Pellova jednadžba u kriptografiji javnog ključa

master's thesis

• Author: Violeta Atanasov
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-05-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Želimo li u današnjem svijetu bez privatnosti osigurati sigurnu komunikaciju, koristit ćemo kriptosustave. Probijanje šifri biva sve češće i sofisticiranije, pa nam je u cilju imati što više raznolikih kriptosustava. Zbog toga se i razne grane matematike, te njihovi rezultati, primjenjuju na njihov razvoj. Kriptosustav opisan u ovom radu, prvi se puta pojavio 1984. godine. Jedna je od varijanti RSA kriptosustava, koja se temelji na Pellovoj jednadžbi \(x^2-{d y}^2 = 1\), sa sigurnosti zasnovanoj na teškoći problema faktorizacije.

Abstract (english)

With the lack of privacy in the world, we use cryptosystems, as we want to provide a safe communication. Code-breaking techniques are becoming more frequent and more sophisticated, so we need different cryptosystems at our disposal. Because of that, many different areas of mathematics and their results have been applied to their development. The cryptosystem described in this work first appeared in 1984. It is a variant of the RSA cryptosystem based on Pell’s Equation \(x^2-{d y}^2 = 1\) with the security based on the factorization problem.

• Keywords: kriptosustav; kriptografija javnog ključa; RSA kriptosustav; Pellova jednadžba
• Keywords (english): cryptosystem; public-key cryptography; RSA cryptosystem; Pell's equation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:736796
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-05-05 12:22:45