20.500.12556/RUL-139403 Kvadratni recipročnostni zakon delo diplomskega seminarja Quadratic reciprocity law 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. 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. kvadratni recipročnostni zakon kvadratni ostanek po modulu p Legendrov simbol Gaussova vsota primitivni koren enote Goldwasser-Micalijev kriptosistem quadratic reciprocity law quadratic residue modulo p Legendre symbol Gauss sum primitive root of unity Goldwasser-Micali cryptosystem true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2022-09-02 08:15:14 2022-09-02 08:15:15 2024-05-29 12:16:39 0000-00-00 00:00:00 2022 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 511 125421 120685827 5206.pdf 5206.pdf 1 1E7825421809F17EF38FE3A1A398F462 ab99941eeeef4d35b40fda37885d3c6935ba3732f6edbdbec15b526d14228d02 91bf0bc1-2a86-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=159964 Fakulteta za matematiko in fiziko 0 0 0