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master's thesis
Eliptičke krivulje u kriptografiji
2021. urn:nbn:hr:126:563752
Kokanović, Anamarija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Kokanović, A. (2021). Eliptičke krivulje u kriptografiji (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:563752

Kokanović, Anamarija. "Eliptičke krivulje u kriptografiji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:563752

Kokanović, Anamarija. "Eliptičke krivulje u kriptografiji." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:563752

Kokanović, A. (2021). 'Eliptičke krivulje u kriptografiji', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 05 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:563752

Kokanović A. Eliptičke krivulje u kriptografiji [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2025 April 05] Available at: https://urn.nsk.hr/urn:nbn:hr:126:563752

A. Kokanović, "Eliptičke krivulje 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:126:563752

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Metadata
TitleEliptičke krivulje u kriptografiji
Title (english)Elliptic Curves in Cryptography
AuthorAnamarija Kokanović
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
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2021-06-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu smo definirali eliptičke krivulje te smo dali geometrijsku i algebarsku interpretaciju operacije uz koju skup točaka na eliptičkoj krivulji E(K) postaje Abelova grupa. Odredili smo problem diskretnog logaritma za eliptičke krivulje (ECDLP) i komentirali vremensku složenost problema. Naveli smo algoritam ”dupliciraj i zbrajaj”, poznat pod nazivom binarne ljestve, za računanje vrijednosti višekratnika neke točke na eliptičkoj krivulji. Opisali smo upotrebu eliptičkih krivulja u kriptografiji kroz eliptički Diffie-Hellman protokol (ECDH) te eliptički ElGamalov kriptosustav zasnovan na problemu računanja diskretnog logaritma u konačnim grupama gdje prilikom šifriranja poruka postaje otprilike četiri puta dulja. Na kraju smo naveli varijantu ElGamalovog kriptosustava pod nazivom MenezesVanstoneov kriptosustav kod kojeg je šifrirana poruka dva puta dulja.
Abstract (english)
In this work, we defined the elliptic curves and gave the geometric and algebraic interpretation of the operation in which a set of points on an elliptic curve E(K) becomes the Abel group. In addition, we determined the elliptic curve discrete logarithm problem (ECDLP) and commented time complexity of algorithm. We have listed a “double-and-add” algorithm, known as a binary ladder, to compute the multiple value of a point on an elliptic curve. Also, we have described the use of elliptic curves in cryptography through the elliptical Diffie-Hellman protocol (ECDH) and the elliptical ElGamal cryptosystem based on the problem of computing a discrete logarithm in finite groups where during encrypting messages become approximately four times longer. Finally, we have listed a variant of ElGamal’s cryptosystem called the Menezes-Vanstone cryptosystem in which the encrypted message is twice as long.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:563752
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-06-28 11:14:27