Original title: Počítání bodů na eliptických křivkách nad konečnými tělesy
Translated title: Counting the points on elliptic curves over finite fields
Authors: Eržiak, Igor ; Šťovíček, Jan (advisor) ; Stanovský, David (referee)
Document type: Bachelor's theses
Year: 2018
Language: eng
Abstract: [eng] [cze]
The goal of this thesis is to explain and implement Schoof's algorithm for counting points on elliptic curves over finite fields. We start by defining elliptic curve as a set of points satisfying certain equation and then proceeding to define an operation on this set. Theoretical background needed for the algorithm is presented in the second chapter. Finally, the Schoof's algorithm is introduced in the third chapter, supplemented by an implementation in SageMath open-source software. Cieľom tejto práce je vysvetliť a naimplementovať Schoofov algoritmus na počítanie bodov na eliptických krivkách nad konečnými telesami. Začneme definíciou eliptickej krivky ako množiny bodov spĺňajúcich istú rovnicu a pokračujeme definovaním operácie na tejto množine. Teoretické poznatky potrebné k algoritmu sú predstavené v druhej kapitole. Napokon je prestavený Schoofov algoritmus v tretej kapitole, doplnený o implementáciu v SageMath open-source software.
Keywords: Division polynomial; Elliptic curve; Frobenius endomorphism; Schoof's algorithm; deliaci polynóm; eliptická krivka; Frobeniov endomorfizmus; Schoofov algoritmus

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/101749

Permalink: http://www.nusl.cz/ntk/nusl-388005


The record appears in these collections:
Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses