Adaptive Double-Spending Attacks on PoW-based Blockchains

Previous state-of-the-art studies have proposed various analytical models to understand the double-spending attacks (DSA) occurred in Proof-of-Work (PoW) based Blockchains. Although many insights behind the double-spending attacks have been disclosed, we still believe that advanced versions of DSA can be developed to create new threats for the PoW-based blockchains such as the Bitcoin blockchain. In this paper, we present two new types of double-spending attacks in the context of the PoW-based blockchain and discuss the insights behind them. By considering more practical network parameters, such as the number of confirmation blocks, the hashpower of the double-spending attacker, the amount of coins in the target transaction, and the network-status parameter, we first analyze the success probability of the conventional double-spending attack, named Naive DSA. Based on Naive DSA, we create two new adaptive DSA, i.e., the Adaptive DSA and the Reinforcement Adaptive DSA (RA-DSA). In our analytical models, a double-spending attack is converted into a Markov Decision Process. We then exploit the Stochastic Dynamic Programming (SDP) approach to obtain the optimal attack strategies under Adaptive DSA and RA-DSA. Numerical simulation results demonstrate the correlations between each critical network parameter and the expected attacker's reward. Through the proposed analytical models, we aim to alert the PoW-based blockchain ecosystem that the threat of double-spending attacks is still at a dangerous level. For example, our findings show that the attacker can launch a successful attack with a small hashpower proportion much lower than 51% under RA-DSA.