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2020-09-04
Elliott, Sean.  2019.  Nash Equilibrium of Multiple, Non-Uniform Bitcoin Block Withholding Attackers. 2019 2nd International Conference on Data Intelligence and Security (ICDIS). :144—151.
This research analyzes a seemingly malicious behavior known as a block withholding (BWH) attack between pools of cryptocurrency miners in Bitcoin-like systems featuring blockchain distributed databases. This work updates and builds on a seminal paper, The Miner's Dilemma, which studied a simplified scenario and showed that a BWH attack can be rational behavior that is profitable for the attacker. The new research presented here provides an in-depth profit analysis of a more complex and realistic BWH attack scenario, which includes mutual attacks between multiple, non-uniform Bitcoin mining pools. As a result of mathematical analysis and MATLAB modeling, this paper illustrates the Nash equilibrium conditions of a system of independent mining pools with varied mining rates and computes the equilibrium rates of mutual BWH attack. The analysis method quantifies the additional profit the largest pools extract from the system at the expense of the smaller pools. The results indicate that while the presence of BWH is a net negative for smaller pools, they must participate in BWH to maximize their remaining profits, and the results quantify the attack rates the smaller pools must maintain. Also, the smallest pools maximize profit by not attacking at all-that is, retaliation is not a rational move for them.
2018-05-24
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.