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undergraduate thesis
Primjene eliptičkih krivulja u kriptografiji
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2023. urn:nbn:hr:168:805277
Maros, Luka
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Maros, L. (2023). Primjene eliptičkih krivulja u kriptografiji (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:805277

Maros, Luka. "Primjene eliptičkih krivulja u kriptografiji." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2023. https://urn.nsk.hr/urn:nbn:hr:168:805277

Maros, Luka. "Primjene eliptičkih krivulja u kriptografiji." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2023. https://urn.nsk.hr/urn:nbn:hr:168:805277

Maros, L. (2023). 'Primjene eliptičkih krivulja u kriptografiji', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 30 June 2024, https://urn.nsk.hr/urn:nbn:hr:168:805277

Maros L. Primjene eliptičkih krivulja u kriptografiji [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2023 [cited 2024 June 30] Available at: https://urn.nsk.hr/urn:nbn:hr:168:805277

L. Maros, "Primjene eliptičkih krivulja u kriptografiji", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:168:805277

Metadata
TitlePrimjene eliptičkih krivulja u kriptografiji
Title (english)Applications of Eliptic Curves in Cryptography
AuthorLuka Maros
MentorMario Krnić (mentor)
Committee memberMario Krnić (predsjednik povjerenstva)
Committee memberTomislav Burić (član povjerenstva)
Committee memberLenka Mihoković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2023-02-08, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
U ovom radu je opisano i objašnjeno kako se eliptičke krivulje mogu iskoristiti u kriptografiji javnog ključa. Najprije se uvodi teoretska podloga i osnovna svojstva eliptičkih krivulja. To uključuje zbrajanje i skalarno množenje točaka te definiranje pojmova konačnog polja, reda grupe i cikličke podgrupe. Potom su definirani Elgamalov i DSA kriptosustavi, popraćeni s definicijama njihovih inačica koje koriste eliptičke krivulje, Menezes-Vanstone i ECDSA kriptosustava. Nakon toga slijedi kratak opis problema diskretnog logaritma kod eliptičkih krivulja (ECDLP), uključujući i moguće napade na ECDLP koji mogu ugroziti sigurnost našeg kriptosustava ako parametre krivulje ne izaberemo pažljivo. Na kraju je ponuđena programska implementacija kriptosustava koji koristi eliptičke krivulje u programskom jeziku Java.
Abstract (english)
This paper seeks to describe and explain how elliptic curves can be used in public-key cryptography. First and foremost, theoretical background and basic properties of elliptic curves are presented. This includes point addition and scalar multiplication along with definitions for terms such as finite field, order of the group and cyclic subgroups. Afterwards the paper continues with the definitions of ElGamal and DSA cryptosystems, followed by their elliptic curve counterparts, Menezes-Vanstone and ECDSA cryptosystems. Then, the elliptic curve discrete logarithm problem (ECDLP) is discussed, including possible attacks on ECDLP that can compromise the safety of our cryptosystem if the curve parameters are not chosen carefully. Finally, Java implementation for a cryptosystem using elliptic curves is given.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:805277
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 on2023-07-13 10:20:41