A. V. Bessalov, O. V. Tsygankova, “Number of curves in the generalized Edwards form with minimal even cofactor of the curve order”, Probl. Peredachi Inf., 2017, Volume 53, Issue 1,Pages <nobr>101

This article is cited in 8 papers

Information Protection

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

A. V. Bessalov^ab, O. V. Tsygankova^a

^a Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine
^b Borys Grinchenko Kyiv University, Kyiv, Ukraine

Abstract: 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.

UDC: 621.391.15:519.7

Received: 15.12.2015
Revised: 23.09.2016