• Journal of the Korea Institute of Information Security & Cryptology
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• v.25 no.3
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• pp.567-571
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• 2015

Brezing and Weng proposed a method to generate CM parameters of pairing-friendly elliptic curves using polynomial representations of a number field, and Freeman generalized the method for the case of abelian varieties. In this paper we derive explicit formulae to find a family of polynomials used in Brezing-Weng method especially in the case of abelian surfaces, and present some examples generated by the proposed method.

• ETRI Journal
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• v.33 no.4
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• pp.656-659
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• 2011

In ICISC 2007, Comuta and others showed that among the methods for constructing pairing-friendly curves, those using cyclotomic polynomials, that is, the Brezing-Weng method and the Freeman-Scott-Teske method, are affected by Cheon's algorithm. This paper proposes a method for searching parameters of pairing-friendly elliptic curves that induces minimal security loss by Cheon's algorithm. We also provide a sample set of parameters of BN-curves, FST-curves, and KSS-curves for pairing-based cryptography.