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International Algorithmic Number Theory Symposium

ANTS 1994: Algorithmic Number Theory pp 250–263Cite as

Constructing elliptic curves with given group order over large finite fields

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 877))

Abstract

A procedure is developed for constructing elliptic curves with given group order over large finite fields. The generality of the construction allows an arbitrary choice of the parameters involved. For instance, it is possible to specify the finite field, the group order or the class number of the endomorphism ring of the elliptic curve. This is important for various applications in computational number theory and cryptography. Moreover, we give a method that yields all representations of a given integer as a norm in an imaginary quadratic field.

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Author information

Authors and Affiliations

  1. Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041, Saarbrücken, Germany

    Georg-Johann Lay & Horst G. Zimmer

Authors
  1. Georg-Johann Lay
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  2. Horst G. Zimmer
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Editor information

Leonard M. Adleman Ming-Deh Huang

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© 1994 Springer-Verlag Berlin Heidelberg

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Lay, GJ., Zimmer, H.G. (1994). Constructing elliptic curves with given group order over large finite fields. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_64

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  • DOI: https://doi.org/10.1007/3-540-58691-1_64

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58691-3

  • Online ISBN: 978-3-540-49044-9

  • eBook Packages: Springer Book Archive

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