Paper 2015/155

On Power Splitting Games in Distributed Computation: The Case of Bitcoin Pooled Mining

Loi Luu, Ratul Saha, Inian Parameshwaran, Prateek Saxena, and Aquinas Hobor


Several new services incentivize clients to compete in solving large computation tasks in exchange for financial rewards. This model of competitive distributed computation enables every user connected to the Internet to participate in a game in which he splits his computational power among a set of competing pools — the game is called a computational power splitting game. We formally model this game and show its utility in analyzing the security of pool protocols that dictate how financial rewards are shared among the members of a pool. As a case study, we analyze the Bitcoin cryptocurrency which attracts computing power roughly equivalent to billions of desk- top machines, over 70% of which is organized into public pools. We show that existing pool reward sharing protocols are insecure in our game-theoretic analysis under an attack strategy called the “block withholding attack”. This attack is a topic of debate, initially thought to be ill-incentivized in today’s pool protocols: i.e., causing a net loss to the attacker, and later argued to be always profitable. Our analysis shows that the attack is always well-incentivized in the long-run, but may not be so for a short duration. This implies that existing pool protocols are insecure, and if the attack is conducted systematically, Bitcoin pools could lose millions of dollars worth in months. The equilibrium state is a mixed strategy—that is—in equilibrium all clients are incentivized to probabilistically attack to maximize their payoffs rather than participate honestly. As a result, a part of the Bitcoin network is incentivized to waste resource competing for higher selfish reward.

Note: Fix typos and update the information of the conference that the paper is published in.

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Publication info
Published elsewhere. Minor revision. 28th IEEE Computer Security Foundations Symposium
Cryptocurrencyblock withholding attackdistributed computation
Contact author(s)
loiluu @ comp nus edu sg
2015-06-01: revised
2015-02-27: received
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      author = {Loi Luu and Ratul Saha and Inian Parameshwaran and Prateek Saxena and Aquinas Hobor},
      title = {On Power Splitting Games in Distributed Computation: The Case of Bitcoin Pooled Mining},
      howpublished = {Cryptology ePrint Archive, Paper 2015/155},
      year = {2015},
      note = {\url{}},
      url = {}
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