### Pairing-Friendly Twisted Hessian Curves

Chitchanok Chuengsatiansup and Chloe Martindale

##### 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.

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Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. INDOCRYPT2018
Keywords
twisted Hessian curvespairing-friendly curvesate pairingdegree-3 twistsexplicit formulas
Contact author(s)
chloemartindale @ gmail com
History
2018-10-27: revised
See all versions
Short URL
https://ia.cr/2018/1026

CC BY

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},
note = {\url{https://eprint.iacr.org/2018/1026}},
url = {https://eprint.iacr.org/2018/1026}
}

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