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Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields

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Abstract

We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves. This result is an improvement relative to prior work which estimated the density of pairing-friendly genus 2 curves heuristically. Second, we present a method for generating pairing-friendly parameters for which \({\rho\approx 8}\) , where ρ is a measure of efficiency in pairing-based cryptography. This method works by solving a system of equations given in terms of coefficients of the Frobenius element. The algorithm is easy to understand and implement.

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Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98052, USA

    Kristin Lauter

  2. Qualcomm Inc., 5775 Morehouse Drive, San Diego, CA, 92121, USA

    Ning Shang

Authors
  1. Kristin Lauter
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  2. Ning Shang
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Correspondence to Ning Shang.

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Communicated by A. Enge.

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Lauter, K., Shang, N. Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields. Des. Codes Cryptogr. 67, 341–355 (2013). https://doi.org/10.1007/s10623-012-9611-8

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  • DOI: https://doi.org/10.1007/s10623-012-9611-8

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