Savršena sigurnost u kriptografiji

master's thesis

• Title (english): Perfect security in cryptography
• Author: Ena Majin
• Mentor: Andrej Dujella (mentor)
• Committee member: Andrej Dujella (predsjednik povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu je detaljno objašnjena savršena sigurnost kriptosustava. Dan je primjer kriptosustava koji nije savršeno siguran te je definiran i prikazan jedan savršeno siguran kriptosustav, Vernamova jednokratna bilježnica. Iskazan je i dokazan Shannonov teorem o nužnim i dovoljnim uvjetima savršene sigurnosti kriptosustava. Definirani su pojmovi entropije, uvjetne entropije i višeznačnosti ključa uz popratne primjere za razumijevanje. Na kraju je pojam entropije povezan sa savršenom sigurnosti.

Abstract (english)

This thesis explains perfect secrecy of cryptosystems in detail. It gives an example of a cryptosystem that is not perfectly secret, and it defines and shows a cryptosystem that is perfectly secret - Vernam cipher known as one-time pad. Shannon’s theorem about necessary and sufficient conditions for perfectly secret cryptosystems is stated and proven in the thesis. Terms of entropy, conditional entropy and key equivocation are introduced with supporting examples for better understanding. In the end, the thesis explains the connection of entropy and perfect secrecy.

• Keywords: kriptosustav; Vernamova jednokratna bilježnica; Shannonov teorem; entropija; uvjetna entropija; višeznačnost ključa
• Keywords (english): cryptosystems; Vernam cipher; one-time pad; Shannon’s theorem; entropy; conditional entropy; key equivocation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:205982
• 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: Embargoed access; Embargo expiration date: 2024-10-28
• Created on: 2022-10-28 11:52:35