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On Using Expansions to the Base of -2

Roberto Avanzi·Gerhard Frey·Tanja Lange·Roger Oyono
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Abstract

This short note investigates the effects of using expansions to the base of -2. The main applications we have in mind are cryptographic protocols, where the crucial operation is computation of scalar multiples. For the recently proposed groups arising from Picard curves this leads to a saving of at least 7% for the computation of an m-fold. For more general non-hyperelliptic genus 3 curves we expect a larger speed-up.

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Roberto Avanzi, Gerhard Frey, Tanja Lange, Roger Oyono. 2003-12-02. On Using Expansions to the Base of -2. https://arxiv.org/abs/math/0312060

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