## Cryptology ePrint Archive: Report 2018/1026

Pairing-Friendly Twisted Hessian Curves

Chitchanok Chuengsatiansup and Chloe Martindale

Abstract: This paper presents efficient 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.

Category / Keywords: public-key cryptography / twisted Hessian curves, pairing-friendly curves, ate pairing, degree-3 twists, explicit formulas

Original Publication (in the same form): INDOCRYPT2018

Date: received 22 Oct 2018, last revised 27 Oct 2018

Contact author: chloemartindale at gmail com

Available format(s): PDF | BibTeX Citation

Note: Something went wrong with the abstract - there were three letters missing

Short URL: ia.cr/2018/1026

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