Biblio

Mining, the process where multiple miners compete to add blocks to Proof-of-Work (PoW) blockchains, is of great importance to maintain the tamper-resistance feature of blockchains. In current blockchain networks, miners usually form groups, called mining pools, to improve their revenues. When multiple pools exist, a fundamental mining pool selection problem arises: which pool should each miner join to maximize its revenue? In addition, the existence of mining pools also leads to another critical issue, i.e., Block WithHolding (BWH) attack, where a pool sends some of its miners as spies to another pool to gain extra revenues without contributing to the mining of the infiltrated pool. This paper therefore aims to investigate the mining pool selection issue (i.e., the stable population distribution of miners in the pools) in the presence of BWH attack from the perspective of evolutionary game theory. We first derive the expected revenue density of each pool to determine the expected payoff of miners in that pool. Based on the expected payoffs, we formulate replicator dynamics to represent the growth rates of the populations in all pools. Using the replicator dynamics, we obtain the rest points of the growth rates and discuss their stability to identify the Evolutionarily Stable States (ESSs) (i.e., stable population distributions) of the game. Simulation and numerical results are also provided to corroborate our analysis and to illustrate the theoretical findings.

In Bitcoin's incentive system that supports open mining pools, block withholding attacks incur huge security threats. In this paper, we investigate the mutual attacks among pools as this determines the macroscopic utility of the whole distributed system. Existing studies on pools' interactive attacks usually employ the conventional game theory, where the strategies of the players are considered pure and equal, neglecting the existence of powerful strategies and the corresponding favorable game results. In this study, we take advantage of the Zero-Determinant (ZD) strategy to analyze the block withholding attack between any two pools, where the ZD adopter has the unilateral control on the expected payoffs of its opponent and itself. In this case, we are faced with the following questions: who can adopt the ZD strategy? individually or simultaneously? what can the ZD player achieve? In order to answer these questions, we derive the conditions under which two pools can individually or simultaneously employ the ZD strategy and demonstrate the effectiveness. To the best of our knowledge, we are the first to use the ZD strategy to analyze the block withholding attack among pools.

The blockchain technology has emerged as an attractive solution to address performance and security issues in distributed systems. Blockchain's public and distributed peer-to-peer ledger capability benefits cloud computing services which require functions such as, assured data provenance, auditing, management of digital assets, and distributed consensus. Blockchain's underlying consensus mechanism allows to build a tamper-proof environment, where transactions on any digital assets are verified by set of authentic participants or miners. With use of strong cryptographic methods, blocks of transactions are chained together to enable immutability on the records. However, achieving consensus demands computational power from the miners in exchange of handsome reward. Therefore, greedy miners always try to exploit the system by augmenting their mining power. In this paper, we first discuss blockchain's capability in providing assured data provenance in cloud and present vulnerabilities in blockchain cloud. We model the block withholding (BWH) attack in a blockchain cloud considering distinct pool reward mechanisms. BWH attack provides rogue miner ample resources in the blockchain cloud for disrupting honest miners' mining efforts, which was verified through simulations.