Paper 2008/061

Abelian varieties with prescribed embedding degree

David Freeman, Peter Stevenhagen, and Marco Streng

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 $A$.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
pairing-friendly curvesembedding degreeabelian varietieshyperelliptic curvesCM methodcomplex multiplication
Contact author(s)
dfreeman @ math berkeley edu
History
2008-02-11: received
Short URL
https://ia.cr/2008/061
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2008/061,
      author = {David Freeman and Peter Stevenhagen and Marco Streng},
      title = {Abelian varieties with prescribed embedding degree},
      howpublished = {Cryptology ePrint Archive, Paper 2008/061},
      year = {2008},
      note = {\url{https://eprint.iacr.org/2008/061}},
      url = {https://eprint.iacr.org/2008/061}
}
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