Paper 2012/551
Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists
Liangze Li, Hongfeng Wu, and Fan Zhang
Abstract
In this paper, we propose an elaborate geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct the Miller function. Then we present explicit formulae for the addition and doubling steps in Miller's algorithm to compute Tate pairing on Jacobi quartic curves. Both the addition step and doubling step of our formulae for Tate pairing computation on Jacobi curves are faster than previously proposed ones. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. For twists of degree 4, both the addition steps and doubling steps in our formulas are faster than the fastest result on Weierstrass curves. For twists of degree 6, the addition steps of our formulae are faster than the fastest result on Weierstrass curves.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Elliptic curveJacobi quartic curveTate pairingMiller function
- Contact author(s)
- whfmath @ gmail com
- History
- 2012-09-24: received
- Short URL
- https://ia.cr/2012/551
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2012/551,
author = {Liangze Li and Hongfeng Wu and Fan Zhang},
title = {Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/551},
year = {2012},
url = {https://eprint.iacr.org/2012/551}
}
