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Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2008) 5209 LNCS 126-135
DOI: 10.1007/978-3-540-85538-5_9
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Abstract

We describe a new method for constructing Brezing-Weng-like pairing-friendly elliptic curves. The new construction uses the minimal polynomials of elements in a cyclotomic field. Using this new construction we present new "record breaking" families of pairing-friendly curves with embedding degrees of k∈ ∈{16,18,36,40}, and some interesting new constructions for the cases k∈ ∈{8,32}. © Springer-Verlag Berlin Heidelberg 2008.

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Kachisa, E. J., Schaefer, E. F., & Scott, M. (2008). Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5209 LNCS, pp. 126–135). https://doi.org/10.1007/978-3-540-85538-5_9

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