Paper 2005/228

Efficient Doubling on Genus 3 Curves over Binary Fields

Xinxin Fan, Thomas Wollinger, and Yumin Wang

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.

Metadata
Available format(s)
PDF PS
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
Hyperelliptic Curve Cryptosystem
Contact author(s)
xxfan @ mail xidian edu cn
History
2005-07-20: received
Short URL
https://ia.cr/2005/228
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2005/228,
      author = {Xinxin Fan and Thomas Wollinger and Yumin Wang},
      title = {Efficient Doubling on Genus 3 Curves over Binary Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/228},
      year = {2005},
      url = {https://eprint.iacr.org/2005/228}
}
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