On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves
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- by Jorge Jiménez Urroz, Florian Luca and Igor E. Shparlinski PDF
- Math. Comp. 81 (2012), 1093-1110 Request permission
Abstract:
We give an upper bound on the number of finite fields over which elliptic curves of cryptographic interest with a given embedding degree and small complex multiplication discriminant may exist, and present some heuristic arguments which indicate that this bound is tight. We also refine some heuristic arguments on the total number of so-called MNT curves with prime cardinalities which have been recently presented by various authors.References
Additional Information
- Jorge Jiménez Urroz
- Affiliation: Departamento de Matemática Aplicada IV, Universidad Politecnica de Catalunya, Barcelona, 08034, España
- Email: jjimenez@ma4.upc.edu
- Florian Luca
- Affiliation: Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
- MR Author ID: 630217
- Email: fluca@matmor.unam.mx
- Igor E. Shparlinski
- Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
- MR Author ID: 192194
- Email: igor.shparlinski@mq.edu.au
- Received by editor(s): February 23, 2010
- Received by editor(s) in revised form: February 11, 2011
- Published electronically: September 29, 2011
- © Copyright 2011 American Mathematical Society
- Journal: Math. Comp. 81 (2012), 1093-1110
- MSC (2010): Primary 11G07, 11T71, 14H52
- DOI: https://doi.org/10.1090/S0025-5718-2011-02543-3
- MathSciNet review: 2869051