Dokazi brez razkritja znanja in njihova uporaba v decentraliziranih sistemih : magistrsko delo

Ševerkar, Nejc (author), Marc, Tilen (mentor)

V magistrski nalogi se ukvarjamo z dokazi brez razkritja znanja. Predstavljen je matematični model imenovan Pinocchio, ki sloni na teoriji eliptičnih krivulj in omogoča konstrukcijo učinkovitih dokazov brez razkritja znanja za probleme, ki se jih da izraziti z aritmetičnimi vezji. Za te dokaze je v delu opisanih nekaj primerov uporabe v decentraliziranih sistemih. Dva takšna primera sta kriptovaluta Zerocash, ki ohranja zasebnost svojih uporabnikov, in implementacija pametne pogodbe, ki omogoča decentralizirane in anonimne volitve.

• Language: Slovenian
• Keywords: dokazi brez razkritja znanja, decentralizirani sistemi, eliptične krivulje, protokol Pinocchio, zk-SNARK
• Work type: Master's thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-143910
• UDC: 519.72
• COBISS.SI-ID: 138161667
• Publication date in RUL: 19.01.2023

Secondary language

• Language: English
• Title: Zero-knowledge proofs and their usage in decentralized systems

Abstract

In the thesis, we study zero-knowledge proofs. We focus on a description of a mathematical model named Pinocchio, which depends on elliptic curve theory and enables the construction of efficient zero-knowledge proofs for problems expressed by arithmetic circuits. For those proofs, we describe some example usages in decentralized systems. The main two examples are the cryptocurrency Zerocash, which preserves its users' anonymity, and an implementation of a decentralized anonymous voting system using a smart contract.

• Keywords: zero-knowledge proofs, decentralized systems, elliptic curves, Pinocchio protocol, zk-SNARK