Biblio

Blockchain, the technology behind the popular Bitcoin, is considered a "security by design" system as it is meant to create security among a group of distrustful parties yet without a central trusted authority. The security of blockchain relies on the premise of honest-majority, namely, the blockchain system is assumed to be secure as long as the majority of consensus voting power is honest. And in the case of proof-of-work (PoW) blockchain, adversaries cannot control more than 50% of the network's gross computing power. However, this 50% threshold is based on the analysis of computing power only, with implicit and idealistic assumptions on the network and node behavior. Recent researches have alluded that factors such as network connectivity, presence of blockchain forks, and mining strategy could undermine the consensus security assured by the honest-majority, but neither concrete analysis nor quantitative evaluation is provided. In this paper we fill the gap by proposing an analytical model to assess the impact of network connectivity on the consensus security of PoW blockchain under different adversary models. We apply our analytical model to two adversarial scenarios: 1) honest-but-potentially-colluding, 2) selfish mining. For each scenario, we quantify the communication capability of nodes involved in a fork race and estimate the adversary's mining revenue and its impact on security properties of the consensus protocol. Simulation results validated our analysis. Our modeling and analysis provide a paradigm for assessing the security impact of various factors in a distributed consensus system.

This paper presents an analytical method for predicting the electromagnetic performance in permanent magnet (PM) machine with the spoke-type rotor (STR) and a proposed hybrid rotor structure (HRS), respectively. The key of this method is to combine magnetic field analysis model (MFAM) with the magnetic equivalent circuit model. The influence of the irregular PM shape is considered by the segmentation calculation. To obtain the boundary condition in the MFAM, respectively, two equivalent methods on the rotor side are proposed. In the STR, the average flux density of the rotor core outer-surface is calculated to solve the Laplace's equation with considering for the rotor core outer-surface eccentric. In the HRS, based on the Thevenin's theorem, the equivalent parameters of PM remanence BreB and thickness hpme are obtained as a given condition, which can be utilized to compute the air-gap flux density by conventional classic magnetic field analysis model of surface-mounted PMs with air-gap region. Finally, the proposed analytical models are verified by the finite element analysis (FEA) with comparisons of the air-gap flux density, flux linkage, back-EMF and electromagnetic torque, respectively. Furthermore, the performance that the machine with the proposed hybrid structure rotor can improve the torque density as explained.