A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two

Izuru Kitamura, Masanobu Katagi, Tsuyoshi Takagi

Research output: Contribution to journalConference articlepeer-review

18 Citations (Scopus)


We deal with a divisor class halving algorithm on hyperelliptic curve cryptosystems (HECC), which can be used for scalar multiplication, instead of a doubling algorithm. It is not obvious how to construct a halving algorithm, due to the complicated addition formula of hyperelliptic curves. In this paper, we propose the first halving algorithm used for HECC of genus 2, which is as efficient as the previously known doubling algorithm. From the explicit formula of the doubling algorithm, we can generate some equations whose common solutions contain the halved value. From these equations we derive four specific equations and show an algorithm that selects the proper halved value using two trace computations in the worst case. If a base point is fixed, we can reduce these extra field operations by using a pre-computed table which shows the correct halving divisor class - the improvement over the previously known fastest doubling algorithm is up to about 10%. This halving algorithm is applicable to DSA and DH based on HECC. Finally, we present the divisor class halving algorithms for not only the most frequent case but also other exceptional cases.

Original languageEnglish
Pages (from-to)146-157
Number of pages12
JournalLecture Notes in Computer Science
Publication statusPublished - 2005
Externally publishedYes
Event10th Australasian Conference on Information Security and Privacy, ACISP 2005 - Brisbane, Australia
Duration: Jul 4 2005Jul 6 2005

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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