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Families of pairing-friendly elliptic curves from a polynomial modification of the Dupont-Enge-Morain method
- Families of pairing-friendly elliptic curves from a polynomial modification of the Dupont-Enge-Morain method
- Lee H.-S.; Lee P.-R.
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- Applied Mathematics and Information Sciences
- vol. 10, no. 2, pp. 571 - 580
- Complete families; Dupont-Enge-Morain method; Pairing-friendly elliptic curves
- Natural Sciences Publishing Co.
- A general method for constructing families of pairing-friendly elliptic curves is the Brezing-Weng method. In many cases, the Brezing-Weng method generates curves with discriminant D = 1 or 3 and restricts the form of r(x) to be a cyclotomic polynomial. However, since we desire a greater degree of randomness on curve parameters to maximize security, there have been studies to develop algorithms that are applicable for almost arbitrary values of D and more various forms of r(x). In this paper, we suggest a new method to construct families of pairing-friendly elliptic curves with variable D and no restriction on the form of r(x) for arbitrary k by extending and modifying the Dupont-Enge-Morain method. As a result, we obtain complete families of curves with improved r-values for k = 8,12,16,20 and 24. We present the algorithm and some examples of our construction. © 2016 NSP.
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