On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves | Macquarie University ResearchOnline

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Title: On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves
Related: Mathematics of computation, Vol. 81, No. 278, (2012), p.1093-1110
DOI: 10.1090/S0025-5718-2011-02543-3
Publisher: American Mathematical Society
Date: 2012
Author/Creator: Urroz, Jorge Jiménez
Author/Creator: Luca, Florian
Author/Creator: Shparlinski, Igor E
Description: 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.
Description: 18 page(s)
Subject Keyword: Elliptic curves
Subject Keyword: Embedding degree
Subject Keyword: MNT curves
Subject Keyword: Pairing based cryptography
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

Identifier: http://hdl.handle.net/1959.14/172505
Identifier: ISSN:0025-5718
Identifier: mq_res-ext-2-s2.0-84858994644
Language: eng
Rights: 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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