Markov chain model and profit analysis of two-selfish-miner strategy in ethereum classic network

doi:10.11772/j.issn.1001-9081.2025050596

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (5): 1526-1533.DOI: 10.11772/j.issn.1001-9081.2025050596

• Cyber security • Previous Articles

Markov chain model and profit analysis of two-selfish-miner strategy in ethereum classic network

Junling WANG, Junjun BIAN(), Jianian LIU, Zhiqiang XU

School of Information Engineering，Jiangxi University of Science and Technology，Ganzhou Jiangxi 341000，China

Received:2025-05-30 Revised:2025-08-11 Accepted:2025-08-20 Online:2025-09-05 Published:2026-05-10
Contact: Junjun BIAN
About author:WANG Junling， born in 1976， Ph. D.， associate professor. His research interests include cyberspace security， computer vision.
LIU Jianian，born in 2001， M. S. candidate. His research interests include path planning of mobile robots.
XU Zhiqiang， born in 1987， Ph. D.， associate professor. His research interests include network attack detection and investigation， host log analysis， artificial intelligence model attack and defense， data mining， deep learning.
Supported by:
National Natural Science Foundation of China(62362038)

以太坊经典网络双自私矿工策略的马尔可夫链模型与收益分析

王俊岭, 边俊君(), 刘佳年, 徐志强

江西理工大学信息工程学院，江西赣州 341000

通讯作者: 边俊君
作者简介:王俊岭（1976—），男，江苏东台人，副教授，博士，主要研究方向：网络空间安全、计算机视觉
刘佳年（2001—），男，甘肃武威人，硕士研究生，主要研究方向：移动机器人路径规划
徐志强（1987—），男，辽宁沈阳人，副教授，博士，主要研究方向：网络攻击检测与调查、主机日志分析、人工智能模型攻击与防御、数据挖掘、深度学习。
基金资助:
国家自然科学基金资助项目(62362038)

Abstract

Abstract:

Selfish mining disrupts the normal consensus process of blockchain networks by concealing mining and delaying the release of new blocks， resulting in increased fork rate and reduced system efficiency. To quantitatively analyze the impact of selfish mining on the EThereum Classic （ETC） network under a multi-attacker environment， a Markov chain model with multiple attackers was constructed aiming at the ETC network's unique uncle block and nephew block reward mechanism， and the revenue dynamics of miners under different scenarios were quantitatively analyzed. Experimental results show that when the attacker's computing power reaches 0.3， a coordinated attack by two selfish mining pools increases the stale block rate from 26.35% to 36.21% and reduces the system throughput （Transactions Per Second （TPS）） from 20.15 to 16.44. Compared with the case of a single-selfish-miner， this attack strategy further increases the attacker's relative revenue while exacerbating the problems of harming honest miners' revenue， increasing the stale block rate， and decreasing the system efficiency. The above reveals the complex revenue mechanism of multi-attacker selfish mining and provides a theoretical and quantitative basis for designing targeted defense strategies.

Key words: EThereum Classic (ETC), selfish mining, Markov chain, uncle block reward, blockchain security

摘要：

自私挖矿通过隐蔽挖掘和延迟发布新区块，扰乱区块链网络的正常共识过程，导致分叉率上升和系统效率降低。为量化分析多攻击者环境下自私挖矿对以太坊经典（ETC）网络的影响，针对ETC网络中特有的叔块和侄块奖励机制，构建包含多攻击者交互的马尔可夫链模型，定量分析了不同场景下矿工群体的收益动态。实验结果表明，在攻击者算力达到0.3时，双自私矿池协同攻击使废块率从26.35%提升至36.21%，系统吞吐量（每秒交易量（TPS））从20.15降至16.44。与单自私矿工情形相比，该攻击策略进一步提升了攻击者的相对收益，同时加剧了诚实矿工收益受损、废块率上升以及系统效率下降等问题。研究结果揭示了多攻击者自私挖矿的复杂收益机制，为设计针对性防御策略提供了理论基础和量化依据。

关键词: 以太坊经典, 自私挖矿, 马尔可夫链, 叔块奖励, 区块链安全

CLC Number:

TP309

Junling WANG, Junjun BIAN, Jianian LIU, Zhiqiang XU. Markov chain model and profit analysis of two-selfish-miner strategy in ethereum classic network[J]. Journal of Computer Applications, 2026, 46(5): 1526-1533.

王俊岭, 边俊君, 刘佳年, 徐志强. 以太坊经典网络双自私矿工策略的马尔可夫链模型与收益分析[J]. 《计算机应用》唯一官方网站, 2026, 46(5): 1526-1533.

Figures/Tables 15

Fig. 1 Uncle and nephew blocks in ETC network

Fig. 2 Examples of system status

Fig. 3 Scenario 1 of selfish miner model

Fig. 4 Scenario 2 of selfish miner model

Fig. 5 Scenario 3 of selfish miner model

Fig. 6 Scenario 1 of honest miner model

Fig. 7 Scenario 2 of honest miner model

Fig. 8 Scenario 3 of honest miner model

Fig. 9 Scenario 4 of honest miner model

Fig. 10 Scenario 5 of honest miner model

Fig. 11 State transition diagram

Fig. 12 Verifying Feng's model is a special case of proposed model

Fig. 13 Relative revenues of selfish mining pools and fork rates under different computing power

Fig. 14 System stable block rates and fork rates of single/double selfish miners under different computing power

Fig. 15 System throughput and fork rates of single/double selfish miners under different computing power

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Markov chain model and profit analysis of two-selfish-miner strategy in ethereum classic network

以太坊经典网络双自私矿工策略的马尔可夫链模型与收益分析

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