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master's thesis
Matematička pozadina AES kriptosustava
2022. urn:nbn:hr:200:985536
Doko, Dubravka
Josip Juraj Strossmayer University of Osijek
Faculty of Electrical Engineering, Computer Science and Information Technology Osijek
Department of Core Courses
Chair of Mathematics, Physics and Mechanical Engineering

Cite this document

Doko, D. (2022). Matematička pozadina AES kriptosustava (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek. Retrieved from https://urn.nsk.hr/urn:nbn:hr:200:985536

Doko, Dubravka. "Matematička pozadina AES kriptosustava." Master's thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, 2022. https://urn.nsk.hr/urn:nbn:hr:200:985536

Doko, Dubravka. "Matematička pozadina AES kriptosustava." Master's thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, 2022. https://urn.nsk.hr/urn:nbn:hr:200:985536

Doko, D. (2022). 'Matematička pozadina AES kriptosustava', Master's thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, accessed 29 January 2025, https://urn.nsk.hr/urn:nbn:hr:200:985536

Doko D. Matematička pozadina AES kriptosustava [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek; 2022 [cited 2025 January 29] Available at: https://urn.nsk.hr/urn:nbn:hr:200:985536

D. Doko, "Matematička pozadina AES kriptosustava", Master's thesis, Josip Juraj Strossmayer University of Osijek, Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:200:985536

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Metadata
TitleMatematička pozadina AES kriptosustava
Title (english)Mathematical background of the AES cryptosystem
AuthorDubravka Doko
MentorAnita Katić (mentor)
MentorKrešimir Grgić (sumentor)
Committee memberAnita Katić (predsjednik povjerenstva)
Committee memberTomislav Rudec (član povjerenstva)
Committee memberVišnja Križanović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Faculty of Electrical Engineering, Computer Science and Information Technology Osijek
(Department of Core Courses)
(Chair of Mathematics, Physics and Mechanical Engineering)
Osijek
Defense date and country2022-09-01, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Telecommunications and Informatics
Abstract
National Institute of Standards and Technology (NIST) je 1997. godine raspisao natječaj za novi napredni standard šifriranja, te je 2000. godine objavio da je odabrao Rijndaela kao AES. Rijndaela je naslijedio DES koji je postajao sve ranjiviji. Advanced Encryption Standard je 2001. godine odobren kao moderni standard za šifriranje podataka. Ima široku primjenu na raznim područjima, od povjerljivih državnih dokumenata do prometa putem Wi-Fi usmjerivača. AES koji koristimo su razvila dva belgijska kriptografa Joan Daemen i Vincent Rijmen. Razvili su šifru Rijandel kojoj veličina bloka varira od 128, 192 do 256 bita. Međutim AES koristi samo veličinu bloka od 128 bita. Vrlo bitno svojstvo AES-a je što koristi isti ključ za proces šifriranja i dešifriranja. Rijndael podržava tri duljine ključa 128, 192 i 256 bita. U procesu šifriranja i dešifriranja razlikujemo tri vrste slojeva: Sloj dodavanja ključa ( eng. Key Addition layer), Sloj zamjene bajtova (eng. Byte Substitution layer (S-Box)) i Difuzijski sloj (eng. Diffusion layer) koji se dijeli na dva podsloja (ShiftRow i MixColumn). U pozadini tih slojeva koristi se nekoliko ključnih matematičkih koncepata iz linearne algebre i teorije prstena. Algoritam uključuje 10 do 14 rundi u kojima se izmjenjuju navedeni slojevi s manjim razlikama u prvoj i zadnjoj rundi izvođenja. U svakom od navedenih koraka AES algoritma vrši se jednostavna radnja s matematičkim izračunima.
Abstract (english)
In 1997, the National Institute of Standards and Technology (NIST) announced a competition for a new advanced encryption standard, and in 2000 announced that it had selected Rijndael as AES. Rijndael was succeeded by DES, which was becoming increasingly vulnerable. The Advanced Encryption Standard was approved in 2001 as the modern-standard for data-encryption. It is widely used in a variety of areas, from classified-government-documents to traffic-through Wi-Fi routers. The AES we use was-developed by two Belgian-cryptographers, Joan-Daemen and Vincent Rijmen. They developed the Rijandel cipher, whose block size varies from 128, 192 to 256 bits. However, AES only uses a block size of 128 bits. A very important property of AES is that it uses the same key for the encryption and decryption process. Rijndael supports three key lengths 128, 192 and 256 bits. In the encryption and decryption process, we distinguish three types of layers: Key Addition layer, Byte Substitution layer (S-Box) and Diffusion layer, which is divided into two sublayers (ShiftRow and MixColumn). In the background of these layers, several key mathematical concepts from linear algebra and ring theory are used. The algorithm includes 10 to 14 rounds in which the specified layers are alternated with minor differences in the first and last rounds of execution. In each of the mentioned steps of the AES algorithm, a simple action with mathematical calculations is performed.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:200:985536
Study programmeTitle: Graduate University Study Programme in Electrical Engineering; specializations in: Communications and Informatics, Power Engineering
Course: Power Engineering
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra inženjer/inženjerka elektrotehnike (magistar/magistra inženjer/inženjerka elektrotehnike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-10-18 14:09:19