International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Efficient Doubling on Genus 3 Curves over Binary Fields

Xinxin Fan
Thomas Wollinger
Yumin Wang
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Abstract: The most important and expensive operation in a hyperelliptic curve cryptosystem (HECC) is scalar multiplication by an integer k, i.e., computing an integer k times a divisor D on the Jacobian. Using some recoding algorithms for scalar $k$, we can reduce a number of divisor class additions during the process of computing scalar multiplication. So divisor doubling will account for the main part in all kinds of scalar multiplication algorithms. In order to accelerate the genus 3 HECC over binary fields we investigate how to compute faster doubling in this paper. By constructing birational transformation of variables, we derive explicit doubling formulae for all types of defining equations of the curve. For each type of curve, we analyze how many field operations are needed. So far all proposed curves are secure, though they are more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only one third the time of an addition in the best case. Furthermore, an actual implementation of the new formulae on a Pentium-M processor shows its practical relevance.
  title={Efficient Doubling on Genus 3 Curves over Binary Fields},
  booktitle={IACR Eprint archive},
  keywords={implementation / Hyperelliptic Curve Cryptosystem},
  note={ 12978 received 14 Jul 2005},
  author={Xinxin Fan and Thomas Wollinger and Yumin Wang},