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Efficient Divisor Class Halving on Genus Two Curves

  • Peter Birkner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4356)

Abstract

Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.

Keywords

hyperelliptic curve divisor class halving binary fields 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Peter Birkner
    • 1
  1. 1.Department of Mathematics, Technical University of Denmark (DTU), Matematiktorvet, Building 303, DK-2800 Kongens LyngbyDenmark

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