Biblio

Mining, the process where multiple miners compete to add blocks to Proof-of-Work (PoW) blockchains, is of great importance to maintain the tamper-resistance feature of blockchains. In current blockchain networks, miners usually form groups, called mining pools, to improve their revenues. When multiple pools exist, a fundamental mining pool selection problem arises: which pool should each miner join to maximize its revenue? In addition, the existence of mining pools also leads to another critical issue, i.e., Block WithHolding (BWH) attack, where a pool sends some of its miners as spies to another pool to gain extra revenues without contributing to the mining of the infiltrated pool. This paper therefore aims to investigate the mining pool selection issue (i.e., the stable population distribution of miners in the pools) in the presence of BWH attack from the perspective of evolutionary game theory. We first derive the expected revenue density of each pool to determine the expected payoff of miners in that pool. Based on the expected payoffs, we formulate replicator dynamics to represent the growth rates of the populations in all pools. Using the replicator dynamics, we obtain the rest points of the growth rates and discuss their stability to identify the Evolutionarily Stable States (ESSs) (i.e., stable population distributions) of the game. Simulation and numerical results are also provided to corroborate our analysis and to illustrate the theoretical findings.

This paper is concerned with the stabilization problem of cyber physical system (CPS) exposed to a random replay attack. The study will ignore the effects of communication delays and packet losses, and the attention will be focused on the effect of replay attack on the stability of (CPS). The closed-loop system is modeled as Markovian jump linear system with two jumping parameters. Linear matrix inequality (LMI) formulation is used to give a condition for stochastic stabilization of the system. Finally the theory is illustrated through a numerical example.

This paper proposes a compensation control scheme against DoS attack for nonlinear cyber-physical systems (CPSs). The dynamical process of the nonlinear CPSs are described by T-S fuzzy model that regulated by the corresponding fuzzy rules. The communication link between the controller and the actuator under consideration may be unreliable, where Denialof-Service (DoS) attack is supposed to invade the communication link randomly. To compensate the negative effect caused by DoS attack, a compensation control scheme is designed to maintain the stability of the closed-loop system. With the aid of the Lyapunov function theory, a sufficient condition is established to ensure the stochastic stability and strict dissipativity of the closed-loop system. Finally, an iterative linearization algorithm is designed to determine the controller gain and the effectiveness of the proposed approach is evaluated through simulations.