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Counting Points on Elliptic Curves Over F2m

  • Alfred Menezes
Chapter
  • 167 Downloads
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 234)

Abstract

In 1985, Schoof [136] presented a polynomial time algorithm for computing #E(F q ), the number of Fq-rational points on an elliptic curve E defined over the field F q . The algorithm has a running time of 0(log8 q) bit operations, and is rather cumbersome in practice. Buchmann and Muller [20] combined Schoof’s algorithm with Shanks’ baby-step giant-step algorithm, and were able to compute orders of curves over Fp, where p is a 27-decimal digit prime. The algorithm took 4.5 hours on a SUN-1 SPARC-station.

Keywords

Elliptic Curve Elliptic Curf Abelian Variety Quadratic Residue Modular Equation 
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 Science+Business Media New York 1993

Authors and Affiliations

  • Alfred Menezes
    • 1
  1. 1.Auburn UniversityAuburn

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