We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham [6]. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k> 12. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Freeman, D. (2006). Constructing pairing-friendly elliptic curves with embedding degree 10. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4076 LNCS, pp. 452–465). Springer Verlag. https://doi.org/10.1007/11792086_32
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