On the number of distinct elliptic curves in some families |
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| Authors: | Reza Rezaeian Farashahi and Igor E. Shparlinski |
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| Affiliation: | (1) Department of Electrical & Computer Engineering, University of Waterloo, 200 University Avenue W., Waterloo, ON, N2L 3G1, Canada |
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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. |
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