[Resource Topic] 2007/110: Construction of Pairing-Friendly Elliptic Curves

Welcome to the resource topic for 2007/110

Title:
Construction of Pairing-Friendly Elliptic Curves

Authors: Woo Sug Kang

Abstract:

We explain a method of finding the polynomials representing \sqrt{-D} and \zeta_k over the field containing \sqrt{-D} and \zeta_k and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing {\mathbb Q} (\zeta_k, \sqrt{-D}) for arbitrary k and D by CP method. By using the factorization of the cyclotomic polynomial combined some polynomial, we extend the construction over cyclotomic fields to the construction over some extensions of the cyclotomic fields containing {\mathbb Q} (\zeta_k, \sqrt{-D}). We explain the limitation of finding more families of pairing friendly elliptic curves with embedding degree 10. For all computation, we use the PARI-GP \cite{GP}.

ePrint: https://eprint.iacr.org/2007/110

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