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Bitcoin, the most popular cryptocurrency used in the blockchain, has miners join mining pools and get rewarded for the proportion of hash rate they have contributed to the mining pool. This work proposes the prediction of the relativegain of the miners by machine learning and deep learning models, the miners' selection of higher relativegain by the Q‐learning model, and an optional stopping theorem for honest miners in the presence of selfish mining attacks. Relativegain is the ratio of the number of blocks mined by selfish miners in the main canonical chain to the blocks of other miners. A Q‐learning agent with ε$\epsilon$‐greedy value iteration, which seeks to increase the relativegain for the selfish miners, that takes into account all the other quintessential parameters, including the hash rate of miners, time warp, the height of the blockchain, the number of times the blockchain was reorganized, and the adjustment of the timestamp of the block, is implemented. Next, the ruin of the honest miners and the optional stopping theorem are analyzed so that the honest miners can quit the mining process before their complete ruin. We obtain a low mean square error of 0.0032 and a mean absolute error of 0.0464 in our deep learning model. Our Q‐learning model exhibits a linearly increasing curve, which denotes the increase in the relativegain caused by the selection of the action of performing the reorganization attack. [ABSTRACT FROM AUTHOR]

Blockchain technology, with its decentralized nature, offers a more secure, reliable, and transparent solution for the Internet of Things (IoT). However, directly deploying existing consensus protocols in many IoT environments can limit scalability, lead to high computational costs and delays, and fail to meet the high responsiveness required for network communication. Additionally, IoT devices vary widely in performance, and lower-performance devices participating as nodes in a decentralized network may not be able to meet the demands of the consensus process, resulting in consensus delays and decreased system stability. This proposal introduces an improved consensus protocol called Ghost-Weight, based on the original Ghost protocol, designed to accommodate the performance-heterogeneous IoT environment with frequent information exchanges. Ghost-Weight introduces the concept of a Dominant Block, which, through a mechanism called the Confinement Edge, incorporates forked blocks within the network in a graph-based manner. The ForkBlock Process then organizes these blocks, removes conflicting transactions, and ultimately achieves global consensus based on weight before publishing them to the network. Furthermore, the protocol proposes a node partitioning strategy, ensuring that devices of all performance levels can participate in the consensus process. Through experiments and theoretical comparisons, we demonstrate that this protocol achieves a 52% increase in throughput, a 23% improvement in transaction confirmation time, and a 56% higher efficiency in processing forked blocks compared to the original Ghost protocol. We also designed a series of experiments to showcase Ghost-Weight’s success in resisting selfish mining attacks and balancing attacks. This proposal effectively addresses the challenge of deploying consensus mechanisms in performance-heterogeneous IoT environments with high responsiveness requirements. Compared to previous designs, it significantly improves network scalability, transaction speed, network efficiency, and overall reliability. [ABSTRACT FROM AUTHOR]

Selfish mining is when a group of miners in a blockchain system work together to cheat and get more rewards by hiding their work from others. This attack makes the blockchain less secure by allowing miners to cheat together, leading to more fraud and less trustworthy transactions. It's very unfair for honest miners, and it's a big problem that needs to be stopped. Despite numerous attempts to prevent selfish mining, none of the existing methods can completely prevent the attack. As prevention is better than detecting or mitigating the selfish mining attack, our main intention is to prevent the selfish mining attack completely without wasting the time and computational power of honest miners. Therefore, we propose a novel method to prevent the attack by adding a "BA: block acceptance" flag in the block header. The key idea of our method is that each block must be broadcast and accepted to set the flag to true. If the flag is false, we cannot use the hash of that block to mine a new block. This ensures that selfish miners cannot build a chain secretly to create branches in the blockchain (a fork). By preventing accidental and intentional forks, we have proven that the probability of a selfish mining attack occurring is zero. We proved our methodology resilient to the selfish mining attack in theoretically. Overall, our proposed method offers a promising solution to prevent selfish mining attacks. [ABSTRACT FROM AUTHOR]

Bitcoin’s core security requires honest participants to control at least 51% of the total hash power. However, it has been shown that several techniques can exploit the fair mining in the Bitcoin network. This study focuses on selfish mining, which is based on the idea, ”keeping blocks secret.” Herein, we analyze selfish mining regarding competition between mining pools. We emphasize that mining-related information is shared between mining pools and participants. Based on shared information about selfish mining, we have developed an effective and practical counter strategy.

Selfish mining is an attack strategy in Proof-of-Work based blockchains, where attackers withhold their mined blocks to intercept the awards of other honest miners, resulting in higher profitability.This attack undermines the incentive compatibility of Proof-of-Work.Although there are various studies from researchers in recent years, there is no effective detection scheme as the vulnerability of blockchain in propagation delay makes it challenging to distinguish the attackers from honest miners.A scheme for selfish mining detection was introduced.In this scheme, a state value was assigned to the new block based on transaction amount and the transaction fee of the block.By analyzing the relationship between state value and transaction characteristics, we can determine if the block was mined by a selfish miner.The scheme is verified by an experiment with an accuracy of 86.02%.

Bitcoin is the most popular cryptocurrency and it uses proof of work protocol for consensus of all transactions in a block. The blocks are to be appended to the digital ledger, the blockchain. The miners compete for the mining of blocks in the main canonical blockchain. A miner can participate in block mining either individually with his computational power or join a mining pool. Here, the classification of crypto address, whether it belongs to a mining pool or an individual miner, is done with a deep learning Keras framework. The classification accuracy of 99.47% is obtained with 100,000 addresses which is higher than the machine learning random forest classification obtained by Kaggle with 22,000 addresses. The miners in mining pools deploy selfish mining or honest mining to mine a block and get the reward accordingly. In block mining, both honest and selfish miners expose the blocks produced by them. The default protocol of the main canonical blockchain leads to the selection of the longest branch of blocks of the selfish miner, discarding the honest miner's block. To alleviate this, we deploy a reinforcement learning algorithm to choose the block with high upper confidence bound value. This selection explores the branch exposed by honest miners. The algorithm is deployed after the first difficulty adjustment algorithm, where there is more selfish mining activity. Our promising results show that the main blockchain exhibits less regret by selecting the honest miner's branch. [ABSTRACT FROM AUTHOR]

This paper proposes a variant of the recently reported pool mining approach and provides a reduction in the energy that is consumed by the blockchain consensus protocol. The novelty of the proposed architecture lies in the employment of an innovative cryptographic puzzle that is based on stream ciphering. This enables flexibility in setting the difficulty parameter of the protocol, and allows for the separation of the energy and memory resources that are required for the puzzle solving. The proposed approach provides high resistance against the following malicious activities of miners in public blockchain systems: (i) the submission of fake work and fictitious computation results; and (ii) some well-known attacks that target the blockchain incentive mechanism. We experimentally evaluate the power consumption of the proposed consensus protocol and compare it with the traditional proof-of-work protocol based on hashing. The obtained results point out the gain that the proposed pool mining provides compared with the traditional types. [ABSTRACT FROM AUTHOR]

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To securely integrate Mobile Edge Computing (MEC) into Wireless Blockchain Network (WBN), this paper proposes a framework for blockchain based offloading strategy, where blockchain nodes are categorized as blockchain users and blockchain miners from a motivation perspective. Particularly, aiming at improving the motivation ability, a block generation process is first designed for blockchain miners’ short transaction processing time lower bound. Then, to further maximize the utilities of both blockchain users and blockchain miners, an optimization problem is formulated to determine an optimal strategy which involves a trade-off between the fast transaction confirmation rate required by blockchain users and the transaction fees obtained by blockchain miners. A Stackelberg game is introduced to model the interaction between the blockchain users and miners. Meanwhile, a distributed algorithm is designed to converge this strategy in an iterative manner based on the buyer-seller negotiation. Additionally, double-spending attack and selfish mining attack are analysed to examine their impact on the system performance in terms of confirmation delay and throughput while guaranteeing the high security level. Finally, extensive experiments have been conducted to show the rightness and effectiveness of the proposed equilibrium-based strategy and mathematical analysis, and some insights are discussed for the further guide as well. [ABSTRACT FROM AUTHOR]

The security and fairness of blockchain are always threatened by selfish mining attacks. To study such selfish mining attacks, some necessary and useful methods need to be developed sufficiently. In this paper, we provide an interesting method for analyzing dynamic decision of blockchain selfish mining by applying the sensitivity-based optimization. Our goal is to find the optimal dynamic blockchain-pegged mining policy of the dishonest mining pool. To this end, we consider a blockchain system with two mining pools: the honest and the dishonest mining pools, where the honest mining pool follows a two-block leading competitive criterion, while the dishonest mining pool follows a modification of two-block leading competitive criterion. To find the optimal blockchain-pegged mining policy, we develop the sensitivity-based optimization to study dynamic decision of blockchain system through setting up a policy-based Poisson equation, and provide an expression for the unique solution of performance potentials. Based on this, we can characterize monotonicity and optimality of the long-run average profit with respect to the blockchain-pegged mining reward. Also, we prove the structure of the optimal blockchain-pegged mining policy. The methodology and results derived in this paper significantly reduce the large search space of finding the optimal policy, thus they can shed light on the optimal dynamic decision research on the selfish mining attacks of blockchain systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As a kind of distributed, decentralized and peer-to-peer transmitted technology, blockchain technology has gradually changed people's lifestyle. However, blockchain technology also faces many problems including selfish mining attack, which causes serious effects to the development of blockchain technology. Selfish mining is a kind of mining strategy where selfish miners increase their profit by selectively publishing hidden blocks. This paper builds the selfish mining model from the perspective of node state conversion and utilize the function extremum method to figure out the optimal profit of this model. Meanwhile, based on the experimental data of honest mining, the author conducts the simulation of selfish mining and discovers that selfish miners are able to acquire more revenue than honest miners when they account for more than 1/3 computing power of the whole system. Lastly, to defend the selfish mining attack, the author also summarizes the existing defending strategies and evaluates every kind of strategy briefly. [ABSTRACT FROM AUTHOR]

In blockchain-based systems whose consensus mechanisms resort to Proof-of-Work (PoW), it is expected that a miner’s share of total block revenue is proportional to their share of hashing power with respect to the rest of the network. The protocol relies on the immediate broadcast of blocks by miners, to earn precedence in peers’ local blockchains. However, a deviation from this strategy named selfish mining (SM), may lead miners to earn more than their “fair share”. In this paper, we introduce an agent-based model to simulate the dynamics of SM behaviour by a single miner as well as mining pools to understand the influence of (a) mining power distribution, (b) overlay network topology, (c) positioning of the selfish nodes within the peer to peer network. Our minimalistic model allows us to find that in high levels of latency, SM is always a more profitable strategy; our results are very robust to different network topologies and mining nodes’ centrality in the network. Moreover, the power-law distribution of the miners’ hashing power can make it harder for a selfish miner to be profitable. In addition, we analyze the effect of SM on system global efficiency and fairness. Our analysis confirms that SM is always more profitable for hashing powers representing more than one-third of the total computing power. Further, it also confirms that SM behaviour could cause a statistically significant high probability of continuously mined blocks opening the door for empirical verification of the phenomenon.

Blockchain technology has gained prominence over the last decade. Numerous achievements have been made regarding how this technology can be utilized in different aspects of the industry, market, and governmental departments. Due to the safety-critical and security-critical nature of their uses, it is pivotal to model the dependability of blockchain-based systems. In this study, we focus on Bitcoin, a blockchain-based peer-to-peer cryptocurrency system. A continuous-time Markov chain-based analytical method is put forward to model and quantify the dependability of the Bitcoin system under selfish mining attacks. Numerical results are provided to examine the influences of several key parameters related to selfish miners’ computing power, attack triggering, and honest miners’ recovery capability. The conclusion made based on this research may contribute to the design of resilience algorithms to enhance the self-defense and robustness of cryptocurrency systems.

We explored mined block temporarily holding (MBTH), MBTH with enforce fork (MBTH-EF), and intermittent MBTH-EF (iMBTH-EF) attacks to understand the effect of selfish mining on winning rate and fairness from the pool operation perspective. The temporary holding time of the current mined block provides a pool additional time to begin mining the next block early with MBTH attack. In this situation, the winning probability increases for the next block, but the pool may risk losing the mined block. One enhanced method to maintain the winning probability of the held block is to ensure the holding pool sends out the mined block once it receives the mined block message from the other pools with the MBTH-EF attack. The explored MBTH attacks differ from the existing selfish miner and pool attacks. The operations and effects of the MBTH-EF attack are different from stubborn mining strategies and a self-holding attack integrates selfish and stubborn mining attacks. We propose a mining competition solution that does not involve actual hash calculation. It entails using one stochastic target hash value for batch racing simulation to evaluate the holding threshold, holding periods, mining time, mining difficulty, pool sizes, and the rate of fork occurrences according to the operation data of the Bitcoin system. Accordingly, the dynamic time-by-time, block-by-block, and pool-by-pool simulations are adopted to study these attacks. We analyzed MBTH and MBTH-EF attacks as well as evaluated the effects of the win rate on when and how long a block is held. Because the periodic adjustment of mining difficulty reduces the holding effect, we further evaluated how an intermittent MBTH-EF (iMBTH-EF) attack model balance the average mining time and mining difficulty according to the mining difficulty adjustment of a stage. The effect of intermittent holding is examined on the mining game win rate for a long-term competition. We also identified suitable attack detection methods for the future work according to the simulation results.

This paper proposes an approach for pool mining in public blockchain systems based on the employment of a recently reported consensus protocol with the puzzle based on a symmetric encryption that provides an energy–space trade-off and reduces energy consumption. The proposed architecture employs a pseudo-symmetric allocation of the resources for the blockchain consensus protocol and provides protection against certain malicious actions of the pool members, as well as a miner's opportunity for selecting the resources required for participation in the consensus protocol. Given that the considered consensus protocol employs two resources, the proposed architecture uses this two-dimensional nature to provide resistance against block withholding and selfish mining attacks, as well as a reduction in energy spending as a trade-off with the employment of certain memory resources. The high resistance of the proposed pool mining approach against the considered attacks appears to be a consequence of the success probability of the pool in comparison with the success probability of malicious miners. Assuming appropriate selection of the puzzle hardness, the probability that malicious miners can solve the puzzle without the support of the pool manager can be arbitrarily small. Implementation of the proposed approach on a modified Ethereum platform and experimental evaluation issues have also been reported. The conceptual novelty of the proposed pool mining approach is the following: Instead of separation of the blockchain consensus protocol and control of pool miners honest work, this paper proposes an approach where honest work of miners and pool managers is provided by a dedicated application of the considered consensus protocol. Advantages of the proposal in comparison with the previously reported ones include the following: (i) high resistance against block withholding and selfish mining attacks without an additional security procedure; (ii) reduction in the energy required, and at the same time preservationthe security of the consensus protocol; (iii) flexibility of the pool miners regarding selection of the resources that should be employed providing a trade-off between required energy and memory resources. The proposed architecture was implemented employing a dedicated modification of the Ethereum platform and the performed experiments confirmed the feasibility and effectiveness of the proposal. [ABSTRACT FROM AUTHOR]

Bitcoin is the first fully decentralized cryptocurrency. The security features of Bitcoin rely on blockchain technology, which comprises each current as well as the past transactions in the system. In a blockchain when more than one block extends from the same preceding block, the situation is termed as fork or Block race. A selfish miner abuses Bit coin's forks method to gain several unfair rewards. To tackle the issues caused by selfish mining, this work proposes a novel scheme called "Towards the Rear Attuned Defense Scheme". Accordingly, to identify the presence of selfish miners, the Newfangled selfish mining revelation algorithm with a Fork Tenacity Strategy is used here. A weighted fork with a secured fail parameter is established here to compete with the block race caused by the selfish miner. Finally, to ensure reliability, a Slice-up Tender mint consensus protocol is used. Thus, our proposed scheme ensures a better defense against the selfish mining attacks and achieves better time convergence with less electricity fee. [ABSTRACT FROM AUTHOR]

In this paper, we focus on mining attacks targeting the Proof of Work (PoW) consensus mechanism in blockchain-based systems. Specifically, we model mining as a game and propose a mining attack – the Selfish mining-based denial of service (SDoS) attack. By studying the choices (mining or stopping) of honest miners under the attack and the adversary’s revenue, we demonstrate that selfish mining is incentive-compatible with game-level denial of service attack, and that SDoS can be more threatening than existing mining attacks. Even under the worst assumption, the adversary only needs to master more than 19.6% of the total mining power to increase the revenue, and can launch a 51% attack with much less than 50%. In addition, we show that honest miners may make decisions based on the overall or current utility, and choosing the current utility is more beneficial to the adversary. [ABSTRACT FROM AUTHOR]

The longest-chain and Greedy Heaviest Observed Subtree (GHOST) protocols are the two most famous chain-selection protocols to address forking in Proof-of-Work (PoW) blockchain systems. Inclusive protocol was proposed to lower the loss of miners who produce stale blocks and increase the blockchain throughput. This paper aims to make an analytical-model-based quantitative comparison of their capabilities against selfish mining attack. Analytical models have been developed for the longest-chain protocol but less to the GHOST protocol. However, the blockchain dynamics and evolution are different when adopting different chain-selection protocols. Therefore, the corresponding analytical models and/or the formulas of calculating metrics (such as miner profitability and system throughput) may be different. To address these challenges, this paper first develops a novel Markov model and the formulas of evaluation metrics, in order to analyze a GHOST-based blockchain system under selfish mining attack. Then extensive experiments are conducted for comparison and we observe that: (i) The GHOST protocol is more resistant to selfish mining attack than the longest-chain protocol from the aspect of relative revenue of selfish miners. (ii) Inclusive protocol can promote the security (evaluated in terms of miner profitability) improvement of the system which has little total computational power or a high forking probability. Additionally, the longest-chain protocol is more sensitive to inclusive protocol than GHOST protocol. (iii) It is hard for each of the two common-used difficulty adjustment algorithms to achieve higher system throughput and security. [ABSTRACT FROM AUTHOR]

In blockchain-based systems whose consensus mechanisms resort to Proof-of-Work (PoW), it is expected that a miner's share of total block revenue is proportional to their share of hashing power with respect to the rest of the network. The protocol relies on the immediate broadcast of blocks by miners, to earn precedence in peers' local blockchains. However, a deviation from this strategy named selfish mining (SM), may lead miners to earn more than their "fair share". In this paper, we introduce an agent-based model to simulate the dynamics of SM behaviour by a single miner as well as mining pools to understand the influence of (a) mining power distribution, (b) overlay network topology, (c) positioning of the selfish nodes within the peer to peer network. Our minimalistic model allows us to find that in high levels of latency, SM is always a more profitable strategy; our results are very robust to different network topologies and mining nodes' centrality in the network. Moreover, the power-law distribution of the miners' hashing power can make it harder for a selfish miner to be profitable. In addition, we analyze the effect of SM on system global efficiency and fairness. Our analysis confirms that SM is always more profitable for hashing powers representing more than one-third of the total computing power. Further, it also confirms that SM behaviour could cause a statistically significant high probability of continuously mined blocks opening the door for empirical verification of the phenomenon. [ABSTRACT FROM AUTHOR]

This paper proposes a variant of the recently reported pool mining approach and provides a reduction in the energy that is consumed by the blockchain consensus protocol. The novelty of the proposed architecture lies in the employment of an innovative cryptographic puzzle that is based on stream ciphering. This enables flexibility in setting the difficulty parameter of the protocol, and allows for the separation of the energy and memory resources that are required for the puzzle solving. The proposed approach provides high resistance against the following malicious activities of miners in public blockchain systems: (i) the submission of fake work and fictitious computation results; and (ii) some well-known attacks that target the blockchain incentive mechanism. We experimentally evaluate the power consumption of the proposed consensus protocol and compare it with the traditional proof-of-work protocol based on hashing. The obtained results point out the gain that the proposed pool mining provides compared with the traditional types.

In this paper, we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting. We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism. Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent, and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix. Also, we use the stationary probability vector to study the influence of orphan blocks on the waste of computing resource. Next, we set up a pyramid Markov reward process to investigate the long-run average mining profits of the honest and dishonest mining pools, respectively. As a by-product, we build one-dimensional Markov reward processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer (2014). Note that the pyramid Markov (reward) processes can open up a new avenue in the study of blockchain selfish mining. Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially. [ABSTRACT FROM AUTHOR]

Ethereum accelerates the transaction process through a quicker block creation design. Since the time interval between the generation of blocks is very short (about 15s), block propagation time in an inefficient network is not negligible compared with the block time interval. This lead to the production of a large number of orphan blocks. In order to solve the security problems that may be caused by the orphan block and improve the transaction processing efficiency, Ethereum introduces the uncle block mechanism, i.e., an orphan block may get part of minted reward if it gets a reference by a regular block. In this paper, we show the weakness of the uncle block mechanism. Firstly, we describe the specific differences of Ethereum selfish and stubborn mining in every state from the ones in Bitcoin. Secondly, we simulate possible attacks, and the results show that the Ethereum selfish and stubborn mining strategies not only increase the reward of an attacker but also decrease the security threshold. The security threshold refers to the proportion of the attacker's computational power that needs to be achieved in order to obtain a higher reward than he should. In a practical network congestion rate, the security threshold are weakened to 0.129 and 0.216 against the Lead stubborn mining strategy and the original selfish mining strategy, respectively. When the congestion rate is rising, the reward is increasing and the threshold is decreasing. Thirdly, possible strategies are evaluated to find out the optimal one in different settings. Fourthly, we also extend the evaluation by combining three eclipse attack strategies with selfish or stubborn mining. Most of combinations bring more advantages to an attacker than a single strategy.

Selfish mining is a typical malicious attack targeting the blockchain-based bitcoin system, an emerging crypto asset. Because of the non-incentive compatibility of the bitcoin mining protocol, the attackers are able to collect unfair mining rewards by intentionally withholding blocks. The existing works on selfish mining mostly focused on cryptography design, and malicious behavior detection based on different approaches, such as machine learning or timestamp. Most defense strategies show their effectiveness in the perspective of reward reduced. No work has been performed to design a defense strategy that aims to improve bitcoin dependability and provide a framework for quantitively evaluating the improvement. In this paper, we contribute by proposing two network-wide defensive strategies: the dynamic difficulty adjustment algorithm (DDAA) and the acceptance limitation policy (ALP). The DDAA increases the mining difficulty dynamically once a selfish mining behavior is detected, while the ALP incorporates a limitation to the acceptance rate when multiple blocks are broadcast at the same time. Both strategies are designed to disincentivize dishonest selfish miners and increase the system’s resilience to the selfish mining attack. A continuous-time Markov chain model is used to quantify the improvement in bitcoin dependability made by the proposed defense strategies. Statistical analysis is applied to evaluate the feasibility of the proposed strategies. The proposed DDAA and ALP methods are also compared to an existing timestamp-based defense strategy, revealing that the DDAA is the most effective in improving bitcoin’s dependability.

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. [ABSTRACT FROM AUTHOR]