Sıfır bilgi aralık ispatları ve dağıtık sistemlerdeki uygulamaları

Appropriate, effective, and efficient use of cryptographic protocols contributes to many novel advances in real-world privacy-preserving constructions. One of the most important cryptographic protocols is the zero-knowledge proofs. The zero-knowledge proofs have recently gained the utmost importance in terms of decentralized systems, especially in the context of privacy. In many decentralized systems, such as electronic voting, e-cash, e-auctions, or anonymous credentials, the zero-knowledge range proofs are used as the building blocks. In this thesis, we examine, summarise and compare range proofs based on zero-knowledge proofs, and examine their applications in decentralized systems such as distributed ledgers, confidential assets and smart contracts. We also, investigate different basis of OR-proofs and compare the efficiency of different basis approaches. To this end, we have modified the Mao's range proof to base-3 with a modified OR-proof. For each basis, we derive the number of computations in modulo exponentiations and the cost of numbers exchanged between parties. Then, we have generalized these costs for base-u construction. At the end of these comparisons, we observe that comparing the number of computations in modulo exponentiations with other base approaches, the base-3 approach is 5.5% more efficient. In addition, comparing the cost of numbers exchanged between prover and verifier, base-3 approach is 7% more efficient than other base approaches.