Email this article Number of curves in the generalized Edwards form with minimal even cofactor of the curve order
- Authors: Bessalov A.V.1,2, Tsygankova O.V.2
-
Affiliations:
- Borys Grinchenko Kyiv University
- Institute of Physics and Technology
- Issue: Vol 53, No 1 (2017)
- Pages: 92-101
- Section: Information Protection
- URL: https://journal-vniispk.ru/0032-9460/article/view/166368
- DOI: https://doi.org/10.1134/S0032946017010082
- ID: 166368
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
A. V. Bessalov
Borys Grinchenko Kyiv University; Institute of Physics and Technology
Author for correspondence.
Email: bessalov15@mail.ru
Ukraine, Kyiv; Kyiv
O. V. Tsygankova
Institute of Physics and Technology
Email: bessalov15@mail.ru
Ukraine, Kyiv
Supplementary files
