Paper 2012/346

Edwards model of elliptic curves defined over any fields

Oumar DIAO and Emmanuel FOUOTSA


In this paper, we present an Edwards model for elliptic curves which is defined over any perfect field and in particular over finite fields. This Edwards model is birationally equivalent to the well known Edwards model over non-binary fields and is ordinary over binary fields. For this, we use theta functions of level four to obtain an intermediate model that we call a level $4$ theta model. This model enables us to obtain the new Edwards model with a complete and unified. Over binary fields, we present an efficient arithmetic of these curves. We also provide competitive differential addition formulas over any perfect field.

Note: Some updates and minor corrections.

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Published elsewhere. Unknown where it was published
Elliptic curvelevel 4 theta modelEdwards modelefficient arithmetictheta functionsRiemann relations
Contact author(s)
oumar diao @ univ-rennes1 fr
2013-01-08: revised
2012-06-22: received
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      author = {Oumar DIAO and Emmanuel FOUOTSA},
      title = {Edwards model of elliptic curves defined over any fields},
      howpublished = {Cryptology ePrint Archive, Paper 2012/346},
      year = {2012},
      note = {\url{}},
      url = {}
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