Cryptology ePrint Archive: Report 2007/452

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

Ezekiel J. Kachisa and Edward F. Schaefer and Michael Scott

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 $k \in \{16,18,36,40\}$, and some interesting new constructions for the cases $k \in \{8,32\}$

Category / Keywords: public-key cryptography / Pairing-based cryptography, Tate Pairing, Eta pairing, Ate pairing

Date: received 5 Dec 2007, last revised 14 Dec 2007

Contact author: mike at computing dcu ie

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Note: Minor corrections

Version: 20071214:105333 (All versions of this report)

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