On the Use of Proof-of-Work in Permissioned Blockchains: Security and Fairness

In permissioned blockchains, a set of identifiable miners validates transactions and creates new blocks. In scholarship, the proposed solution for the consensus protocol is usually inspired by the Byzantine fault tolerance (BFT) based on voting rather than the proof-of-work (PoW). The advantage of PoW with respect to BFT is that it allows the final user to evaluate the cost required to change a confirmed transaction without the need to trust the consortium of miners. In this paper, we analyse the problems that arise from the application of PoW in permissioned blockchains. In standard PoW, it may be easy for colluded miners to temporarily reach 50% of the total hash power (HP). Moreover, since mining rewards are not usually expected in permissioned contexts, the problem of balancing the computational efforts among the miners becomes crucial. We propose a solution based on a sliding window algorithm to address these problems and analyse its effectiveness in terms of fairness and security. Furthermore, we present a quantitative, analytical model in order to assess its capacity to balance the hash power provided by heterogeneous miners. Our study considers the trade-off between the need to trust the entire consortium of miners guaranteed by the global HP invested by the mining process and the need to prevent collusion among malicious miners aimed at reaching 50% of the total HP. As a result, the model can be used to find the optimal parameters for the sliding window protocol

Verifier’s Dilemma in Ethereum Blockchain: A Quantitative Analysis

A blockchain is an immutable ledger driven by a distributed consensus protocol. In public blockchains such as Bitcoin and Ethereum consensus is established through a computational effort called Proof-of-Work (PoW). Special users called miners contribute to the PoW computational effort in exchange for a fee and also verify the data stored in blocks mined by the other miners. Here is where the Verifier’s Dilemma emerges. To maximise their profits, miners are incentivized to invest their resources in PoW, because they do not receive any incentives for the verification phase. In this paper, we study the Verifier’s Dilemma using a quantitative model based on PEPA. The analysis demonstrates the circumstances under which non-verifying miners gain fees higher than that of verifying miners. Moreover, we consider a mitigation approach consisting of the injection of invalid blocks to disturb the mining process of non-verifying miners. The model allows us to derive the optimal rate at which invalid blocks must be injected, so that skipping the verifying phase becomes economically disadvantageous while the throughput of the blockchain is only minimally reduced. The impact on miners’ rewards and overall performance is also assessed