Original title: Schoofův algoritmus pro Weierstrassovy křivky
Translated title: Schoof's algorithm for Weierstrass curves
Authors: Zvoníček, Václav ; Drápal, Aleš (advisor) ; Mareš, Martin (referee)
Document type: Bachelor's theses
Year: 2023
Language: eng
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
Keywords: elliptic curve|Weierstrass curve|Hasse's theorem|division polynomial|Schoof's algorithm; eliptická křivka|Weierstrassova křivka|Hasseho věta|dělící polynom|Schoofův algoritmus

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/183048

Permalink: http://www.nusl.cz/ntk/nusl-532264


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses