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 many orphan blocks on the waste of computing resource. Next, we set up a pyramid Markov reward process to investigate the long-run average profits of the honest and dishonest mining pools, respectively. As a by-product, we build three approximative Markov 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.
In this paper, we provide a novel dynamic decision method of blockchain selfish mining by applying the sensitivity-based optimization theory. Our aim is to find the optimal dynamic blockchain-pegged policy of the dishonest mining pool. To study the selfish mining attacks, two mining pools is designed by means of different competitive criterions, 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 through using a blockchain-pegged policy. To find the optimal blockchain-p…
Selfish mining is a well known vulnerability in blockchains exploited by miners to steal block rewards. In this paper, we explore a new form of selfish mining attack that guarantees high rewards with low cost. We show the feasibility of this attack facilitated by recent developments in blockchain technology opening new attack avenues. By outlining the limitations of existing countermeasures, we highlight a need for new defense strategies to counter this attack, and leverage key system parameters in blockchain applications to propose an algorithm that enforces fair mining. We use the expected t…
This paper studies a fundamental problem regarding the security of blockchain on how the existence of multiple misbehaving pools influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it public opportunistically for the purpose of acquiring more rewards incommensurate to his Hashrate. We establish a novel Markov chain model to characterize all the state transitions of public and private chains. The minimum requirement of Hashrate together with the minimum delay of being profitable is derived in close-form. The former reduces to 21.48% with the sy…
In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, we study the effect of propagation delay on the evolution of the Bitcoin blockchain. First, we use a simplified Markov model that tracks the contrasting states of belief about the blockchain of a small pool of miners and the `rest of the community' to establish that the use of block-hiding strategies, such as selfish-mine, causes the rate of production of orphan blocks to increase. Then we use a spatial Poisson process model to study values of Eyal and Sirer's parameter $γ$, which denotes the proportion of the honest com…
Mining blocks on a blockchain equipped with a proof of work consensus protocol is well-known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. This paper aims at quantifying the profitability of mining when the possible event of ruin is also considered. This is done by formulating a tractable stochastic model and using tools from applied probability and analysis, including the explicit solution of a certain type of advanced functional differential equation. The ex…
Towards Secure Decentralized Applications and Consensus Protocols in Blockchains (on Selfish Mining, Undercutting Attacks, DAG-Based Blockchains, E-Voting, Cryptocurrency Wallets, Secure-Logging, and CBDC)
Most public blockchain protocols, including the popular Bitcoin and Ethereum blockchains, do not formally specify the order in which miners should select transactions from the pool of pending (or uncommitted) transactions for inclusion in the blockchain. Over the years, informal conventions or "norms" for transaction ordering have, however, emerged via the use of shared software by miners, e.g., the GetBlockTemplate (GBT) mining protocol in Bitcoin Core. Today, a widely held view is that Bitcoin miners prioritize transactions based on their offered "transaction fee-per-byte." Bitcoin users are…
One major shortcoming of permissionless blockchains such as Bitcoin and Ethereum is that they are unsuitable for running Computationally Intensive smart Contracts (CICs). This prevents such blockchains from running Machine Learning algorithms, Zero-Knowledge proofs, etc. which may need non-trivial computation. In this paper, we present YODA, which is to the best of our knowledge the first solution for efficient computation of CICs in permissionless blockchains with guarantees for a threat model with both Byzantine and selfish nodes. YODA selects one or more execution sets (ES) via Sortition to…
Proof-of-Work blockchain, despite its numerous benefits, is still not an entirely secure technology due to the existence of Selfish Mining (SM) strategies that can disrupt the system and its mining economy. While the effect of SM has been studied mostly in a two-miners scenario, it has not been investigated in a more practical context where there are multiple malicious miners individually performing SM. To fill this gap, we carry out an empirical study that separately accounts for different numbers of SM miners (who always perform SM) and strategic miners (who choose either SM or Nakamoto's mi…
Bitcoin and Ethereum are the top two blockchain-based cryptocurrencies whether from cryptocurrency market cap or popularity. However, they are vulnerable to selfish mining and stubborn mining due to that both of them adopt Proof-of-Work consensus mechanism. In this paper, we develop a novel Markov model, which can study selfish mining and seven kinds of stubborn mining in both Bitcoin and Ethereum. The formulas are derived to calculate several key metrics, including relative revenue of miners, blockchain performance in terms of stale block ratio and transactions per second, and blockchain secu…
A proof of work (PoW) blockchain protocol distributes rewards to its participants, called miners, according to their share of the total computational power. Sufficiently large miners can perform selfish mining - deviate from the protocol to gain more than their fair share. Such systems are thus secure if all miners are smaller than a threshold size so their best response is following the protocol. To find the threshold, one has to identify the optimal strategy for miners of different sizes, i.e., solve a Markov Decision Process (MDP). However, because of the PoW difficulty adjustment mechanism…
Incentive mechanisms are central to the functionality of permissionless blockchains: they incentivize participants to run and secure the underlying consensus protocol. Designing incentive-compatible incentive mechanisms is notoriously challenging, however. As a result, most public blockchains today use incentive mechanisms whose security properties are poorly understood and largely untested. In this work, we propose SquirRL, a framework for using deep reinforcement learning to analyze attacks on blockchain incentive mechanisms. We demonstrate SquirRL's power by first recovering known attacks: …
In this paper, we systematically explore the attack surface of the Blockchain technology, with an emphasis on public Blockchains. Towards this goal, we attribute attack viability in the attack surface to 1) the Blockchain cryptographic constructs, 2) the distributed architecture of the systems using Blockchain, and 3) the Blockchain application context. To each of those contributing factors, we outline several attacks, including selfish mining, the 51% attack, Domain Name System (DNS) attacks, distributed denial-of-service (DDoS) attacks, consensus delay (due to selfish behavior or distributed…
Many of today's crypto currencies use blockchains as decentralized ledgers and secure them with proof of work. In case of a fork of the chain, Bitcoin's rule for achieving consensus is selecting the longest chain and discarding the other chain as stale. It has been demonstrated that this consensus rule has a weakness against selfish mining in which the selfish miner exploits the variance in block generation by partially withholding blocks. In Ethereum, however, under certain conditions stale blocks don't have to be discarded but can be referenced from the main chain as uncle blocks yielding a …
The selfish mining attack, arguably the most famous game-theoretic attack in blockchain, indicates that the Bitcoin protocol is not incentive-compatible. Most subsequent works mainly focus on strengthening the selfish mining strategy, thus enabling a single strategic agent more likely to deviate. In sharp contrast, little attention has been paid to the resistant behavior against the selfish mining attack, let alone further equilibrium analysis for miners and mining pools in the blockchain as a multi-agent system. In this paper, first, we propose a strategy called insightful mining to counterac…
GHOST, like the longest-chain protocol, is a chain selection protocol and its capability in resisting selfish mining attack has been validated in imperfect blockchains of Bitcoin and its variants (Bitcoin-like). This paper explores an analytical-model-based method to investigate the impact of stubborn mining attack in imperfect GHOST Bitcoin-like blockchains. We first quantify chain dynamics based on Markov chain and then derive the formulas of miner revenue and system throughput. We also propose a new metric, "Hazard Index", which can be used to compare attack severity and also assist attacke…
Blockchain systems are designed to produce blocks at a constant average rate. The most popular systems currently employ a Proof of Work (PoW) algorithm as a means of creating these blocks. Bitcoin produces, on average, one block every 10 minutes. An unfortunate limitation of all deployed PoW blockchain systems is that the time between blocks has high variance. For example, 5% of the time, Bitcoin's inter-block time is at least 40 minutes. This variance impedes the consistent flow of validated transactions through the system. We propose an alternative process for PoW-based block discovery that …
Bitcoin was recently introduced as a peer-to-peer electronic currency in order to facilitate transactions outside the traditional financial system. The core of Bitcoin, the Blockchain, is the history of the transactions in the system maintained by all miners as a distributed shared register. New blocks in the Blockchain contain the last transactions in the system and are added by miners after a block mining process that consists in solving a resource consuming proof-of-work (cryptographic puzzle). The reward is a motivation for mining process but also could be an incentive for attacks such as …
Several attacks have been proposed against Proof-of-Work blockchains, which may increase the attacker's share of mining rewards (e.g., selfish mining, block withholding). A further impact of such attacks, which has not been considered in prior work, is that decreasing the profitability of mining for honest nodes incentivizes them to stop mining or to leave the attacked chain for a more profitable one. The departure of honest nodes exacerbates the attack and may further decrease profitability and incentivize more honest nodes to leave. In this paper, we first present an empirical analysis showi…
As the core technology behind Bitcoin, Blockchain's decentralized, tamper-proof, and traceable features make it the preferred platform for organizational innovation. In current Bitcoin, block reward is halved every four years, and transaction fees are expected to become the majority of miner revenues around 2140. When transaction fee dominates mining rewards, strategic deviations such as Selfish Mining, Undercutting, and Mining Gap could threaten the integrity and security of the Blockchain. This paper proposes a set of Dynamic Transaction Storage (DTS) strategies for maintaining a sustainable…
The Bitcoin cryptocurrency records its transactions in a public log called the blockchain. Its security rests critically on the distributed protocol that maintains the blockchain, run by participants called miners. Conventional wisdom asserts that the protocol is incentive-compatible and secure against colluding minority groups, i.e., it incentivizes miners to follow the protocol as prescribed. We show that the Bitcoin protocol is not incentive-compatible. We present an attack with which colluding miners obtain a revenue larger than their fair share. This attack can have significant consequenc…
Inside Qubic's Selfish Mining Campaign on Monero: Evidence, Tactics, and Limits
ShardLab, Seoul, Republic of Korea（ShardLab）；Hashed Open Research, Seoul, Republic of Korea（Hashed Open Research）；Korea University, Seoul, Republic of Korea（韩国大学）
Learning Automaton (LA) is an adaptive self-organized model that improves its action-selection through interaction with an unknown environment. LA with finite action set can be classified into two main categories: fixed and variable structure. Furthermore, variable action-set learning automaton (VASLA) is one of the main subsets of variable structure learning automaton. In this paper, we propose VDHLA, a novel hybrid learning automaton model, which is a combination of fixed structure and variable action set learning automaton. In the proposed model, variable action set learning automaton can i…
It is interesting but difficult and challenging to study Ethereum with multiple mining pools. One of the main difficulties comes from not only how to represent such a general tree with multiple block branches (or sub-chains) related to the multiple mining pools, but also how to analyze a multi-dimensional stochastic system due to the mining competition among the multiple mining pools. In this paper, we first set up a mathematical representation for the tree with multiple block branches. Then we provide a block classification of Ethereum: Regular blocks (in the main chain), orphan blocks, uncle…
Cryptocurrency achieves distributed consensus using proof of work (PoW). Prior research in blockchain security identified financially incentivized attacks based on withholding blocks which have the attacker compromise a victim pool and pose as a PoW contributor by submitting the shares (earning credit for mining) but withholding the blocks (no actual contributions to the pool). We advance such threats to generate greater reward advantage to the attackers while undermining the other miners and introduce the share withholding attack (SWH). SWH withholds shares to increase the attacker's reward p…
Blockchain, the technology behind the popular Bitcoin, is considered a "security by design" system as it is meant to create security among a group of distrustful parties yet without a central trusted authority. The security of blockchain relies on the premise of honest-majority, namely, the blockchain system is assumed to be secure as long as the majority of consensus voting power is honest. And in the case of proof-of-work (PoW) blockchain, adversaries cannot control more than 50% of the network's gross computing power. However, this 50% threshold is based on the analysis of computing power o…
