Profitability Analysis of Time-Restricted Double-Spending Attack on PoW-Based Large Scale Blockchain With the Aid of Multiple Types of Attacks

We consider the time-restricted double-spending attack (TR-DSA) on the Proof-of-Work-based blockchain, where an adversary conducts a DSA within a finite timeframe and simultaneously launches multiple types of attacks on the blockchain. To be specific, the adversary can conduct attacks to isolate some honest miners and cause block propagation delays among miners to enhance the success probability of the TR-DSA. We first develop the closed-form expression for the success probability of a TR-DSA with the aid of multiple types of attacks, which is leveraged to develop the closed-form expression for the expected profit of a TR-DSA. The numerical analysis reveals that in scenarios where an adversary lacks the majority of computational power in the blockchain network, it is advisable for the adversary to refrain from indefinitely conducting a DSA, and moreover, the adversary can repeatedly launch "short-time" TR-DSAs to obtain their maximum expected profit. Notably, by leveraging the closed-form expression for the expected profit of a TR-DSA, the blockchain network designer can reduce the expected profit of a TR-DSA and therefore significantly mitigate the risk of TR-DSAs by adjusting system parameters, such as the number of blocks required for transaction confirmation, mining reward, and mining cost.