Бессалов, Анатолій Володимирович and Ковальчук, Людмила Василівна (2015) Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field Кибернетика и системный анализ, 51 (2). pp. 3-12. ISSN 0023-1274
Preview |
Text
A_Bessalov_Kovalchuk_CSA_51_2_2015_FITU.pdf Download (70kB) | Preview |
Abstract
The necessary and sufficient conditions for the parameters of the curve in the canonical form with two points of order 4 are found. It is proved two lemmas about the properties of quadratic residues, using the Gauss scheme for quadratic residues and non-residues. Based on this lemmas the exact formulas for calculating the number of elliptic curves with non-zero parameters a and b and two points of fourth-order that are isomorphic to Edwards curves over the prime field. It is proved that for a large fields proportion of such curves is close to ¼.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | canonical form of an elliptic curve, Edwards curve, twisted curve, curve parameters, isomorphism, quadratic residue, quadratic non-residue. |
| Subjects: | Статті у наукометричних базах > РИНЦ Статті у наукометричних базах > Scopus Статті у наукометричних базах > Web of Science |
| Divisions: | Це архівні підрозділи > Кафедра комп'ютерних наук і математики |
| Depositing User: | професор Анатолій Володимирович Бессалов |
| Date Deposited: | 21 Dec 2017 08:45 |
| Last Modified: | 08 Jan 2019 11:57 |
| URI: | https://elibrary.kubg.edu.ua/id/eprint/22330 |
Actions (login required)
 |
View Item |