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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN 印刷: 0040-2508
ISSN オンライン: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v74.i11.50
pages 1013-1023

NEW PROPERTIES OF THE EDWARDS FORM ELLIPTIC CURVE OVER A PRIME FIELD

A.V. Bessalov
Institute of Physics and Technology, NTUU "КPI" 37, Peremogy Ave., Kyiv, 03056, Ukraine
O.V. Tsygankova
Donetsk National University, 24 Universitetskaya St., Donetsk, 83001, Ukraine; KPI National Technological University, 37 Peremoha Ave., 03056, Kyiv, Ukraine

要約

Modification of the law of addition of points on the Edwards curve over a simple field is offered. The necessary and sufficient condition of dividing of the point by 2 is obtained. The theorem about a degenerate pair of torsion curves when the curve parameter d = 2 is proved. The algorithm of finding all unknown points kP of the Edwards curve with 1/8 part of the known points is offered.


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