As one of the most popular cryptocurrencies, Bitcoin is essentially a decentralized ledger. Each node maintains the security of the blockchain through the workload proof mechanism, and the block that obtains the accounting right will receive a block reward in the form of Bitcoin. Because the Bitcoin system follows the “longest legal chain” principle, when a fork occurs, orphan blocks will inevitably be generated, and some miners’ computing power will be a waste. In recent years, researchers have discovered that miners can obtain profits disproportionate to their own computing power by deviating from Bitcoin’s honest mining. Selfish Mining (SM1) is a case in dishonest mining strategy, and dishonest miners (attackers) can obtain higher returns by retaining the blocks they create and selectively delaying their release. The stubborn mining strategy is a generalized form of selfish mining. It increases the revenue of the stubborn miner by adopting a wider range of parameters. Its three mining strategies are: Lead-Stubborn, Equal Fork stubborn and Trail stubborn.

The mining problem can be formulated as a Markov Decision Process (MDP), which can be resolved to give the optimal mining strategy. This work describes the three mining strategies of stubborn mining as a Markov decision process, solves it and gives the lower bound of the highest return under the optimal stubborn mining strategy. Our experimental results demonstrate that the revenue of the optimal stubborn mining strategy is higher than SM1 under certain circumstances, and this strategy allows dishonest miners (stubborn miners) to obtain revenue that does not match the actual computing power paid.

This study is supported by the Foundation of National Natural Science Foundation of China (Grant No.: 62072273, 72111530206, 61962009, 61873117, 61832012, 61771231, 61771289); The Major Basic Research Project of Natural Science Foundation of Shandong Province of China (ZR2019ZD10); Natural Science Foundation of Shandong Province (ZR2019MF062); Shandong University Science and Technology Program Project (J18A326); Guangxi Key Laboratory of Cryptography and Information Security (No: GCIS202112); The Major Basic Research Project of Natural Science Foundation of Shandong Province of China (ZR2018ZC0438); Major Scientific and Technological Special Project of Guizhou Province (20183001), Foundation of Guizhou Provincial Key Laboratory of Public Big Data (No. 2019BD-KFJJ009), Talent project of Guizhou Big Data Academy. Guizhou Provincial Key Laboratory of Public Big Data. ([2018]01).

Authors and Affiliations

1. School of Computer Science, Qufu Normal University, Rizhao, China

   Yiting Zhang, Ming Liu, Jianan Guo, Zhaojie Wang & Yilei Wang

2. China Institute of Artificial Intelligence and Blockchain, Guangzhou University, Guangzhou, China

   Tiancai Liang

3. CCET, Panjab University, Chandigarh, India

   Sunil Kumar Singh

Corresponding author

Correspondence toYilei Wang.

Editors and Affiliations

1. School of Computing and Informatics, University of Louisiana at Lafayette, Lafayette, IN, USA

   Yuan Xu

2. Institute of Artificial Intelligence and Blockchain, Guangzhou University, Guangzhou, China

   Hongyang Yan

3. Institute of Artificial Intelligence and Blockchain, Guangzhou University, Guangzhou, China

   Huang Teng

4. Guangdong Polytechnic Normal University, Guangzhou, China

   Jun Cai

5. Institute of Artificial Intelligence and Blockchain, Guangzhou University, Guangzhou, China

   Jin Li

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