CONSTRUCTING FAMILIES OF PAIRING-FRIENDLY ELLIPTIC CURVES.

cryptography, pairings, elliptic curves, embedding degree 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