On Using Expansions to the Base of -2

Details On Using Expansions to the Base of -2 On Using Expansions to the Base of -2

2003-12-02

arxiv.org/abs/math/0312060v1

Mathematics

Number Theory

5 pages

Scientific paper

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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