Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605519374 | ||
| 003 | CHVBK | ||
| 005 | 20210128100730.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150301xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10559-015-9709-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10559-015-9709-x | ||
| 245 | 0 | 0 | |a Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field |h [Elektronische Daten] |c [A. Bessalov, L. Kovalchuk] |
| 520 | 3 | |a The necessary and sufficient conditions for the parameters of the curve in the canonical form with two points of order 4 are found. Two lemmas about the properties of quadratic residues are proved, using the Gauss scheme for quadratic residues and non-residues. Based on this lemmas, the exact formulas are derived for the number of elliptic curves with non-zero parameters a and b and two points of order 4 that are isomorphic to Edwards curves over the prime field. It is proved that for large fields the share of such curves is close to 1/4. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 690 | 7 | |a canonical elliptic curve |2 nationallicence | |
| 690 | 7 | |a Edwards curve |2 nationallicence | |
| 690 | 7 | |a twist curve |2 nationallicence | |
| 690 | 7 | |a curve parameters |2 nationallicence | |
| 690 | 7 | |a isomorphism |2 nationallicence | |
| 690 | 7 | |a quadratic residue |2 nationallicence | |
| 690 | 7 | |a quadratic non-residue |2 nationallicence | |
| 700 | 1 | |a Bessalov |D A. |u Institute of Physics and Technology, National Technical University of Ukraine "Kyiv Polytechnic Institute”, Kyiv, Ukraine |4 aut | |
| 700 | 1 | |a Kovalchuk |D L. |u Institute of Special Communication and Information Security, National Technical University of Ukraine "Kyiv Polytechnic Institute”, Kyiv, Ukraine |4 aut | |
| 773 | 0 | |t Cybernetics and Systems Analysis |d Springer US; http://www.springer-ny.com |g 51/2(2015-03-01), 165-172 |x 1060-0396 |q 51:2<165 |1 2015 |2 51 |o 10559 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10559-015-9709-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10559-015-9709-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bessalov |D A. |u Institute of Physics and Technology, National Technical University of Ukraine "Kyiv Polytechnic Institute”, Kyiv, Ukraine |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Kovalchuk |D L. |u Institute of Special Communication and Information Security, National Technical University of Ukraine "Kyiv Polytechnic Institute”, Kyiv, Ukraine |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Cybernetics and Systems Analysis |d Springer US; http://www.springer-ny.com |g 51/2(2015-03-01), 165-172 |x 1060-0396 |q 51:2<165 |1 2015 |2 51 |o 10559 | ||