Cryptology ePrint Archive: Report 2012/346

Edwards model of elliptic curves defined over any fields

Oumar DIAO and Emmanuel FOUOTSA

Abstract: 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.

Category / Keywords: Elliptic curve, level 4 theta model, Edwards model, efficient arithmetic, theta functions, Riemann relations

Date: received 18 Jun 2012, last revised 8 Jan 2013

Contact author: oumar diao at univ-rennes1 fr

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Note: Some updates and minor corrections.

Version: 20130108:172814 (All versions of this report)

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