On the number of distinct elliptic curves in some families

Authors:
Reza Rezaeian Farashahi;Igor E. Shparlinski
Affiliations:
Department of Computing, Macquarie University, Sydney, Australia 2109 and Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran;Department of Computing, Macquarie University, Sydney, Australia 2109
Venue:
Designs, Codes and Cryptography
Year:
2010

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Abstract

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.