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master's thesis
Usporedba probabilističkih testova prostosti
2023. urn:nbn:hr:166:383009
Jerković, Dino
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Jerković, D. (2023). Usporedba probabilističkih testova prostosti (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:383009

Jerković, Dino. "Usporedba probabilističkih testova prostosti." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:383009

Jerković, Dino. "Usporedba probabilističkih testova prostosti." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:383009

Jerković, D. (2023). 'Usporedba probabilističkih testova prostosti', Master's thesis, University of Split, Faculty of Science, accessed 18 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:383009

Jerković D. Usporedba probabilističkih testova prostosti [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 November 18] Available at: https://urn.nsk.hr/urn:nbn:hr:166:383009

D. Jerković, "Usporedba probabilističkih testova prostosti", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:383009

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Metadata
TitleUsporedba probabilističkih testova prostosti
Title (english)Comparison of Probabilistic Primality Tests
AuthorDino Jerković
MentorMarija Bliznac Trebješanin (mentor)
Committee memberMarija Bliznac Trebješanin (predsjednik povjerenstva)
Committee memberBorka Jadrijević (član povjerenstva)
Committee memberDomagoj Jelić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-02-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Prosti brojevi imaju važnu ulogu u području kriptografije, a samim time imaju i probabilistički testovi prostosti. Cilj ovog rada bio je napraviti usporedbu Miller-Rabinova, Fermatova i Solovay-Strassenova testa te iskazati prednosti i nedostatke svakog od njih. Kroz rad smo se upoznali sa bitnim stvarima u području teorije brojeva kao i sa osnovama testova prostosti. Takoder smo se dotakli i matematičke pozadine svakog testa. Na kraju rada smo napravili teorijsku usporedbu testova kao i njihovu implementaciju u programskom jeziku Python. Analizu smo radili na malim brojevima, testirajući točnost svakog testa. Tim eksperimentom smo potvrdili očekivano, da nam najveću točnost ima Miller-Rabinov test prostosti.
Abstract (english)
Prime numbers have an important role in the field of cryptography, as do primality probabilistic tests. The aim of this work was to compare the Miller-Rabin, Fermat and Solovay-Strassen tests and show the advantages and disadvantages of each of them. Through the work, we got acquainted with important things in the field of number theory, as well as with the basics of primality tests. We also touched on the mathematical background of each test. At the end of the work, we made a theoretical comparison of the tests as well as their implementation in the programming language Python. We performed the analysis on small numbers, testing the accuracy of each test. With this experiment, we confirmed as expected, that the Miller-Rabin test is the most accurate.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:383009
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in statistics and computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2023-03-03 12:52:53