Afrika Matematika

, Volume 26, Issue 3–4, pp 283–301 | Cite as

Arithmetic of the level four theta model of elliptic curves

  • Oumar Diao
  • Emmanuel Fouotsa


In this paper, we present a new model for elliptic curves that we call the level four theta model. This model is defined over any finite field and is obtained from Riemann theta functions of level four. We show that the group law is unified and study its completeness. Over binary fields, we present an efficient arithmetic of this curve. We also provide competitive differential addition formulas over non-binary fields and we show in particular that in binary fields, the level four theta model presents the fastest formulas for differential addition among well known models of elliptic curves.


Elliptic curve Level four theta model Efficient arithmetic Theta functions Riemann relations 

Mathematics Subject Classification (2000)

14H52 1990S 



The authors are grateful to David Lubicz and Marc Joye for their helpful comments. The authors deeply thank the anonymous reviewers for their extended critical suggestions that greatly improved the quality of this paper.


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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Laboratoire IRMARUniversité de Rennes IRennes CedexFrance
  2. 2.Department of Mathematics, Higher Teachers’ Training CollegeUniversity of BamendaBamendaCameroon

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