Pairing-Friendly Twisted Hessian Curves

Chitchanok Cheungsatiansup, Chloe Martindale

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)


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 G1×G2 and G2×G1. 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.
Original languageEnglish
Title of host publicationProgress in Cryptology – INDOCRYPT 2018
Publication statusPublished - 2018


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