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)


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.


Elliptic Curf Abelian Variety Characteristic Zero Hyperelliptic Curve Discrete Logarithm Problem 
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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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