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More Sparse Families of Pairing-Friendly Elliptic Curves

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Cryptology and Network Security (CANS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8813))

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Abstract

Generating pairing-friendly elliptic curves is a crucial step in the deployment of pairing-based cryptographic applications. The most efficient method for their construction is based on polynomial families, namely complete families, complete families with variable discriminant and sparse families. In this work we further study the case of sparse families which seem to produce more pairing-friendly elliptic curves than the other two polynomial families and also can lead to better ρ-values in many cases. We present two general methods for producing sparse families and we apply them for four embedding degrees \(k \in \lbrace 5, 8, 10, 12 \rbrace\). Particularly for k = 5 we introduce for the first time the use of Pell equations by setting a record with ρ = 3/2 and we present a family that has better chances in producing suitable curve parameters than any other reported family for \(k \notin \lbrace 3, 4, 6 \rbrace\). In addition we generalise some existing examples of sparse families for k = 8, 12 and provide extensive experimental results for every new sparse family for \(k \in \lbrace 5, 8, 10, 12 \rbrace\) regarding the number of the constructed elliptic curve parameters.

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Author information

Authors and Affiliations

  1. Department of Information and Communication Systems Engineering, University of the Aegean, 83200, Karlovassi, Samos, Greece

    Georgios Fotiadis & Elisavet Konstantinou

Authors
  1. Georgios Fotiadis
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  2. Elisavet Konstantinou
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Editor information

Editors and Affiliations

  1. Department of Informatics, Athens University of Economics & Business, 76, Patission Str., 10434, Athens, Greece

    Dimitris Gritzalis

  2. Department of Informatics and Telecommunications, Panepistimiopolis, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Aggelos Kiayias

  3. FORTH-ICS, Vassilika Vouton, P.O. Box 1385, 711 10, Heraklion, Crete, Greece

    Ioannis Askoxylakis

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Fotiadis, G., Konstantinou, E. (2014). More Sparse Families of Pairing-Friendly Elliptic Curves. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds) Cryptology and Network Security. CANS 2014. Lecture Notes in Computer Science, vol 8813. Springer, Cham. https://doi.org/10.1007/978-3-319-12280-9_25

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  • DOI: https://doi.org/10.1007/978-3-319-12280-9_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12279-3

  • Online ISBN: 978-3-319-12280-9

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