Schoof's algorithm for Weierstrass curves
Schoofův algoritmus pro Weierstrassovy křivky
bachelor thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/183048Identifiers
Study Information System: 257747
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- Kvalifikační práce [11267]
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Computer Science with specialisation in General Computer Science
Department
Department of Algebra
Date of defense
29. 6. 2023
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Very good
Keywords (Czech)
eliptická křivka|Weierstrassova křivka|Hasseho věta|dělící polynom|Schoofův algoritmusKeywords (English)
elliptic curve|Weierstrass curve|Hasse's theorem|division polynomial|Schoof's algorithmSchoof'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