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

Emmanuel Fouotsa 1  and Abdoul Aziz Ciss 2
  • 1 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
  • 2 Laboratoire de Traitement de l'Information et Systèmes Intelligents, Ecole Polytechnique de Thies, Senegal

Abstract

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 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.

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Groups – Complexity – Cryptology is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, computer algebra, complexity theory, and cryptology. GCC primarily publishes research papers, but comprehensive and timely survey articles on a topic inside the scope of the journal are also welcome.

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