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Generating Pairing-Friendly Curves with the CM Equation of Degree 1

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Pairing-Based Cryptography – Pairing 2009 (Pairing 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5671))

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Abstract

Refinements of the Brezing-Weng method have provided families of pairing-friendly curves with improved ρ-values by using non-cyclotomic polynomials that define cyclotomic fields. We revisit these methods via a change-of-basis matrix and completely classify a basis for a cyclotomic field to produce a family of pairing-friendly curves with a CM equation of degree 1. Using this classification, we propose a new algorithm to construct Brezing-Weng-like elliptic curves having the CM equation of degree 1, and we present new families of curves with larger discriminants.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ewha Womans University, Seoul, 120-750, South Korea

    Hyang-Sook Lee & Cheol-Min Park

Authors
  1. Hyang-Sook Lee
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  2. Cheol-Min Park
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of California, San Diego, 9500 Gilman Drive, MC 0404, 92093-0404, La Jolla, CA, USA

    Hovav Shacham

  2. University of Texas at Austin Department of Computer Science, 1 University Station C0500 Taylor Hall 2.124, 78712-1188, Austin, TX, USA

    Brent Waters

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Lee, HS., Park, CM. (2009). Generating Pairing-Friendly Curves with the CM Equation of Degree 1. In: Shacham, H., Waters, B. (eds) Pairing-Based Cryptography – Pairing 2009. Pairing 2009. Lecture Notes in Computer Science, vol 5671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03298-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-03298-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03297-4

  • Online ISBN: 978-3-642-03298-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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