Pairing-friendly twisted Hessian curves

Chitchanok Chuengsatiansup, C.R. Martindale

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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.

Original languageEnglish
Title of host publicationProgress in Cryptology - INDOCRYPT 2018
Subtitle of host publicationAsymmetic Key Cryptography and Cryptanalysis
EditorsDebrup Chakraborty, Tetsu Iwata
Place of PublicationBerlin
PublisherSpringer
Pages228-247
Number of pages20
ISBN (Electronic)978-3-030-05378-9
ISBN (Print)978-3-030-05377-2
DOIs
Publication statusPublished - 2018

Publication series

NameLecture Notes in Computer Science
Volume11356

Keywords

  • Ate pairing
  • Degree-3 twists
  • Explicit formulas
  • Pairing-friendly curves
  • Twisted Hessian curves

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  • Cite this

    Chuengsatiansup, C., & Martindale, C. R. (2018). Pairing-friendly twisted Hessian curves. In D. Chakraborty, & T. Iwata (Eds.), Progress in Cryptology - INDOCRYPT 2018: Asymmetic Key Cryptography and Cryptanalysis (pp. 228-247). (Lecture Notes in Computer Science; Vol. 11356). Berlin: Springer. https://doi.org/10.1007/978-3-030-05378-9_13