The goal of this paper is to establish the general framework of consensus equilibria for Mining-Pool Games in Blockchain Ecosystems, and with the explanation for the stability of in terms of the existence of consensus equilibria related to mining gap game's behaviors by using one new concept called consensus games in Blockchain Ecosystems, here, the Blockchain ecosystem mainly means the economic activities by taking into the account of three types of different factors which are expenses, reward mechanism and mining power for the work on blockschain by applying the key consensus called Proof of Work due to Nakamoto in 2008.
In order to do so, we first give an outline how the general existence of consensus equilibria for Mining Pool Games is formulated, and then used to explain the stable for Gap Games for Bitcoin in the sense by the existence of consensus equilibria under the framework of Blockchain consensus, we then establish a general existence result for consensus equilibria of general mining gap games by using the profit functions for miners as the payoffs in game theory. As applications, the general existence results for consensus equilibria of Gap games are established, which not only help us to claim the existence for the general stability for Gap games under the general framework of Blockchain ecosystems, but also allow us to illustrate a number of different phenomenon on the study of mining-pool games with possible impacts due to miners's gap behaviors with scenarios embedded n Bitcoin economics. Our study on the explanation for the stability of mining gap game for Blockchain ecosystems shows that the concept of consensus equilibria may play a important role for the development of fundamental theory for consensus economics.
We introduce a new cryptographic protocol, called Deep Ocean, that implements a blockchain-agnostic dark pool for cryptocurrencies. Deep Ocean is a layer-two protocol, meaning that it can work with any two cryptocurrencies, as long as there exists an underlying settlement mechanism, for example performing atomic swaps.
In Proof-of-Work (PoW) blockchains, the average waiting time to generate a block is inversely proportional to the computing power of the miner. To reduce the average block generation time, a group of individual miners can form a mining pool to aggregate their computing power to solve the puzzle together and share the reward contained in the block. However, if the aggregated computing power of the pool forms a substantial portion of the total computing power in the network, the pooled mining undermines the core spirit of blockchain, i.e., the decentralization, and harms its security. To discour…
In 2015, Eyal proposed the first game-theoretical model for analyzing the equilibrium of blockchain pooling: when the blockchain pools are abstracted as a non-cooperative game, two pools can reach a Nash equilibrium with a closed-form formula; Moreover, an arbitrary number of pools still exhibit an equilibrium as long as the pools have an equal number of miners. Nevertheless, whether an equilibrium exists for three or more pools of distinct sizes remains an open problem. To this end, this paper studies the equilibrium in a blockchain of arbitrary pools. First, we show that the equilibrium amon…
Blockchain-based cryptocurrencies, such as Bitcoin, have seen on the rise in their popularity and value, making them a target to several forms of Denial-of-Service (DoS) attacks, and calling for a better understanding of their attack surface from both security and distributed systems standpoints. In this paper, and in the pursuit of understanding the attack surface of blockchains, we explore a new form of attack that can be carried out on the memory pools (mempools) and mainly targets blockchain-based cryptocurrencies. We study this attack on Bitcoin mempool and explore the attack effects on t…
The resource-consuming mining of blocks on a blockchain equipped with a proof of work consensus protocol bears the risk of ruin, namely when the operational costs for the mining exceed the received rewards. In this paper we investigate to what extent it is of interest to join a mining pool that reduces the variance of the return of a miner for a specified cost for participation. Using methodology from ruin theory and risk sharing in insurance, we quantitatively study the effects of pooling in this context and derive several explicit formulas for quantities of interest. The results are illustra…
We model and analyze blockchain miners who seek to maximize the compound return of their mining businesses. The analysis of the optimal strategies finds a new equilibrium point among the miners and the mining pools, which predicts the market share of each miner or mining pool. The cost of mining determines the share of each miner or mining pool at equilibrium. We conclude that neither miners nor mining pools who seek to maximize their compound return will have a financial incentive to occupy more than 50% of the hash rate if the cost of mining is at the same level for all. However, if there is…
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…
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…
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…
Ethereum prospered the inception of a plethora of smart contract applications, ranging from gambling games to decentralized finance. However, Ethereum is also considered a highly adversarial environment, where vulnerable smart contracts will eventually be exploited. Recently, Ethereum's pool of pending transaction has become a far more aggressive environment. In the hope of making some profit, attackers continuously monitor the transaction pool and try to frontrun their victims' transactions by either displacing or suppressing them, or strategically inserting their transactions. This paper aim…
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…
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…
Cooperation is fundamental for human prosperity. Blockchain, as a trust machine, is a cooperative institution in cyberspace that supports cooperation through distributed trust with consensus protocols. While studies in computer science focus on fault tolerance problems with consensus algorithms, economic research utilizes incentive designs to analyze agent behaviors. To achieve cooperation on blockchains, emerging interdisciplinary research introduces rationality and game-theoretical solution concepts to study the equilibrium outcomes of various consensus protocols. However, existing studies d…
We study efficiency in a proof-of-work blockchain with non-zero latencies, focusing in particular on the (inequality in) individual miners' efficiencies. Prior work attributed differences in miners' efficiencies mostly to attacks, but we pursue a different question: Can inequality in miners' efficiencies be explained by delays, even when all miners are honest? Traditionally, such efficiency-related questions were tackled only at the level of the overall system, and in a peer-to-peer (P2P) setting where miners directly connect to one another. Despite it being common today for miners to pool com…
Proof of work (PoW), the most popular consensus mechanism for Blockchain, requires ridiculously large amounts of energy but without any useful outcome beyond determining accounting rights among miners. To tackle the drawback of PoW, we propose a novel energy-recycling consensus algorithm, namely proof of federated learning (PoFL), where the energy originally wasted to solve difficult but meaningless puzzles in PoW is reinvested to federated learning. Federated learning and pooled-ming, a trend of PoW, have a natural fit in terms of organization structure. However, the separation between the da…
A problem of developing the consensus protocols in public blockchain systems which spend a combination of energy and space resources is addressed. A technique is proposed that provides a flexibility for selection of the energy and space resources which should be spent by a player participating in the consensus procedure. The technique originates from the cryptographic time-memory-data trade-off approaches for cryptanalysis. The proposed technique avoids the limitations of Proof-of-Work (PoW) and Proof-of Space (PoS) which require spending of only energy and space, respectively. Also, it provid…
It is an important decision-making problem for a miner in the blockchain networks if he/she participates in the mining so that he/she earns a reward by creating a new block earlier than other miners. We formulate this decision-making problem as a noncooperative game, because the probability of creating a block depends not only on one's own available computational resources, but also those of other miners. Through theoretical and numerical analyses, we show a hysteresis phenomenon of Nash equilibria depending on the reward and a jump phenomenon of miner decisions by a slight change in reward. W…
The arisen of Bitcoin has led to much enthusiasm for blockchain research and block mining, and the extensive existence of mining pools helps its participants (i.e., miners) gain reward more frequently. Recently, the mining pools are proved to be vulnerable for several possible attacks, and pool block withholding attack is one of them: one strategic pool manager sends some of her miners to other pools and these miners pretend to work on the puzzles but actually do nothing. And these miners still get reward since the pool manager can not recognize these malicious miners. In this work, we revisit…
With the development of decentralized consensus protocols, permissionless blockchains have been envisioned as a promising enabler for the general-purpose transaction-driven, autonomous systems. However, most of the prevalent blockchain networks are built upon the consensus protocols under the crypto-puzzle framework known as proof-of-work. Such protocols face the inherent problem of transaction-processing bottleneck, as the networks achieve the decentralized consensus for transaction confirmation at the cost of very high latency. In this paper, we study the problem of consensus formation in a …
Proof-of-Work (PoW) is a Sybil control mechanism adopted in blockchain-based cryptocurrencies. It prevents the attempt of malicious actors to manipulate distributed ledgers. Bitcoin has successfully suppressed double-spending by accepting the longest PoW chain. Nevertheless, PoW encountered several major security issues surrounding mining competition. One of them is a Block WithHolding (BWH) attack that can exploit a widespread and cooperative environment called a mining pool. This attack takes advantage of untrustworthy relationships between mining pools and participating agents. Moreover, de…
To participate in the distributed consensus of permissionless blockchains, prospective nodes -- or miners -- provide proof of designated, costly resources. However, in contrast to the intended decentralization, current data on blockchain mining unveils increased concentration of these resources in a few major entities, typically mining pools. To study strategic considerations in this setting, we employ the concept of Oceanic Games, Milnor and Shapley (1978). Oceanic Games have been used to analyze decision making in corporate settings with small numbers of dominant players (shareholders) and l…
We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are paid when they create a node (mine a block) which will end up in the path of the tree that is adopted by all. Since the miners can hide newly mined nodes, they play a game with incomplete information. Here we consider two simplified forms of this game in which the miners have complete information. In the simplest game the miners release every mined block imm…
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 vec…
Resilient Federated Chain: Transforming Blockchain Consensus into an Active Defense Layer for Federated Learning
Department of Computer Science and Artificial Intelligence（计算机科学与人工智能系）；Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI)（数据科学与计算智能安达卢西亚研究 institute）；University of Granada（格拉纳达大学）
Stratum, the de-facto mining communication protocol used by blockchain based cryptocurrency systems, enables miners to reliably and efficiently fetch jobs from mining pool servers. In this paper we exploit Stratum's lack of encryption to develop passive and active attacks on Bitcoin's mining protocol, with important implications on the privacy, security and even safety of mining equipment owners. We introduce StraTap and ISP Log attacks, that infer miner earnings if given access to miner communications, or even their logs. We develop BiteCoin, an active attack that hijacks shares submitted by …
Cryptocurrencies, arguably the most prominent application of blockchains, have been on the rise with a wide mainstream acceptance. A central concept in cryptocurrencies is "mining pools", groups of cooperating cryptocurrency miners who agree to share block rewards in proportion to their contributed mining power. Despite many promised benefits of cryptocurrencies, they are equally utilized for malicious activities; e.g., ransomware payments, stealthy command, control, etc. Thus, understanding the interplay between cryptocurrencies, particularly the mining pools, and other essential infrastructu…
Bitcoin draws the highest degree of attention among cryptocurrencies, while coin mining is one of the most important fashion of profiting in the Bitcoin ecosystem. This paper constructs fresh coin circulation networks by tracking the fresh coin transfer routes with transaction referencing in Bitcoin blockchain. This paper proposes a heuristic algorithm to identifying coin miners by comparing coin circulation networks from different mining pools and thereby inferring the common profit distribution schemes of Bitcoin mining pools. Furthermore, this paper characterizes the increasing trend of Bit…
Mining is the foundation of blockchain-based cryptocurrencies such as Bitcoin rewarding the miner for finding blocks for new transactions. The Monero currency enables mining with standard hardware in contrast to special hardware (ASICs) as often used in Bitcoin, paving the way for in-browser mining as a new revenue model for website operators. In this work, we study the prevalence of this new phenomenon. We identify and classify mining websites in 138M domains and present a new fingerprinting method which finds up to a factor of 5.7 more miners than publicly available block lists. Our work ide…
