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Families of Pairing-Friendly Elliptic Curves from a Polynomial Modification of the Dupont-Enge-Morain Method |
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PP: 571-580 |
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doi:10.18576/amis/100218
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Author(s) |
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Hyang-Sook Lee,
Pa-Ra Lee,
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Abstract |
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| 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. |
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