Afrika Matematika

, Volume 26, Issue 3–4, pp 283–301

# Arithmetic of the level four theta model of elliptic curves

• Oumar Diao
• Emmanuel Fouotsa
Article

## Abstract

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.

## Keywords

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

14H52 1990S

## Notes

### Acknowledgments

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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