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Paper: Abelian varieties with prescribed embedding degree

Authors:
David Freeman
Peter Stevenhagen
Marco Streng
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URL: http://eprint.iacr.org/2008/061
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Abstract: We present an algorithm that, on input of a CM-field $K$, an integer $k \ge 1$, and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$ corresponding to an ordinary, simple abelian variety $A$ over the field $\F$ of $q$ elements that has an $\F$-rational point of order $r$ and embedding degree $k$ with respect to $r$. We then discuss how CM-methods over $K$ can be used to explicitly construct $A$.
BibTeX
@misc{eprint-2008-17738,
  title={Abelian varieties with prescribed embedding degree},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / pairing-friendly curves, embedding degree, abelian varieties, hyperelliptic curves, CM method, complex multiplication},
  url={http://eprint.iacr.org/2008/061},
  note={ dfreeman@math.berkeley.edu 13913 received 3 Feb 2008},
  author={David Freeman and Peter Stevenhagen and Marco Streng},
  year=2008
}