Paper 2011/206

Isomorphism classes of Edwards curves over finite fields

R. Farashahi, D. Moody, and H. Wu


Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of $\Fq$-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski.

Note: After submission, we (Moody and Wu) became aware of independent work by R. Farashahi which has similar results. We have combined our work into this one article, so there will not be duplicate work in the literature.

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Published elsewhere. Unknown where it was published
Elliptic curvesEdwards curvesIsomorphisms
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dbmoody25 @ gmail com
2011-10-17: last of 2 revisions
2011-04-25: received
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      author = {R.  Farashahi and D.  Moody and H.  Wu},
      title = {Isomorphism classes of Edwards curves over finite fields},
      howpublished = {Cryptology ePrint Archive, Paper 2011/206},
      year = {2011},
      note = {\url{}},
      url = {}
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