On the number of distinct elliptic curves in some families

  • Reza Rezaeian Farashahi
  • Igor E. Shparlinski


We give explicit formulas for the number of distinct elliptic curves over a finite field (up to isomorphism over the algebraic closure of the ground field) in several families of curves of cryptographic interest such as Edwards curves and their generalization due to D. J. Bernstein and T. Lange as well as the curves introduced by C. Doche, T. Icart and D. R. Kohel.


Elliptic curve Edwards curve j-Invariant Cryptography 

Mathematics Subject Classifications (2000)

11G05 11T06 14H52 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Reza Rezaeian Farashahi
    • 1
    • 2
  • Igor E. Shparlinski
    • 1
  1. 1.Department of ComputingMacquarie UniversitySydneyAustralia
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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