Cryptology ePrint Archive: Report 2008/155

A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties

David Freeman

Abstract: We give an algorithm that produces families of Weil numbers for ordinary abelian varieties over finite fields with prescribed embedding degree. The algorithm uses the ideas of Freeman, Stevenhagen, and Streng to generalize the Brezing-Weng construction of pairing-friendly elliptic curves. We discuss how CM methods can be used to construct these varieties, and we use our algorithm to give examples of pairing-friendly ordinary abelian varieties of dimension 2 and 3 that are absolutely simple and have smaller $\rho$-values than any previous such example.

Category / Keywords: public-key cryptography / Abelian varieties, hyperelliptic curves, pairing-based cryptosystems, embedding degree, pairing-friendly varieties

Date: received 4 Apr 2008, last revised 5 Apr 2008

Contact author: dfreeman at math berkeley edu

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Note: Additional examples are available at

Version: 20080408:092135 (All versions of this report)

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