Kvadratni recipročnostni zakon

delo diplomskega seminarja

Dejan Perić (Author), Aleš Vavpetič (Mentor)

Abstract

V delu je predstavljen problem rešljivosti kvadratne enačbe v kolobarju ostankov. Definiran je Legendrov simbol, ki poda rešljivost določene kvadratne enačbe. S tem simbolom je formuliran kvadratni recipročnostni zakon in njuna dodatka. Ti izreki so dokazani z uporabo primitivnih n-tih korenov enote in Gaussovimi vsotami ter služijo ugotavljanju vrednosti Legendrovega simbola. Iz teh rezultatov je prikazana uporaba Goldwasser-Micalijevega kriptosistema.

Keywords

matematika;kvadratni recipročnostni zakon;kvadratni ostanek po modulu p;Legendrov simbol;Gaussova vsota;primitivni koren enote;Goldwasser-Micalijev kriptosistem;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[D. Perić]
UDC:	511
COBISS:	120685827
Views:	505
Downloads:	53
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Quadratic reciprocity law
Secondary abstract:	In this thesis, the problem of a solvability of quadratic equation in a residue ring is presented. Legendre symbol is defined, which indices the solvability of a certain quadratic equation. This symbol is used in the formulation of the quadratic reciprocity law and its two supplements. These theorems are proved with the use of primitive nth roots of unity and the Gauss sums, and are used for specifying the value of the Legendre symbol. With the use of the results in this thesis the use of Goldwasser-Micali cryptosystem is shown.
Secondary keywords:	mathematics;quadratic reciprocity law;quadratic residue modulo p;Legendre symbol;Gauss sum;primitive root of unity;Goldwasser-Micali cryptosystem;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	25 str.
ID:	16345593