Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle. In this paper, we give a rigorous stochastic analysis of an attack where the goal of the adversary is to double-spend while mining selfishly. To do so, we first combine stubborn and selfish mining attacks,i.e., construct a strategy where the attacker acts stubborn until its private branch reaches a certain length and then switches to act selfish. We provide the optimal stubbornness for each parameter regime. Next, we provide the maximum stubbornness that is still more profitable than honest mining and argue a connection between the level of stubbornness and thek-confirmation rule. We show that, at each attack cycle, if the level of stubbornness is higher thank, the adversary gets a free shot at double-spending. At each cycle, for a given stubbornness level, we rigorously formulate how great the probability of double-spending is. We further modify the attack in the stubborn regime in order to conceal the attack and increase the double-spending probability.

We study security-latency bounds for Nakamoto consensus, i.e., how secure a block is after it becomes k-deep in the chain. We improve the state-of-the-art bounds by analyzing the race between adversarial and honest chains in three different phases. We find the probability distribution of the growth of the adversarial chains under models similar to those in Guo and Ren (2022) when a target block becomes k-deep in the chain. We analyze certain properties of this race to model each phase with random walks that provide tighter bounds than the existing results. Combining all three phases provides novel upper and lower bounds for blockchains with small$\lambda \Delta $.

We analyze how secure a block is after the block becomes$k-\mathbf{deep}$, i.e., security-latency, for Nakamoto consensus under an exponential network delay model. We give parameter regimes for which transactions are safe when sufficiently deep in the chain. Next, modeling the blockchain system as a batch service queue with exponential network delay, we connect the security-latency analysis to sustainable transaction rate of the queue system. We modify the selfish-mining attack to hamper the service process and consider its effect on the sustainable transaction rate of the queue.

Safety guarantees and security-latency problem of Nakamoto consensus have been extensively studied in the last decade with a bounded delay model. Recent studies have shown that PoW protocol is secure under random delay models as well. In this paper, we analyze the security-latency problem, i.e., how secure a block is, after it becomes k-deep in the blockchain, under general random delay distributions. We provide tight and explicit bounds which only require determining the distribution of the number of Poisson arrivals during the random delay. We further consider potential effects of recent Bitcoin halving on the security-latency problem by extending our results.

We improve security-latency bounds of Nakamoto consensus by analyzing the race between adversarial and honest chains in three different phases: pre-mining, confirmation and post-confirmation. We find the probability distribution of the length of the adversarial chain and the rigged adversarial chain under jumper models during the confirmation interval. We analyze certain properties of this race to model pre-mining and post-confirmation phases with random walks that provide tighter bounds than existing results. Combining all three phases provides novel upper and lower bounds for blockchains with small λΔ.