2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107626We 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. 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.Number TheoryCryptography and Security14H52; 11G20; 94A60text