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undergraduate thesis
RSA kriptografija
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. urn:nbn:hr:168:380522
Jelić, Jure
University of Zagreb
Faculty of Electrical Engineering and Computing

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Jelić, J. (2021). RSA kriptografija (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:380522

Jelić, Jure. "RSA kriptografija." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. https://urn.nsk.hr/urn:nbn:hr:168:380522

Jelić, Jure. "RSA kriptografija." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2021. https://urn.nsk.hr/urn:nbn:hr:168:380522

Jelić, J. (2021). 'RSA kriptografija', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:380522

Jelić J. RSA kriptografija [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2021 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:168:380522

J. Jelić, "RSA kriptografija", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:168:380522

Metadata
TitleRSA kriptografija
Title (english)RSA cryptography
AuthorJure Jelić
MentorMate Puljiz (mentor)
Committee memberMate Puljiz (predsjednik povjerenstva)
Committee memberLana Horvat Dmitrović (član povjerenstva)
Committee memberAna Žgaljić Keko (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2021-09-08, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
U ovom radu obradili smo matematičku pozadinu RSA algoritma. U prvom dijelu obradili smo: Eulerov teorem, Fermatov mali teorem, Kineski teorem o ostacima. U drugom dijelu uveli smo RSA kriptosustav. Pokazali smo kako šifriramo i kako dešifriramo u RSA kriptosustavu te prikazali i generiranje ključeva. Dokazali smo ispravnost RSA kriptosustava, prikazali smo kako generiramo velike proste brojeve i obradili algoritam za testiranje prostosti, od kojih smo detaljnije obradili Fermatov test prostosti. Prikazali smo kako funkcionira Euklidov algoritam i prošireni Euklidov algoritam. Pokazali smo kako ubrzati RSA algoritam koristeći tehniku brzog potenciranja i algoritam “Kvadriraj i množi“. Obradili smo još i brzo šifriranje s kratkim eksponentom i brzo dešifriranje pomoću „Kineskog teorema o ostacima“.
Abstract (english)
In this thesis we covered the mathematical background of RSA algorithm. In the first chapter we covered: Euler's theorem, Fermat's little theorem, and the Chinese remainder theorem. In the second chapter of this thesis, we introduced the RSA cryptosystem. We showed how encryption, decryption and key generation work in the RSA cryptosystems. We proved the validity of the RSA algorithm, demonstrated how to generate large prime numbers, and how to test for primality, with an emphasis on Fermat's primality test. We demonstrated the Euclidean algorithm and the extended Euclidean algorithm. We showed how to speed up the RSA algorithm by means of fast modular exponentiation and the „Square and multiply“ algorithm. We also covered fast encryption with small exponents in RSA and fast decryption using the Chinese remainder theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:380522
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2023-01-13 09:10:08