Dijeljenje tajni

master's thesis

• Author: Vedrana Milutinović
• Mentor: Matija Kazalicki (mentor)
• Committee member: Matija Kazalicki (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Dragutin Svrtan (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu vidjeli smo neke od osnovnih shema (metoda) dijeljenja tajni, ponajprije one Shamira i Blakleya koji su i idejni začetnici metode dijeljenja tajni. Metodama se tajni podatak od strane djelitelja D podijeli na dijelove i distribuira medu grupom učesnika tako da svaki od učesnika dobije pojedini dio tajne pri čemu se ni s jednim od dijelova ne može otkriti ni jedna informacija o tajni. Definiranjem (t; n)-shemu praga rekonstrukcija tajne moguća je jedino oporabom t ili više dijelova koje posjeduju članovi. Za svaki strogo manji broj dijelova od t dijelova nemoguće je otkriti bilo koju informaciju o tajni. Sheme poput Shamirove i Asmuth-Bloomove su se pokazale i kao savršene, dok ostale nisu. Autoriziranim skupovima dostupne familije skupova definirani su oni skupovi pomoću kojih možemo otkriti tajnu na osnovu dijelova članova istog. Kod vizualne kriptografije osim što je isto (t; n)-shema praga i konstrukcija tajne odnosno pripadnih dijelova sadrži u pozadini matematički račun, za njenu rekonstrukciju koriste se prije svega čovjekov vid.

Abstract (english)

In this thesis we have seen some of the basic secret sharing schemes (methods), primarily Shamir’s and Blakely’s who are also initiators of the idea of the secret sharing method. By using secret sharing schemes, the dealer D splits the secret into shares and distributes them among the group of participants. Each participant gets a single share of the secret which does not give them any clue about the secret itself. By defining a (t,n)-threshold scheme, the reconstruction of the secret is possible only by combining shares of t or more participants. For any group with less than t participants no information of the secret can be gained. Shamir’s and Asmut-Bloom’s schemes have shown to be perfect, while others have not. An access structure defines the authorized sets of participants who are qualified to reconstruct the secret using their shares. In visual cryptography, apart from it being a (t, n)-threshold scheme, the construction of the secret and its belonging shares holds a mathematical calculation in the background, while the secret is reconstructed using human sight.

• Keywords: metoda dijeljenja tajni; Shamirova shema; Asmuth-Bloomova shema; vizualna kriptografija
• Keywords (english): sharing schemes methods; Shamir’s sheme; Asmut-Bloom’s scheme; visual cryptography
• Language: croatian
• URN:NBN: urn:nbn:hr:217:066902
• 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: 2019-01-24 16:49:33