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

Jorge Jiménez Urroz; Florian Luca; Igor E. Shparlinski

doi:10.1090/S0025-5718-2011-02543-3

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

School of Computing

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

62 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 language	English
Pages (from-to)	1093-1110
Number of pages	18
Journal	Mathematics of Computation
Volume	81
Issue number	278
DOIs	https://doi.org/10.1090/S0025-5718-2011-02543-3
Publication status	Published - 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

Access to Document

10.1090/S0025-5718-2011-02543-3

Publisher version (open access).pdfFinal published version, 268 KB

Cite this

@article{11bb829a43e54e9391242ac56b3eea2f,

title = "On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves",

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.",

author = "Urroz, \{Jorge Jim{\'e}nez\} and Florian Luca and Shparlinski, \{Igor E.\}",

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",

year = "2012",

doi = "10.1090/S0025-5718-2011-02543-3",

language = "English",

volume = "81",

pages = "1093--1110",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "278",

}

TY - JOUR

T1 - On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves

AU - Urroz, Jorge Jiménez

AU - Luca, Florian

AU - Shparlinski, Igor E.

N1 - 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

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84858994644

U2 - 10.1090/S0025-5718-2011-02543-3

DO - 10.1090/S0025-5718-2011-02543-3

M3 - Article

AN - SCOPUS:84858994644

SN - 0025-5718

VL - 81

SP - 1093

EP - 1110

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 278

ER -

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

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this