Paillierjev kriptosistem

diplomsko delo

Lucija Koprivc (Author), Tilen Marc (Mentor)

Abstract

Kriptosistemi temeljijo na težkih matematičnih problemih, kot sta problem faktorizacije in problem diskretnega logaritma. Pascal Paillier je preučeval problem razreda sestavljenih ostankov, ki predstavlja nov težek problem. Na tem problemu temelji varnost kriptosistema, ki ga je opisal leta 1999. Homomorfna lastnost Paillierjevega kriptosistema omogoča nove aplikacije, kot je na primer uporaba v elektronskih volitvah. V diplomski nalogi opišemo Paillierjev kriptosistem in njegove homomorfne lastnosti, ki nam omogočajo izvajanje operacij nad šifriranimi podatki, ne da bi jih dešifrirali. Dokažemo tudi njegovo pravilnost in varnost. Kriptosistem uporabimo kot osnovo za protokole elektronskih volitev v delno poštenem modelu. Zaključimo z opisom treh volilnih protokolov, ki se med seboj razlikujejo po številu kandidatov, za katere lahko glasujemo.

Keywords

kriptografija;Paillierjev kriptosistem;elektronske volitve;homomorfno šifriranje;problem razreda sestavljenih ostankov;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2024
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[L. Koprivc]
UDC:	004.056.55:324(043.2)
COBISS:	190844931
Views:	43
Downloads:	6
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Paillier cryptosystem
Secondary abstract:	Cryptosystems are based on various computationally hard problems, such as the factorization problem and the discrete logarithm problem. Pascal Paillier studied the Composite Residuosity Class Problem, which represents a new computationally hard problem. In 1999, he proposed a new cryptosystem whose security is based on this problem. The homomorphic property of the Paillier cryptosystem enables new applications, such as the use in electronic elections. In this thesis, we study the Paillier cryptosystem and its homomorphic properties, which allow us to perform operations on encrypted data without decrypting it in the process. We prove its correctness and security. We use the cryptosystem as the basis for electronic voting in the semi-honest model. We conclude by describing three voting protocols, which differ from each other in terms of the number of candidates for which we can vote.
Secondary keywords:	cryptography;Paillier cryptosystem;electronic voting;homomorphic encryption;Composite Residuosity Class Problem;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;Vizualna kriptografija;Elektronsko glasovanje;Matematika;Računalništvo;Univerzitetna in visokošolska dela;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	55 str.
ID:	23467870