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master's thesis
Aritmetika konačnih polja
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:417776
Matijević, Martin
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Matijević, M. (2022). Aritmetika konačnih polja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:417776

Matijević, Martin. "Aritmetika konačnih polja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:417776

Matijević, Martin. "Aritmetika konačnih polja." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:417776

Matijević, M. (2022). 'Aritmetika konačnih polja', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:417776

Matijević M. Aritmetika konačnih polja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:417776

M. Matijević, "Aritmetika konačnih polja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:417776

Metadata
TitleAritmetika konačnih polja
Title (english)Arithmetic of finite fields
AuthorMartin Matijević
MentorAndrej Dujella (mentor)
Committee memberAndrej Dujella (predsjednik povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu smo obradili pitanja reprezentacije elemenata u konačnim poljima te efiksne implementacije operacija na konačnim poljima. Na početku smo se prisjetili osnovnih algebarskih struktura - grupa, prstena i polja. Uveli smo pojam konačnog, prostog i proširenog polja. Konačna polja smo reprezentirali ireducibilnim polinomima. Pokazali smo kako u programskom paketu PARI/GP odraditi aritmetičke operacije na polinomima iz F2[x]. Objasnili smo kako odabrati definirajući polinom nekog proširenog polja Fpn . Pokazali smo kako implementirati zbrajanje, oduzimanje i množenje u proširenim poljima karakteristike 2 i 3. Za algoritam množenja smo pojasnili ubrzanje algoritma u vidu češalj metoda. Dali smo algoritam za modularnu redukciju. Dali smo algoritme za računanje inverza - Euklidov i binarni te ubrzanje binarnog.
Abstract (english)
In this paper, we dealt with the issues of representation of elements in finite fields and efficient implementation of operations on finite fields. At the beginning, we remind ourselves of the basic algebraic structures - groups, rings and fields. We have introduced the concept of finite, prime and extended field. We represented the finite fields with irreducible polynomials. We have shown how to perform arithmetic operations on polynomials from F2[x] in the program package PARI/GP. We explained how to choose defining polynomial of some extended field Fpn . We have shown how to implement addition, subtraction and multiplication in the extended fields of characteristics 2 and 3. For the multiplication algorithm, we have clarified the acceleration of the algorithm in the form of comb methods. We have provided an algorithm for modular reduction. We have provided algorithms for calculating the inverse - Euclidean and binary and acceleration of the binary.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:417776
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-11-03 10:41:18