Pairing-friendly twisted Hessian curves

Chitchanok Chuengsatiansup; C.R. Martindale

doi:10.1007/978-3-030-05378-9_13

Pairing-friendly twisted Hessian curves

Chitchanok Chuengsatiansup, C.R. Martindale

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

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 language	English
Title of host publication	Progress in Cryptology - INDOCRYPT 2018
Subtitle of host publication	Asymmetic Key Cryptography and Cryptanalysis
Editors	Debrup Chakraborty, Tetsu Iwata
Place of Publication	Berlin
Publisher	Springer
Pages	228-247
Number of pages	20
ISBN (Electronic)	978-3-030-05378-9
ISBN (Print)	978-3-030-05377-2
DOIs	https://doi.org/10.1007/978-3-030-05378-9_13
Publication status	Published - 2018

Publication series

Name	Lecture Notes in Computer Science
Volume	11356

Keywords

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

Access to Document

10.1007/978-3-030-05378-9_13

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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

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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.",

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Pairing-friendly twisted Hessian curves. / Chuengsatiansup, Chitchanok; Martindale, C.R.

Progress in Cryptology - INDOCRYPT 2018: Asymmetic Key Cryptography and Cryptanalysis. ed. / Debrup Chakraborty; Tetsu Iwata. Berlin : Springer, 2018. p. 228-247 (Lecture Notes in Computer Science; Vol. 11356).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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