Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Faster Ate pairing computation on Selmer's model of elliptic curves 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 (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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

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

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


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 = . Keywords: Selmer curves, Miller's algorithm, Tate pairing, Ate pairing, optimal pairing MSC 2010: 14H52 1 Introduction Introduced in cryptography for the first time in [10], pairings are bilinear maps defined on the group of rational points of elliptic curves. Pairings first enabled to transfer the Elliptic Curve Discrete Logarithm to the Finite Field Discrete algorithm [10]. However many constructive pairing-based protocols have been realised [3, 7, 14]. Since then, pairing-based cryptography has received a lot of attention during the last decade. The most interesting pairing computed on elliptic curves is the so-called Tate pairing. For its efficient computation, one uses Miller's algorithm [15]. Depending on the number of iterations of this algorithm and the field on which the elliptic curve is defined, one obtains other variants of the Tate pairing like: the Ate and twisted Ate pairings introduced in [13]. These pairings can be more efficient than the Tate pairing since the number of Miller iterations is reduced. the Eta-pairing [2] which are defined on supersingular elliptic curves. the optimal pairing and pairing lattices that can be computed using the smallest number of basic Miller iterations are defined in [16] and [12]. In their paper [17], Zhang, Wang, Wang and Ye presented the arithmetic of the Selmer model of an elliptic curve and...
Loading next page...
 
/lp/de-gruyter/faster-ate-pairing-computation-on-selmer-s-model-of-elliptic-curves-cdtLf0R3PZ
Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2016-0005
Publisher site
See Article on Publisher Site

Abstract

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 (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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2016

References