Parallelizing pairings on Hessian elliptic curves
type: Item
instance of: scholarly article
title: Parallelizing pairings on Hessian elliptic curves
zbMATH Open document ID: 1405.14080
author: Emmanuel Fouotsa
published in: Arab Journal of Mathematical Sciences
publication date: 2019-01-30T00:00:00Z
review text: The paper under review deals with the computation of the Ate pairing on the Hessian model of elliptic curves. Explicit addition formulas for the Ate pairing on Hessian curves are given by using a specific representation of points. Using these addition formulas, the efficient computation of the Ate pairing and the parallelization of both the Tate and the Ate pairings on Hessian curves are succeeded. Furthermore, Sage software is provided to ensure the correctness of the obtained formulas. These results extend the results of \textit{H. Gu} et al., [Lect. Notes Comput. Sci. 6829, 169--176 (2011; Zbl 1292.94068)].
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14G50
zbMATH DE Number: 7008431
zbMATH Keywords: Hessian curves
zbMATH Keywords: Tate and Ate pairings
zbMATH Keywords: parallel computation
reviewed by: Dimitros Poulakis
describes a project that uses: SageMath
MaRDI profile type: Publication
full work available at URL: j.ajmsc.2018.06.001
OpenAlex ID: W2809474924
cites work: Implementing Pairings at the 192-Bit Security Level
cites work: Faster Explicit Formulas for Computing Pairings over Ordinary Curves
cites work: Faster computation of the Tate pairing
cites work: Handbook of Elliptic and Hyperelliptic Curve Cryptography
cites work: Efficient implementation of pairing-based cryptosystems
cites work: Identity-Based Encryption from the Weil Pairing
cites work: Q4783728
cites work: Sequences of numbers generated by addition in formal groups and new primality and factorization tests
cites work: Faster Pairing Computations on Curves with High-Degree Twists
cites work: Pairing Computation on Twisted Edwards Form Elliptic Curves
cites work: Efficient computation of pairings on Jacobi quartic elliptic curves
cites work: Memory-saving computation of the pairing final exponentiation on BN curves
cites work: Efficient Arithmetic on Hessian Curves
cites work: The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
cites work: Efficient Pairing Computation on Elliptic Curves in Hessian Form
cites work: Pairing Lattices
cites work: The Eta Pairing Revisited
cites work: Exceptional Procedure Attack on Elliptic Curve Cryptosystems
cites work: Q2739458
cites work: Q4797815
cites work: A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
cites work: Q4797388
cites work: Optimal Pairings
cites work: Another Elliptic Curve Model for Faster Pairing Computation
Wikidata QID: Q129654527
DOI: 10.1016/J.AJMSC.2018.06.001
description: scientific article; zbMATH DE number 7008431