SUPERSINGULARITY OF ELLIPTIC AND EDWARDS CURVES OVER Fpn
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 1
Abstract
We consider the algebraic curves which have form of Edwards and elliptic curves with coordinates in Fnp. These curves are most effective support for a cyclic group of points which have many applications now. In this paper it was found conditions of supersingularity for Edwards curve and same case of twisted Edwards and Montgomery curves over Fnp where p≡3mod4. There was proved that projective twisted Edwards curve is not elliptic. Some properties of this curve were investigated. Conditions of minimal cofactor of twisted Edwards curve were founded. Construction of a curve with given order and minimal cofactor was made.
Authors and Affiliations
R. V. Skuratovskii
Keywords
Related Articles
- EP ID EP558759
- DOI 10.18524/2519-206x.2018.1(31).134622
- Views 82
- Downloads 0
Generalization of averaging conditions in the optimal control problem with fast and slow variables
The optimal control problem is described by the system of differential equations with fast and slow variables and by the terminal criterion of quality. There is a generalization of averaging conditions. There is proved t...
Analogs of single parametric aggregationiterative method for equations with non constant sign operators
We establish sufficient conditions for the convergence of a class of one-parameter aggregation-iterative methods. Obtained results do not include conditions about positiveness of operators and aggregate functionals, and...
One generalization of the classical orthogonal polynomials
The differential equation of the second order, generalizing the differential equations leaded to Jacobi, Laguerre and Hermite polynomials, is considered in the paper. The orthogonality of the polynomials, which are the s...
ON A REDUCTION OF A LINEAR HOMOGENEOUS DIFFERENTIAL SYSTEM WITH OSCILLATING COEFFICIENTS TO A SYSTEM WITH SLOWLY-VARYING COEFFICIENTS
For the linear homogeneous differential system, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly-varying coefficients and frequency, conditions of existence of the l...
QA-DEFORMATION OF SURFACE OF NEGATIVE GAUSSIAN CURVATURE
An infinitesimal deformation with the given law of changing the element of area of a surface in Euclidean three-space was considered in this article. Such deformation in the article was called the quasiareal infinitesima...