| dc.contributor.advisor | Drápal, Aleš | |
| dc.creator | Zvoníček, Václav | |
| dc.date.accessioned | 2023-07-24T12:18:34Z | |
| dc.date.available | 2023-07-24T12:18:34Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/183048 | |
| dc.description.abstract | Schoof's algorithm is the starting point for the most efficient methods for determining the number of rational points on an elliptic curve defined over a finite field. The goal of this thesis is to introduce the subject of elliptic curves, with the emphasis on Weierstrass curves over a finite field, to describe Schoof's algorithm and its time complexity, and, finally, to implement it in C++ with the support of NTL. The implementation provides a user with a reasonably fast utility for determining the order of Weierstrass curves over finite fields of size up to 128 bits. 1 | en_US |
| dc.language | English | cs_CZ |
| dc.language.iso | en_US | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.subject | elliptic curve|Weierstrass curve|Hasse's theorem|division polynomial|Schoof's algorithm | en_US |
| dc.subject | eliptická křivka|Weierstrassova křivka|Hasseho věta|dělící polynom|Schoofův algoritmus | cs_CZ |
| dc.title | Schoof's algorithm for Weierstrass curves | en_US |
| dc.type | bakalářská práce | cs_CZ |
| dcterms.created | 2023 | |
| dcterms.dateAccepted | 2023-06-29 | |
| dc.description.department | Katedra algebry | cs_CZ |
| dc.description.department | Department of Algebra | en_US |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.identifier.repId | 257747 | |
| dc.title.translated | Schoofův algoritmus pro Weierstrassovy křivky | cs_CZ |
| dc.contributor.referee | Mareš, Martin | |
| thesis.degree.name | Bc. | |
| thesis.degree.level | bakalářské | cs_CZ |
| thesis.degree.discipline | Informatika se specializací Obecná informatika | cs_CZ |
| thesis.degree.discipline | Computer Science with specialisation in General Computer Science | en_US |
| thesis.degree.program | Informatika | cs_CZ |
| thesis.degree.program | Computer Science | en_US |
| uk.thesis.type | bakalářská práce | cs_CZ |
| uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra algebry | cs_CZ |
| uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Algebra | en_US |
| uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
| uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
| uk.faculty-abbr.cs | MFF | cs_CZ |
| uk.degree-discipline.cs | Informatika se specializací Obecná informatika | cs_CZ |
| uk.degree-discipline.en | Computer Science with specialisation in General Computer Science | en_US |
| uk.degree-program.cs | Informatika | cs_CZ |
| uk.degree-program.en | Computer Science | en_US |
| thesis.grade.cs | Velmi dobře | cs_CZ |
| thesis.grade.en | Very good | en_US |
| uk.abstract.en | Schoof's algorithm is the starting point for the most efficient methods for determining the number of rational points on an elliptic curve defined over a finite field. The goal of this thesis is to introduce the subject of elliptic curves, with the emphasis on Weierstrass curves over a finite field, to describe Schoof's algorithm and its time complexity, and, finally, to implement it in C++ with the support of NTL. The implementation provides a user with a reasonably fast utility for determining the order of Weierstrass curves over finite fields of size up to 128 bits. 1 | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra algebry | cs_CZ |
| thesis.grade.code | 2 | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | O | |
