Qianlan Bai

Qianlan Bai, Yuedong Xu, Nianyi Liu et al.

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.

Qianlan Bai, Chao Zhang, Yuedong Xu et al.

Ethereum is one of the most popular blockchain systems that supports more than half a million transactions every day and fosters miscellaneous decentralized applications with its Turing-complete smart contract machine. Whereas it remains mysterious what the transaction pattern of Ethereum is and how it evolves over time. In this paper, we study the evolutionary behavior of Ethereum transactions from a temporal graph point of view. We first develop a data analytics platform to collect external transactions associated with users as well as internal transactions initiated by smart contracts. Three types of temporal graphs, user-to-user, contract-to-contract and user-contract graphs, are constructed according to trading relationship and are segmented with an appropriate time window. We observe a strong correlation between the size of user-to-user transaction graph and the average Ether price in a time window, while no evidence of such linkage is shown at the average degree, average edge weights and average triplet closure duration. The macroscopic and microscopic burstiness of Ethereum transactions is validated. We analyze the Gini indexes of the transaction graphs and the user wealth in which Ethereum is found to be very unfair since the very beginning, in a sense, "the rich is already very rich".

Qianlan Bai, Xinyan Zhou, Xing Wang et al.

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.