On using expansions to the base of -2

Roberto Avanzi, Gerhard Frey, Tanja Lange, Roger Oyono

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)403-406
Number of pages4
JournalInternational Journal of Computer Mathematics
Issue number4
StatePublished - Apr 2004
Externally publishedYes


  • Exponentiation algorithms
  • Integer recodings
  • Public key cryptography

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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