Number of curves in the generalized Edwards form with minimal even cofactor of the curve order

Аннотация

We analyze properties of points of orders 2, 4, and 8 of a curve in the generalized Edwards form. Arithmetic for group operations with singular points of these curves is introduced. We propose a classification of curves in the Edwards form into three disjoint classes. Formulas for the number of curves of order 4n of different classes are obtained. Works of other authors are critically analyzed.