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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

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Faster Ate pairing computation on Selmer's model of elliptic curves

Emmanuel Fouotsa
  • Laboratoire de Mathématiques Nicolas Oresme(LMNO), Université de Caen, Basse Normandie B.P. 5186, 14032 Caen Cedex, France; and Department of Mathematics, Higher Teacher Training College, University of Bamenda, P.O. Box 39, Bambili, Cameroon
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/ Abdoul Aziz Ciss
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  • Laboratoire de Traitement de l'Information et Systèmes Intelligents, Ecole Polytechnique de Thies, Senegal
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Published Online: 2016-04-07 | DOI: https://doi.org/10.1515/gcc-2016-0005


This paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye [17] to the computation of other variants of the Tate pairing on this curve. Especially, we show that the Selmer model of an elliptic curve presents faster formulas for the computation of the Ate and optimal Ate pairings with respect to Weierstrass elliptic curves. We show how to parallelise the computation of these pairings and we obtained very fast results. We also present an example of optimal pairing on a pairing-friendly Selmer curve of embedding degree k = 12.

Keywords: Selmer curves; Miller's algorithm; Tate pairing; Ate pairing; optimal pairing

MSC: 14H52


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About the article

Received: 2015-07-22

Published Online: 2016-04-07

Published in Print: 2016-05-01

Funding Source: ANR SIMPATIC

Award identifier / Grant number: ANR-12-INSE-0014

Funding Source: Simons Foundation

Award identifier / Grant number: Pole of Research in Mathematics with applications to Information Security, Subsaharan Africa

The first author is a postdoctoral researcher supported by French ANR SIMPATIC project (ANR-12-INSE-0014). The authors acknowledge support from MACISA-LIRIMA project and the Simons Foundation through Pole of Research in Mathematics with applications to Information Security, Subsaharan Africa.

Citation Information: Groups Complexity Cryptology, Volume 8, Issue 1, Pages 55–67, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2016-0005.

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