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Constructing Families of Pairing-Friendly Elliptic Curves

Freeman, David

HPL-2005-155

Keyword(s): cryptography; pairings; elliptic curves; embedding degree

Abstract: We present a general method for constructing families of elliptic curves with prescribed embedding degree and prime order. We demonstrate this method by constructing curves of embedding degree k = 10, a value which has not previously appeared in the literature, and we show that our method applies to existing constructions for k = 3, 4, 6, and 12. We give evidence that our method is unlikely to produce infinite families of curves for embedding degrees k > 12.

15 Pages

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