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master's thesis
Napadi na RSA kriptosustav s malim tajnim eksponentom
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. urn:nbn:hr:126:491755
Jović, Monika
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Jović, M. (2016). Napadi na RSA kriptosustav s malim tajnim eksponentom (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:491755

Jović, Monika. "Napadi na RSA kriptosustav s malim tajnim eksponentom." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:491755

Jović, Monika. "Napadi na RSA kriptosustav s malim tajnim eksponentom." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:491755

Jović, M. (2016). 'Napadi na RSA kriptosustav s malim tajnim eksponentom', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:491755

Jović M. Napadi na RSA kriptosustav s malim tajnim eksponentom [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:491755

M. Jović, "Napadi na RSA kriptosustav s malim tajnim eksponentom", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:491755

Metadata
TitleNapadi na RSA kriptosustav s malim tajnim eksponentom
Title (english)Attacks on RSA cryptosystem with small private exponent
AuthorMonika Jović
MentorIvan Matić (mentor)
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 country2016-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu predstavljeni su rizici RSA kriptosustava sa malim tajnim eksponentom. Rad se sastoji od tri cjeline. Prvi dio sadrži matematičku osnovu potrebnu za razumijevanje teme diplomskog rada. U sklopu drugog dijela dana je teorijska osnova za shvaćanje RSA kriptosustava, prvog kriptosustava s javnim ključem, kao i sama implementacija RSA kriptosustava. Također, u ovom dijelu opisana je sigurnost RSA kriptosustava te potencijalni rizici. Posljedni dio sadži neke od napada na RSA kriptosustav s malim tajnim eksponentom. Primjenom grube sile moguće je probiti svaki kriptosustav, no taj posao nije efikasan. Javljaju se algoritmi koji koriste neke slabosti kriptosustava, te u razumnom vremenu razbijaju kriptosustav. Obrađeni napadi probijaju RSA kriptosustav s malim tajnim eksponentom do N^{\delta } za \delta ≥ 1/4. Najpoznatiji od njih je Wienerov napad koji koristi verižne razlomke, a najjači je Boneh i Durfee napad koji koristi rešetke.
Abstract (english)
This paper presents the risks of RSA with small private exponent. The paper consists of three parts. The first part provides the mathematical basis needed for the understanding of the thesis. Within the second part, the theoretical basis for the understanding of RSA, the first public key cryptosystem, is given, as well as its implementation. Further more, this part explains the security of RSA and the potential risks. The last part contains some of the attacks on the RSA cryptosystem with small private exponent. Every cryptosystem can be broken using brute-force search attack. However, this is not practical. Advanced algorithms use some of the weaknesses of cryptosystem, and are able to break cryptosystem in a reasonable time. All of the attacks can efficiently break RSA with private exponents up to N^{\delta } for some \delta ≥ 1/4.The best known of these algorithms is the Wiener’s attack that uses a continued fractions, but the strongest is Boneh and Durfee’s attack that uses the lattice.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:491755
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 on2016-10-18 07:03:07