@inproceedings{3de1150a5a4145d5a30a98c48c28f0b3,
title = "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 G 1 × G 2 and G 2 × 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. ",
keywords = "Ate pairing, Degree-3 twists, Explicit formulas, Pairing-friendly curves, Twisted Hessian curves",
author = "Chitchanok Chuengsatiansup and C.R. Martindale",
year = "2018",
doi = "10.1007/978-3-030-05378-9_13",
language = "English",
isbn = "978-3-030-05377-2",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "228--247",
editor = "Debrup Chakraborty and Tetsu Iwata",
booktitle = "Progress in Cryptology - INDOCRYPT 2018",
address = "Germany",
}