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Probl. Peredachi Inf., 2017, Volume 53, Issue 1, Pages 101–111 (Mi ppi2231)  

Information Protection

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

A. V. Bessalovab, O. V. Tsygankovaa

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.

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English version:
Problems of Information Transmission, 2017, 53:1, 92–101

Bibliographic databases:

UDC: 621.391.15:519.7
Received: 15.12.2015
Revised: 23.09.2016

Citation: 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., 53:1 (2017), 101–111; Problems Inform. Transmission, 53:1 (2017), 92–101

Citation in format AMSBIB
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\by A.~V.~Bessalov, O.~V.~Tsygankova
\paper Number of curves in the generalized Edwards form with minimal even cofactor of the curve order
\jour Probl. Peredachi Inf.
\yr 2017
\vol 53
\issue 1
\pages 101--111
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\transl
\jour Problems Inform. Transmission
\yr 2017
\vol 53
\issue 1
\pages 92--101
\crossref{https://doi.org/10.1134/S0032946017010082}
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