Paper 2012/670 Original: eprint.iacr.org/2012/670 ↗
Fast Cryptography in Genus 2
Abstract
In this paper we highlight the benefits of using genus 2 curves in public-key cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically more involved but allows us to work with moduli of half the size. We give a taxonomy of the best known techniques to realize genus 2 based cryptography, which includes fast formulas on the Kummer surface and efficient 4-dimensional GLV decompositions. By studying different modular arithmetic approaches on these curves, we present a range of genus 2 implementations. On a single core of an Intel Core i7-3520M (Ivy Bridge), our implementation on the Kummer surface breaks the 125 thousand cycle barrier which sets a new software speed record at the 128-bit security level for constant-time scalar multiplications compared to all previous genus 1 and genus 2 implementations.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2014-03-13: last updated
- 2012-11-28: published
- Short URL
- https://ia.cr/2012/670
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/670,
author = {Joppe W. Bos and Craig Costello and Huseyin Hisil and Kristin Lauter},
title = {Fast Cryptography in Genus 2},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/670},
year = {2012},
url = {https://eprint.iacr.org/2012/670}
}