Homomorfni kriptosustavi

master's thesis

• Author: Tanja Zrilić
• Mentor: Andrej Dujella (mentor)
• Committee member: Andrej Dujella (predsjednik povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad proučava homomorfne kriptosustave koji omogućavaju obavljanje matematičkih operacija nad šifriranim podacima bez potrebe da se podaci prije toga dešifriraju. Rad se može promatrati kroz tri osnovne cjeline. Prvi dio rada odnosi se na prvo poglavlje u kojem smo definirali homomorfizam i homomorfne kriptosustave. Drugi dio rada opisuje djelomične homomorfne kriptosustave koji zadovoljavaju svojstvo homomorfizma samo nad nekim matematičkim operacijama.Takvih kriptosustava ima više, a obrađeni u ovom radu su RSA, ElGamalov i Paillierov kriptosustav. Svaki kriptosustav prikazan je na isti način u više koraka, a to su: generiranje ključa, šifriranje, dešifriranje, svojstvo homomorfizma i sigurnost. Na kraju svakog kriptosustava naveden je primjer u kojem je ilustrirano njihovo izvođenje. Treći dio rada odnosi se na potpune homomorfne kriptosustave koji zadovoljavaju svojstvo homomorfizma nad svim matematičkim operacijama. Prvo ćemo definirati samo značenje potpunog homomorfnog kriptosustava, a zatim prikazati njegov povijesni razvoj. Na samom kraju pokazat ćemo kako preko jednostavnijih donekle potpunih doći do potpunih homomorfnih kriptosustava uz objašnjenja njihovih prednosti i nedostataka.

Abstract (english)

This thesis studies homomorphic encryption which allows specific types of computations to be carried out on cyphertexts and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. It may be divided into three fundamental parts. The first part includes the first chapters where we have defined homomorphism and homomorphic encryption. In the second part we describe partially homomorphic cryptosystems which allows only one operation is possible (usually addition or multiplication in the plaintext space) to be able to manipulate the plaintext by using only the cyphertext. There is a lot of partially homomorphic cryptosystems, but in this thesis processed are RSA, ElGamal and Paillier’s cryptosystems. Every encryption scheme consists of the same components: the key generation, the encryption algorithm, the decryption algorithm, homomorphic property and security. At the end, each cryptosystem is confirmed with example which illustrate their execution. The third part of the thesis refers to the fully homomorphic encryption which allows one to evaluate both addition and multiplication of plaintext, while remaining encrypted. First we described fully homomorphic encryption in general and introduce some of its properties. Then we gave a historical overview. At the end we showed connection between simple somewhat encryption scheme and fully homomorphic encryption scheme with all the advantages and disadvantages.

• Keywords: homomorfni kriptosustav; homomorfizam; RSA kriptosustav; ElGamalov kriptosustav; Paillierov kriptosustav
• Keywords (english): homomorphic encryption; homomorphism; RSA cryptosystem; ElGamal and Paillier’s cryptosystem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:930413
• 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: 2019-07-09 10:29:49