Arithmetic of the level four theta model of elliptic curves

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.