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.