20.500.12556/RUL-169878 Polinomske zaveze: kriptografsko ozadje in praktične aplikacije Polynomial commitments: cryptographic foundations and practical applications V diplomski nalogi obravnavamo problem konstrukcije učinkovitih in varnih polinomskih zavez brez razkritja njihovih koeficientov. Glavni cilj je predstaviti kriptografski mehanizem, imenovan polinomske zaveze, ter podrobno analizirati njegovo varnost, učinkovitost in uporabnost. Osredotočimo se na zavezo KZG, ki temelji na bilinearnih parjenjih in omogoča kratke, preverljive zaveze in dokaze o evalvacijah polinoma. Predstavimo formalne definicije in varnostne predpostavke ter analiziramo njene najpomembnejše lastnosti. Praktični prispevek naloge vključuje implementacijo zaveze KZG in Verklovega drevesa, ki predstavlja ključno komponento prihodnje nadgradnje decentraliziranega sistema Ethereum. In this thesis, we address the problem of constructing efficient and secure polynomial commitments without revealing their coefficients. The main objective is to present a cryptographic mechanism called polynomial commitments and to thoroughly analyze its security, efficiency, and applicability. We focus on the KZG commitment scheme, which is based on bilinear pairings and enables short, verifiable commitments and proofs of polynomial evaluations. We introduce formal definitions, security assumptions, and analyze its most important properties. The practical contribution of the thesis includes an implementation of the KZG commitment scheme and a Verkle tree, which represents a key component of a future upgrade to the decentralized Ethereum system. polinomske zaveze kriptografija varnost decentralizirani sistemi polynomial commitments cryptography security decentralized systems true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2025-06-13 10:45:03 2025-06-13 10:45:17 2025-06-16 11:04:11 0000-00-00 00:00:00 2025 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 38249 239443203 Gantar_Gal_-_Polinomske_zaveze_kriptografsko_ozadje_in_prakticne_aplikacije.pdf Gantar_Gal_-_Polinomske_zaveze_kriptografsko_ozadje_in_prakticne_aplikacije.pdf 1 18147BE6F27618E4B349F4FD99753C8D e5c2c48235e7a019527bd015aae1274ceb044d890b311e8abae9062d91dcd623 36cdefb3-4831-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=211630 Fakulteta za računalništvo in informatiko 0 0 0