A Deep Dive into Blockchain Selfish Mining

This paper studies a fundamental problem regarding the security of blockchain on how the existence of multiple misbehaving pools influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it public opportunistically for the purpose of acquiring more rewards incommensurate to his Hashrate. We establish a novel Markov chain model to characterize all the state transitions of public and private chains. The minimum requirement of Hashrate together with the minimum delay of being profitable is derived in close-form. The former reduces to 21.48% with the symmetric selfish miners, while their competition with asymmetric Hashrates puts forward a higher requirement of the profitable threshold. The profitable delay increases with the decrease of the Hashrate of selfish miners, making the mining pools more cautious on performing selfish mining.Comment: 6 pages, 13 figure

Blockchain Mining with Multiple Selfish Miners

This paper studies a fundamental problem regarding the security of blockchain PoW consensus on how the existence of multiple misbehaving miners influences the profitability of selfish mining. Each selfish miner (or attacker interchangeably) maintains a private chain and makes it public opportunistically for acquiring more rewards incommensurate to his Hash power. We first establish a general Markov chain model to characterize the state transition of public and private chains for Basic Selfish Mining (BSM), and derive the stationary profitable threshold of Hash power in closed-form. It reduces from 25% for a single attacker to below 21.48% for two symmetric attackers theoretically, and further reduces to around 10% with eight symmetric attackers experimentally. We next explore the profitable threshold when one of the attackers performs strategic mining based on Partially Observable Markov Decision Process (POMDP) that only half of the attributes pertinent to a mining state are observable to him. An online algorithm is presented to compute the nearly optimal policy efficiently despite the large state space and high dimensional belief space. The strategic attacker mines selfishly and more agilely than BSM attacker when his Hash power is relatively high, and mines honestly otherwise, thus leading to a much lower profitable threshold. Last, we formulate a simple model of absolute mining revenue that yields an interesting observation: selfish mining is never profitable at the first difficulty adjustment period, but replying on the reimbursement of stationary selfish mining gains in the future periods. The delay till being profitable of an attacker increases with the decrease of his Hash power, making blockchain miners more cautious on performing selfish mining.Comment: arXiv admin note: substantial text overlap with arXiv:1811.0826

Experiments and Numerical Simulation of Performances and Internal Flow for High-Speed Rescue Pump with Variable Speeds

The model pump is a high-speed, high-power pump designed to achieve rapid mine flooding rescue. This study conducted experiments to investigate pump performance curves, including head, efficiency, and power for the following six different rotation speeds: 3000, 3600, 4200, 4800, 5400, and 6000 rpm. Then, the numerical simulation method based on computational fluid dynamics commercial code Ansys was used to present the internal flow of the pump for the six different rotation speeds through steady and unsteady analyses. Results show that the numerical results agree well with experimental data. The designs of outlet and inlet angles of the impeller match each other well at high rotation speeds. The pressure pulsation coefficient Cp in the impeller and the diffuser channel remain constant at the same monitor point under different rotation speed conditions. The varying trend of the pressure-augmented coefficient ΔP indicates that, with the increase in rotation speed, the effect on pressure rise induced by the back part of the impeller channel is more evident than that by the front part. Also, the main frequency components of ΔP are concentrated on the region with low frequency. Moreover, the rotation speed has no significant effect on ΔP in the diffuser region. This study provides effective guidance and valuable reference for the design of high-speed, high-power pumps