A theta model for elliptic curves (Q2363002)

In the paper under review, the authors present a new model for elliptic curves which is defined over any finite field called ``a theta model for elliptic curves''. For this they apply an isogeny of order two to the level four theta model defined in [\textit{O. Diao} and \textit{E. Fouotsa}, Afr. Mat. 26, No. 3--4, 283--301 (2015; Zbl 1327.14155)]. In the new model they present unified addition formulas which are valid over any finite field and the connection via birational equivalence of the new model with other models of elliptic curves, such as the Weierstrass model and the Edwards model. They completely describe the geometric interpretation of the group law by rational functions, which enables the computation of bilinear maps on elliptic curves. Furthermore, they compare points operation in eight different models in binary fields which shows efficiency of the new model. The results are interesting and useful in the construction of many cryptographic protocols.