20.500.12556/RUL-155811 Paillierjev kriptosistem Paillier cryptosystem 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. 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. kriptografija Paillierjev kriptosistem elektronske volitve homomorfno šifriranje problem razreda sestavljenih ostankov cryptography Paillier cryptosystem electronic voting homomorphic encryption Composite Residuosity Class Problem true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-04-19 12:29:16 2024-04-19 12:29:16 2024-05-17 06:22:56 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 36635 190844931 Koprivc_Lucija_-_Paillierjev_kriptosistem.pdf Koprivc_Lucija_-_Paillierjev_kriptosistem.pdf 1 12FF099B6EFD16BE69A1CD011681D593 8068a3d3c7d763a658d38eb71ad8709e2772b0e8de503b65577f60aaa8065c3a ab30982c-fe37-11ee-9e65-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182913 Fakulteta za računalništvo in informatiko Fakulteta za matematiko in fiziko 0 0 0