On isogeny classes of Edwards curves over finite fields

@article{Ahmadi2011OnIC,
  title={On isogeny classes of Edwards curves over finite fields},
  author={Omran Ahmadi and Robert Granger},
  journal={IACR Cryptology ePrint Archive},
  year={2011},
  volume={2011},
  pages={135}
}
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over IFq if and only if its group order is divisible by 8 if q ≡ −1 (mod 4), and 16 if q ≡ 1 (mod 4). Furthermore, we give formulae for the proportion of d ∈ IFq \ {0, 1} for which the Edwards curve Ed is complete or… CONTINUE READING

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References

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Showing 1-10 of 27 references

Diophantine problems in geometry and elliptic ternary forms

  • Gerald B. Huff
  • Duke Math. J.,
  • 1948
Highly Influential
6 Excerpts

Advances in elliptic curve cryptography, volume 317 of London Mathematical Society Lecture Note Series

  • Ian F. Blake, Gadiel Seroussi, Nigel P. Smart, editors
  • 2005
Highly Influential
9 Excerpts

Finite transformation formulae involving the Legendre symbol

  • Kenneth S. Williams
  • Pacific J. Math.,
  • 1970
Highly Influential
2 Excerpts

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