Discouraging pool block withholding attacks in Bitcoin

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. Moreover, with only two minority mining pools, no-pool-attacks is the unique Nash equilibrium