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Probabilistic Micropayments
(2022)
Probabilistic micropayments are important cryptography research topics in electronic commerce. The Probabilistic micropayments have the potential to be researched in order to obtain efficient algorithms with low transaction costs and high speeding computer power. To delve into the topic, it is vital to scrutinize the cryptographic preliminaries such as hash functions and digital signatures. This thesis investigates the important probabilistic methods based on a centralized or decentralized network. Firstly, centralized networks such as lottery-based tickets, Payword, coin-flipping, and MR2 are described, and an approach based on blind signatures is also discussed. Then, decentralized network methods such as MICROPAY3, a transferable scheme on the blockchain network, along with an efficient model for cryptocurrencies, are explained. Then we compare the different probabilistic micropayment methods by improving their drawback with a new technique. To set the results from the theoretical analysis of different methods into some context, we analyze the attacks that reduce the security and, therefore, the system’s efficiency. Particularly, we discuss various methods for detecting double-spending and eclipse attacks occurrence
Mathematics Behind the Zcash
(2020)
Among all the new developed cryptocurrencies from Bitcoin, Zcash comes out to be the strongest cryptocurrency providing both transparency and anonymity to the transactions and its users by deploying the strong mathematics of zk-SNARKs.
We discussed the zero knowledge proofs which is a basic building block for providing the functionality to zk-SNARKs. It offers schnorr and sigma protocols with interactive and noninteractive versions. Non-interactive proofs are further used in Zcash transactions where the validation of sent transaction is proved by cryptographic proof.
Further, we deploy zk-SNARKs proofs following common reference string as public parameter when transaction is made. The proof allows sender to prove that she knows a secret for an instance such that the proof is succinct, can be verified very efficiently and does not leak the
secret. Non-malleability, small proofs and very effective verification make zk-SNARKs a classic tool in Zcash. Since we deal with NP problems therefore we have considered the elliptic curve cryptography to provide the same security like RSA but with smaller parameter size.
Lastly, we explain Zcash transaction process after minting the coin, the corresponding transaction completely hides the sender, receiver and amount of transaction using zero knowledge proof.
As future considerations, we talk about the improvements that can be done in term of decentralization, efficiency by comparing with top ranked cryptocurrencies namely Ethereum and Monero, privacy preserving against the thread of quantum computers and enhancements in shielded transactions.
With the growing market of cryptocurrencies, blockchain is becoming central to various research areas relevant from a mathematical and cryptographic point of view. Moreover, it is capable of transforming the traditional methods involving centralized network operations into decentralized peer-to-peer functionalities. At the same time, it provides an alternative to digital payments in a robust and tamperproof manner by adding the element of cryptography, consequently making it traversable for an individual who is a part of the blockchain network. Furthermore, for a blockchain to be optimal and efficient, it must handle the blockchain trilemma of security, decentralization, and scalability constraints in an effective manner. Algorand, a blockchain cryptocurrency protocol intended to solve blockchain’s trilemma, has been studied and discussed. It is a permissionless (public) blockchain protocol and uses pure proof of stake as its consensus mechanism.
As the cryptocurrency ecosystem rapidly grows, interoperability has become increasingly crucial, enabling assets and data to interact seamlessly across multiple chains. This work describes the concept and implementation of a trustless connection between the Bitcoin Lightning Network and EVM-compatible blockchains, allowing the transfer of assets between the two ecosystems. Establishing such a connection can significantly contribute to the growth of both ecosystems as they can benefit from each other’s advantages and emerge new pos- sibilities.