Paper 2018/1026 Original: eprint.iacr.org/2018/1026 ↗
Pairing-Friendly Twisted Hessian Curves
Abstract
This paper presents efficient formulas to compute Miller doubling and Miller addition utilizing degree-3 twists on curves with j-invariant 0 written in Hessian form. We give the formulas for both odd and even embedding degrees and for pairings on both $\mathbb{G}_1\times\mathbb{G}_2$ and $\mathbb{G}_2\times\mathbb{G}_1$. We propose the use of embedding degrees 15 and 21 for 128-bit and 192-bit security respectively in light of the NFS attacks and their variants. We give a comprehensive comparison with other curve models; our formulas give the fastest known pairing computation for embedding degrees 15, 21, and 24.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2018-10-27: last updated
- 2018-10-26: published
- Short URL
- https://ia.cr/2018/1026
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/1026,
author = {Chitchanok Chuengsatiansup and Chloe Martindale},
title = {Pairing-Friendly Twisted Hessian Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/1026},
year = {2018},
url = {https://eprint.iacr.org/2018/1026}
}