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Hu, Qin, Wang, Shengling, Cheng, Xiuzhen.  2019.  A Game Theoretic Analysis on Block Withholding Attacks Using the Zero-Determinant Strategy. 2019 IEEE/ACM 27th International Symposium on Quality of Service (IWQoS). :1–10.
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.
Tosh, D. K., Shetty, S., Liang, X., Kamhoua, C. A., Kwiat, K. A., Njilla, L..  2017.  Security Implications of Blockchain Cloud with Analysis of Block Withholding Attack. 2017 17th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID). :458–467.

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.