Discouraging pool block withholding attacks in Bitcoin

Zhihuai Chen, Bo Li, Xiaohan Shan, Xiaoming Sun, Jialin Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


The existence of mining pools in Bitcoin enables the miners to gain more stable reward. However, it is proved that the pools are vulnerable for security attacks. A strategic pool manager has strong incentive to launch pool block withholding attack by sending some of her miners to infiltrate the other pools. The infiltrating miners try to find (partial) proof-of-work solutions but discard the solution that can actually create blocks. As it is hard to recognize malicious miners,these miners still get reward in the infiltrated pools. In this work, we revisit the game-theoretic model for pool block withholding attacks and propose a revised approach to reallocate the reward to the miners. Instead of proportionally allocating the reward to all miners, a pool manager deducts a fraction from the reward to award the miner who actually mined the block. Accordingly, we prove that, under our scheme, for any number of mining pools, no-pool-attacks is always a Nash equilibrium.

Original languageEnglish
Pages (from-to)444-459
Number of pages16
JournalJournal of Combinatorial Optimization
Issue number2
Publication statusPublished - Mar 2022


  • Bitcoin
  • Block withholding attack
  • Mining pool
  • Nash equilibrium

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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