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master's thesis
Osnovni algoritmi teorije brojeva u kriptografiji
2021. urn:nbn:hr:126:342822
Bertok, Pamela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Bertok, P. (2021). Osnovni algoritmi teorije brojeva u kriptografiji (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:342822

Bertok, Pamela. "Osnovni algoritmi teorije brojeva u kriptografiji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:342822

Bertok, Pamela. "Osnovni algoritmi teorije brojeva u kriptografiji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:342822

Bertok, P. (2021). 'Osnovni algoritmi teorije brojeva u kriptografiji', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 04 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:342822

Bertok P. Osnovni algoritmi teorije brojeva u kriptografiji [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 December 04] Available at: https://urn.nsk.hr/urn:nbn:hr:126:342822

P. Bertok, "Osnovni algoritmi teorije brojeva u kriptografiji", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:342822

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Metadata
TitleOsnovni algoritmi teorije brojeva u kriptografiji
Title (english)Number Theory Algorithms in Cryptography
AuthorPamela Bertok
MentorIvan Matić (mentor)
Committee memberTomislav Marošević (predsjednik povjerenstva)
Committee memberIvan Matić (član povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-11-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Ovaj rad proučava algoritme teorije brojeva i njihovu primjenu u kriptografiji javnog ključa te se može promatrati kroz tri osnovne cjeline. Prvi dio odnosi se na osnovne pojmove kriptografije te definicije i kriptoanalizu nekoliko jednostavnih kriptosustava. Drugi dio rada govori o teoriji brojeva i algoritmima teorije brojeva čiju primjenu nalazimo u kriptografiji. Takvih algoritama i pojmova iz teorije brojeva ima mnoštvo, a u ovom radu opisani su: složenost algoritama, osnovne računske operacije, Euklidov algoritam, verižni razlomci, kvadratne kongruencije te prostost i faktorizacija. Treći dio rada govori o kriptografiji javnog ključa te opisuje dva najpoznatija kriptosustava s javnim ključem, a to su RSA i Rabinov kriptosustav. Kod svakoga od njih nalazimo opis, definiciju, implementaciju i primjer.
Abstract (english)
This thesis studies algorithms of number theory and their application in public-key cryptography and can be observed through three basic units. The first part refers the basic concepts of cryptography, definition and cryptanalysis of several simple cryptosystems. The second part of this thesis discusses number theory and algorithms of number theory whose application we find in cryptography. There are many such algorithms and concepts from number theory, and here are described: algorithmic complexity, basic computational operations, Euclid’s algorithm, continued fractions, quadratic congruences, primality and factoring. The third part discusses public key cryptography and describes the two most well-known public key cryptosystems, namely RSA and Rabin’s cryptosystem. In each of them we find a description, definition, implementation and example.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:342822
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-11-23 07:39:45