Abstract
Selfish mining is an attack on the integrity of a blockchain network. Inspired by J. Göbel’s selfish mining model in the presence of propagation delay, we propose a competition model based on spatial Poisson process to study how delay influences the revenue distribution when there are more than one selfish miners. Based on our model, we derive the exact expression of the revenue distribution, and prove that the difference of propagation delays between two selfish miners significantly affects the distribution of mining rewards. Additionally, we find that the required threshold of the mining power for multiple selfish miners is larger than that for a single one. Finally, we discuss how the propagation delay impacts the state transfer machine of each selfish miner.
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References
Yu K, Tan L, Aloqaily M, Yang H, Jararweh Y (2021) Blockchain-enhanced data sharing with traceable and direct revocation in iiot. IEEE Transactions on Industrial Informatics
Yu K, Tan L, Shang X, Huang J, Srivastava G, Chatterjee P (2020) Efficient and privacy-preserving medical research support platform against covid-19: A blockchain-based approach. IEEE Consumer Electronics Magazine
Shi N, Tan L, Li W, Qi X, Yu K (2020) A blockchain-empowered aaa scheme in the large-scale hetnet. Digital Communications and Networks
Feng C, Yu K, Aloqaily M, Alazab M, Lv Z, Mumtaz S (2020) Attribute-based encryption with parallel outsourced decryption for edge intelligent iov. IEEE Trans Veh Technol 69(11):13784–13795
Iansiti M, Lakhani K (2017) The truth about blockchain. Harvard Business Review 95:118–127
Wang W, Hoang D T, Xiong Z, Niyato D, Wang P, Hu P, Wen Y (2018) A survey on consensus mechanisms and mining management in blockchain networks. CoRR arXiv:abs/1805.02707
Nakamoto S et al (2008) Bitcoin. A peer-to-peer electronic cash system
Eyal I, Sirer E G (2018) Majority is not enough: Bitcoin mining is vulnerable. Commun ACM 61(7):95–102
Göbel J, Keeler HP, Krzesinski AE, Taylor PG (2016) Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay. Perform Eval 104:23–41
Kingman JFC (2005) Poisson processes. Encyclopedia of biostatistics 6
Bastiaan M (2015) Preventing the 51%-attack: a stochastic analysis of two phase proof of work in bitcoin. In: Availab le at http://referaat.cs.utwente.nl/conference/22/paper/7473/preventingthe-51-attack-a-stochasticanalysis-oftwo-phase-proof-of-work-in-bitcoin.pdf
Saad M, Njilla L, Kamhoua C, Mohaisen A (2019) Countering selfish mining in blockchains. In: 2019 International conference on computing, networking and communications (ICNC), IEEE, pp 360–364
Sapirshtein A, Sompolinsky Y, Zohar A (2016) Optimal selfish mining strategies in bitcoin. In: International conference on financial cryptography and data security, Springer, pp 515–532
Hou C, Zhou M, Ji Y, Daian P, Tramèr F, Fanti G, Juels A (2019) Squirrl: Automating attack discovery on blockchain incentive mechanisms with deep reinforcement learning. CoRR arXiv:abs/1912.01798
Baccelli F, Norros I, Mathieu F (2011) Performance of p2p networks with spatial interactions of peers. RR-771, arXiv:1108.4129: 3
Decker C, Wattenhofer R (2013) Information propagation in the bitcoin network. In: IEEE P2P 2013 Proceedings, IEEE, pp 1–10
Donet JAD, Pérez-Sola C, Herrera-Joancomartí J (2014) The bitcoin p2p network. pp 87–102
Aoki Y, Otsuki K, Kaneko T, Banno R, Shudo K (2019) Simblock: A blockchain network simulator. In: IEEE INFOCOM 2019-IEEE conference on computer communications workshops, INFOCOM WKSHPS, IEEE, pp 325–329
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This work is sponsored by the National Natural Science Foundation of China under contract No. 61976142.
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This article belongs to the Topical Collection: Special Issue on Blockchain for Peer-to-Peer Computing
Guest Editors: Keping Yu, Chunming Rong, Yang Cao, and Wenjuan Li
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Wang, H., Yan, Q. & Leung, V.C.M. The impact of propagation delay to different selfish miners in proof-of-work blockchains. Peer-to-Peer Netw. Appl. 14, 2735–2742 (2021). https://doi.org/10.1007/s12083-021-01087-5
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DOI: https://doi.org/10.1007/s12083-021-01087-5