Quantities of points on some Edwards curves

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dc.contributor.authorRybak, Oleksandr
dc.date.accessioned2023-05-11T13:22:23Z
dc.date.available2023-05-11T13:22:23Z
dc.date.issued2021
dc.description.abstractThe Edwards curves of the form x2 + y2 = 1 + dx2y2 are investigated in this article. An exact formula for the quantity of points on x2 + y2 = 1 + dx2y2 over a field Fp is obtained for odd prime numbers p. The special attention is paid to the curves with exactly p+1 points over the field Fp. These curves are called supersingular. They are not recommended for usage in cryptography, because their structure is relatively simple. The supersingularity of the curve is proved for any prime p = 4m+3. Also, some other values of d, for which x2 + y2 is equivalent to 1 + dx2y2 (mod p) is supersingular, are found.uk
dc.format.pagerangePp. 27-32uk
dc.identifier.citationRybak, O. Quantities of points on some Edwards curves / Oleksandr Rybak // Theoretical and Applied Cybersecurity : scientific journal. – 2021. – Vol. 3, Iss. 1. – Pp. 27–32. – Bibliogr.: 5 ref.uk
dc.identifier.doihttps://doi.org/10.20535/tacs.2664-29132021.1.251297
dc.identifier.urihttps://ela.kpi.ua/handle/123456789/55579
dc.language.isoenuk
dc.publisherIgor Sikorsky Kyiv Polytechnic Instituteuk
dc.publisher.placeKyivuk
dc.relation.ispartofTheoretical and Applied Cybersecurity: scientific journal, Vol. 3, No. 1uk
dc.subjectEdwards curveuk
dc.subjectelliptic curveuk
dc.subjectequation over a finite fielduk
dc.subjectsupersingularityuk
dc.subject.udc512.624.3uk
dc.titleQuantities of points on some Edwards curvesuk
dc.typeArticleuk

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Theoretical and Applied Cybersecurity: scientific journal, Vol. 3, No. 1