Original title: Kvazigrupy s málo asociativními trojicemi
Translated title: Quasigroups with few associative triples
Authors: Valent, Viliam ; Drápal, Aleš (advisor) ; Kepka, Tomáš (referee)
Document type: Bachelor's theses
Year: 2016
Language: eng
Abstract: [eng] [cze]
This bachelor thesis deals with quasigroups with a small number of associative triples. They were studied from the algebraic point of view by Drápal, Ježek and Kepka, Kotzig, and recently by Grošek and Horák. The aim of this thesis is to build on the research of Grošek and Horák, replicate and improve their findings concerning the minimum number of associative triples in small quasigroups. Another important part is an establishment of a new upper bound on the minimum number of associative triples among all quasigroups of the same order. We provide an algorithm that can produce quasigroups with the number of associative triples less or equal to the second power of their order. We also present the applications of such quasigroups in cryptography, namely in hash functions and zero-knowledge protocols. Powered by TCPDF (www.tcpdf.org) Táto bakalárska práca sa zaoberá kvazigrupami s malým počtom asociatívnych trojíc. Tie už boli predmetom algebraického štúdia Drápala, Ježka a Kepku, Kotziga a nedávno Grošeka a Horáka. Cieľom tejto práce je budovať na výskume Ǧrošeka a Horáka, replikovať a zlepšiť ich výsledky ohľadom minimálneho počtu asociatívnych trojíc v malých kvazigrupách. Ďalšou dôležitou časťou je zavedenie novej hornej medze na minimálny počet asociatívnych trojíc medzi všetkými kvazigrupami rovnakého stupňa. Poskytneme algoritmus, ktorý konštruuje kvazigrupy s počtom asociatívnych trojíc menším alebo rovným druhej mocnine ich stupňa. Takisto prezentujeme aplikácie takýchto kvazigrúp v kryptografii, hlavne v hašovacích funkciách a zero-knowledge protokoloch. Powered by TCPDF (www.tcpdf.org)
Keywords: associativity index; latin squares; quasigroups; index asociativity; kvazigrupy; Latinské čtverce

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/74010

Permalink: http://www.nusl.cz/ntk/nusl-343343


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