The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic

  • Reza Rezaeian Farashahi
  • Ruud Pellikaan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve \(\mathcal{C}\), defined over \(\mathbb{F}_{q^2}\), where q is some power of an odd prime. Our extractor, for a given point P on \(\mathcal{C}\), outputs the first \(\mathbb{F}_{q}\)-coefficient of the abscissa of the point P. We show that if a point P is chosen uniformly at random in \(\mathcal{C}\), the element extracted from the point P is indistinguishable from a uniformly random variable in \(\mathbb{F}_q\).


Elliptic curve Hyperelliptic curve Deterministic extractor 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Reza Rezaeian Farashahi
    • 1
    • 2
  • Ruud Pellikaan
    • 1
  1. 1.Dept. of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB EindhovenThe Netherlands
  2. 2.Dept. of Mathematical Sciences, Isfahan University of Technology, P.O. Box 85145 IsfahanIran

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