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Taylor and Francis Group, International Journal of Computer Mathematics, 4(81), p. 403-406

DOI: 10.1080/00207160410001661311

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On using expansions to the base of -2

Journal article published in 2004 by Roberto Maria Avanzi, Roberto Avanzi*, Rm Roberto Avanzi, Gerhard Frey†, Roger Oyono¶, Gerhard Frey, Tanja Lange, Roger Oyono
This paper is available in a repository.
This paper is available in a repository.

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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. ; Comment: 5 pages