On using expansions to the base of −2

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.

^*E-mail: [email protected]

^†E-mail: [email protected]

^¶E-mail: [email protected]

Keywords:

• Exponentiation algorithms
• Public key cryptography
• Integer recodings

Notes

^*E-mail: [email protected]

^†E-mail: [email protected]

^¶E-mail: [email protected]