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master's thesis
Polialfabetske supstitucijske šifre
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. urn:nbn:hr:126:255999
Kobašević, Valentina
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 Computer Science

Cite this document

Kobašević, V. (2019). Polialfabetske supstitucijske šifre (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:255999

Kobašević, Valentina. "Polialfabetske supstitucijske šifre." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:255999

Kobašević, Valentina. "Polialfabetske supstitucijske šifre." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:255999

Kobašević, V. (2019). 'Polialfabetske supstitucijske šifre', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 16 July 2024, https://urn.nsk.hr/urn:nbn:hr:126:255999

Kobašević V. Polialfabetske supstitucijske šifre [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 July 16] Available at: https://urn.nsk.hr/urn:nbn:hr:126:255999

V. Kobašević, "Polialfabetske supstitucijske šifre", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:255999

Metadata
TitlePolialfabetske supstitucijske šifre
Title (english)Polyalphabetic Substitution Ciphers
AuthorValentina Kobašević
MentorIvan Soldo (mentor)
Committee memberZoran Tomljanović (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberIvan Matić (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 country2019-02-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Polialfabetske supstitucijske šifre, od kojih je prva bila Albertijeva šifra, predstavile su značajan napredak nad monoalfabetskim supstitucijskim šiframa u pogledu korištenja više supstitucijskih alfabeta u postupku šifriranja. Svaka sljedeća koja je nastala pokušala je popraviti neku ranjivost prethodne. Tako je Trithemiusova šifra za svako slovo teksta koristila drugi alfabet. Vigenerova šifra više nije imala linearno kretanje po tablici slova (tzv. tabuli recti) kao što je to Trithemiusova imala, dok je Beaufortova šifra bila varijanta Vigenerove šifre. Playfairova šifra predstavila je novi pogled na problem šifriranja koristeći bigrame i 5 × 5 matrice slova.Šifra četiri kvadrata može se smatrati njenim sigurnijim proširenjem jer sličnu logiku primijenjuje na četiri takve matrice, dok je šifra dva kvadrata pokušaj da se dobije najbolje od ta dva kriptosustava – veća sigurnost od Playfairove šifre uz jednostavnije šifriranje i dešifriranje od šifre četiri kvadrata. Na kraju, potpuno nov pogled na problem šifriranja i dešifriranja pružio je Hill sa svojom šifrom koja je bazirana na linearnoj algebri.
Abstract (english)
Polyalphabetic substitution ciphers, from which the first one was Alberti cipher, were an advancement over monoalphabetic substitution ciphers simply because of their use of multiple alphabets in the encipherment process. Each one that followed the Alberti cipher tried to improve a vulnerability that the previous one possessed. The Trithemius cipher used a different alphabet for every letter that it processed, the Vigen`ere cipher didn’t have linear movement over the so-called tabula recta, while the Beaufort cipher is considered to be a variant of the Vigen`ere cipher. Furthermore, the Playfair cipher had a new perspective of the encipherment problem using bigrams and 5×5 letter matrix. The four-square cipher can be considered as an extension of the Playfair cipher with improved security because it applies a similar logic to four such matrices, while the two-square cipher attempts to obtain the best of these two cryptosystems – better text encryption then the Playfair cipher while being easier to use then the four-square cipher. Finally, a completely new perspective on the encipherment problem was provided by Hill’s cipher based on linear algebra.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:255999
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-11 11:15:23