A type of block withholding delay attack and the countermeasure based on type-2 fuzzy inference

We proposed a new type of bitcoin withholding attack named block withholding delay (BWD). It is different from the traditional withholding attacks which always drop valid blocks. BWD attackers never discard blocks but they delay the submissions of blocks to the pool managers, resulting the pool failed in the mining competitions and loss of rewards. We analyzed the optimum strategy of a BWD attacker who split its computing power into two parts, one was utilized to launch BWD attacks on the victim pools, while the other part was used for solo mining. We present detailed quantitative analysis of the maximum incentive that an attacker can earn by carefully splitting its computing power, and demonstrated that the attacker can obtain higher incentives than its contribution to the network in different conditions. Furthermore, we proposed a countermeasure against BWD based on the interval type-2 Takagi-Sugeno-Kang fuzzy inference system (IT2-TSK-FIS). The principle is to modify the private payoff scheme of pools to increase the risk of losing revenues of the rogue miners who deliberately delay block submissions. The scheme dealing the uncertain cause of block delay using fuzzy inference, and it is so designed that it does not require modifications of public mining protocols or data structures of the bitcoin network, which makes it applicable in practical pools.