Constructing pairing-friendly elliptic curves with embedding degree 10

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dc.creatorFreeman, David
dc.date2006-01-20
dc.date.accessioned2026-07-07T06:59:06Z
dc.date.available2026-07-07T06:59:06Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0601487
dc.identifierhttp://arxiv.org/abs/math/0601487
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107626
dc.subjectNumber Theory
dc.subjectCryptography and Security
dc.subject14H52; 11G20; 94A60
dc.titleConstructing pairing-friendly elliptic curves with embedding degree 10
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