### 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.

Note: Additional examples are available at http://math.berkeley.edu/~dfreeman/papers/gen-bw-examples.pdf.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Abelian varietieshyperelliptic curvespairing-based cryptosystemsembedding degreepairing-friendly varieties
Contact author(s)
dfreeman @ math berkeley edu
History
Short URL
https://ia.cr/2008/155

CC BY

BibTeX

@misc{cryptoeprint:2008/155,
author = {David Freeman},
title = {A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties},
howpublished = {Cryptology ePrint Archive, Paper 2008/155},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/155}},
url = {https://eprint.iacr.org/2008/155}
}

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