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Abelian Varieties with Prescribed Embedding Degree

  • David Freeman
  • Peter Stevenhagen
  • Marco Streng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5011)

Abstract

We present an algorithm that, on input of a CM-field K, an integer k ≥ 1, and a prime \(r\equiv1\bmod k\), constructs a q-Weil number \(\pi\in\O_K\) corresponding to an ordinary, simple abelian variety A over the field Open image in new window of q elements that has an Open image in new window -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.

Keywords

Elliptic Curf Abelian Variety Characteristic Zero Hyperelliptic Curve Discrete Logarithm Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • David Freeman
    • 1
  • Peter Stevenhagen
    • 2
  • Marco Streng
    • 2
  1. 1.University of CaliforniaBerkeley
  2. 2.Mathematisch InstituutUniversiteit Leiden 

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