[Resource Topic] 2018/1026: Pairing-Friendly Twisted Hessian Curves

Welcome to the resource topic for 2018/1026

Pairing-Friendly Twisted Hessian Curves

Authors: Chitchanok Chuengsatiansup, Chloe Martindale


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.

ePrint: https://eprint.iacr.org/2018/1026

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