Polinomske zaveze

kriptografsko ozadje in praktične aplikacije

Gal Gantar (Author), Tilen Marc (Mentor)

Abstract

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.

Keywords

polinomske zaveze;kriptografija;varnost;decentralizirani sistemi;računalništvo;matematika;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2025
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[G. Gantar]
UDC:	512.622:004(043.2)
COBISS:	239443203
Views:	252
Downloads:	111
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Polynomial commitments: cryptographic foundations and practical applications
Secondary abstract:	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.
Secondary keywords:	polynomial commitments;cryptography;security;decentralized systems;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000407
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	1 spletni vir (1 datoteka PDF (51 str.))
ID:	26579263