Analysis of 2-Isogeny Properties of Generalized Form Edwards Curves.
A. V. Bessalov, Lyudmila Kovalchuk, Volodymyr Sokolov, Pavlo M. Skladannyi, Тамара Радівілова · Borys Grinchenko Kyiv University Institutional repository (Borys Grinchenko Kyiv University) · 2020
The analysis of the 2-isogeny existence conditions of generalized Edwards form curves over a prime field, including complete, quadratic, and twisted Edwards curves, is presented. An overview of the properties of these three classes of curves is given. Generalization of the results known for the classes of complete and quadratic curves to the class of twisted Edwards curves is obtained. A modified law of point’s addition is used to correctly determine the isogeny degree.