations. This can be useful in the fast computation of exponentiations. Contrary to existing algorithms, the digits are scanned from left to right (i.e., from the most significant position to the least significant position). This may lead to better performances in both hardware and software.
A new minimal average weight representation for lefttoright point multiplication methods
"... This paper introduces a new radix2 representation with the same average weight as the widthw nonadjacent form (wNAF). In both wNAF and the proposed representations, each nonzero digit is an odd integer with absolute value less than M. However, for wNAF, M is of the form 2 w−1, while for the pro ..."
Abstract

Cited by 4 (0 self)
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This paper introduces a new radix2 representation with the same average weight as the widthw nonadjacent form (wNAF). In both wNAF and the proposed representations, each nonzero digit is an odd integer with absolute value less than M. However, for wNAF, 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 wNAF is that it can be obtained by scanning the bits from lefttoright. This property is also useful for memoryconstrained devices because it can reduce both the time and space complexity of fast point multiplication techniques.