On the number of distinct elliptic curves in some families

Reza Rezaeian Farashahi; Igor E. Shparlinski

doi:10.1007/s10623-009-9310-2

On the number of distinct elliptic curves in some families

Reza Rezaeian Farashahi, Igor E. Shparlinski

School of Computing

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

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.

Original language	English
Pages (from-to)	83-99
Number of pages	17
Journal	Designs, Codes and Cryptography
Volume	54
Issue number	1
DOIs	https://doi.org/10.1007/s10623-009-9310-2
Publication status	Published - Jan 2010

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AB - 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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On the number of distinct elliptic curves in some families

Abstract

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