Selfish mining attacks sabotage the blockchain systems by utilizing the vulnerabilities of consensus mechanism. The attackers' main target is to obtain higher revenues compared with honest parties. More specifically, the essence of selfish mining is to waste the power of honest parties by generating a private chain. However, these attacks are not practical due to high forking rate. The honest parties may quit the blockchain system once they detect the abnormal forking rate, which impairs their revenues. While selfish mining attacks make no sense anymore with the honest parties' departure. Therefore, selfish miners need to restrain when launch selfish mining attacks such that the forking rate is not preposterously higher than normal level. The crux is how to illustrate the attacks toward the view of honest parties, who are blind to the private chain. Generally, previous works, especially those using Markov decision processes, stress on the increment of attackers' revenues, while overlooking the detection on forking rate. In this paper, we propose, to maintain the benefit from selfish mining, an improved selfish mining based on hidden Markov decision processes (SMHMDP). To reduce the forking rate, we also relax the behaviors of selfish miners (also known as semi-selfish miners), who mine on the private chain, to mine on public chain with a small

Selfish mining attacks get a high prize due to the additional rewards unproportionate to their mining power (mining pools have particular advantages). Generally, this category of attacks stresses decreasing the threshold to maximize the rewards toward the view of attackers. Semi‐selfish mining falls into the family of selfish mining attacks, where the threshold value is approximately 15%. However, it gets little attention to implement these attacks in practical. In this paper, we focus on the validity of semi‐selfish mining attacks considering the probability of being detected. More specifically, we discuss mining strategies through backward deduction. That is to say that the attacking states derived from the observable states, which with normal forking rate, just as without semi‐selfish mining attacks, toward the view of the honest miners. Rewards distribution is further investigated concerning these strategies. The simulation results indicate that it does not necessarily bring rewards advantage over large pools. Instead, the small pools have an advantage over the additional rewards. However, the probability for small pools to successfully implement these strategies is pretty low. That is, it is impossible for the pools, although profitable for them, to sponsor semi‐selfish mining attacks without being detected.

vMixing coins strategy can realize the anonymity of user information, thereby protecting the user's privacy. Ideally, the blacklist is public information and all bad coins are recorded in it. However, due to the failure of some bad

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