On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves

Jorge Jiménez Urroz*, Florian Luca, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Citations (Scopus)
4 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)1093-1110
Number of pages18
JournalMathematics of Computation
Volume81
Issue number278
DOIs
Publication statusPublished - 2012

Bibliographical note

Copyright 2011 American Mathematical Society. First published in Mathematics of computation, Vol. 81, No. 278, pp.1093-1110, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0025-5718-2011-02543-3

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