The Bitcoin network is burning a large amount of energy for mining. In this paper we estimate the lower bound for the global energy cost for a period of ten years from 2010, taking into account changing oil costs, improvements in hashing technologies and hashing activity. Despite a ten-billion-fold increase in hashing activity and a ten-million-fold increase in total energy consumption, we find the cost relative to the volume of transactions has not increased nor decreased since 2010. This is consistent with the perspective that, in order to keep a the Blockchain system secure from double spending attacks, the proof or work must cost a sizable fraction of the value that can be transferred through the network. We estimate that in the Bitcoin network this fraction is of the order of 1%.
We give an explicit definition of decentralization and show you that decentralization is almost impossible for the current stage and Bitcoin is the first truly noncentralized currency in the currency history. We propose a new framework of noncentralized cryptocurrency system with an assumption of the existence of a weak adversary for a bank alliance. It abandons the mining process and blockchain, and removes history transactions from data synchronization. We propose a consensus algorithm named Converged Consensus for a noncentralized cryptocurrency system.
Since Bitcoin's inception in 2008, it has became attractive investments for both trading and mining. To mine Bitcoins, a miner has to invest in computing power and pay for electricity to solve cryptographic puzzles for rewards, if it becomes the first to solve a puzzle, paid in Bitcoin. Given that mining is such a resource intensive effort, miners seek new strategies trying to make the mining process more profitable.
AsicBoost is a method to speed up Bitcoin mining by a factor of approximately 20%. The performance gain is achieved through a high-level optimization of the Bitcoin mining algorithm which allows for drastic reduction in gate count on the mining chip. AsicBoost is applicable to all types of mining hardware and chip designs. This paper presents the idea behind the method and describes the information flow in implementations of AsicBoost.
Bitcoin-NG, a scalable blockchain protocol, divides each block into a key block and many micro blocks to effectively improve the transaction processing capacity. Bitcoin-NG has a special incentive mechanism (i.e. splitting transaction fees to the current and the next leader) to maintain its security. However, this design of the incentive mechanism ignores the joint effect of transaction fees, mint coins and mining duration lengths on the expected mining reward. In this paper, we identify the advanced mining attack that deliberately ignores micro blocks to enlarge the mining duration length to …
Bitcoin mining presents a significant economic incentive for efficient hashing and broadcast of data, both parameters stemming from the Proofs of Work used to advance the network. This incentive has led to the development of Bitcoin specific application specific integrated circuits and centralized mining pools, undermining the decentralized motivations behind Bitcoin's design. In addition, the imminent block reward halving threatens the profitability of mining at any scale. Some work has been done in formal models for miner profitability, but existing models do not account for conditions such …
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…
The world economy is experiencing the novel adoption of distributed currencies that are free from the control of central banks. Distributed currencies suffer from extreme volatility, and this can lead to catastrophic implications during future economic crisis. Understanding the dynamics of this new type of currencies is vital for empowering supervisory bodies from current reactive and manual incident responders to more proactive and well-informed planners. Bitcoin, the first and dominant distributed cryptocurrency, is still notoriously vague, especially for a financial instrument with market v…
In Aug. 2017, Bitcoin was split into the original Bitcoin (BTC) and Bitcoin Cash (BCH). Since then, miners have had a choice between BTC and BCH mining because they have compatible proof-of-work algorithms. Therefore, they can freely choose which coin to mine for higher profit, where the profitability depends on both the coin price and mining difficulty. Some miners can immediately switch the coin to mine only when mining difficulty changes because the difficulty changes are more predictable than that for the coin price, and we call this behavior fickle mining. In this paper, we study the effe…
Miners play a key role in cryptocurrencies such as Bitcoin: they invest substantial computational resources in processing transactions and minting new currency units. It is well known that an attacker controlling more than half of the network's mining power could manipulate the state of the system at will. While the influence of large mining pools appears evenly split, the actual distribution of mining power within these pools and their economic relationships with other actors remain undisclosed. To this end, we conduct the first in-depth analysis of mining reward distribution within three of …
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…
We give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to compute stationary probabilities on Markov chain nor stopping times for Poisson processes as it was previously done. We consider also several other block withholding strategies.
Soon after its introduction in 2009, Bitcoin has been adopted by cyber-criminals, which rely on its pseudonymity to implement virtually untraceable scams. One of the typical scams that operate on Bitcoin are the so-called Ponzi schemes. These are fraudulent investments which repay users with the funds invested by new users that join the scheme, and implode when it is no longer possible to find new investments. Despite being illegal in many countries, Ponzi schemes are now proliferating on Bitcoin, and they keep alluring new victims, who are plundered of millions of dollars. We apply data minin…
The main goal of this article is to present a direct approach for the formula giving the long-term apparent hashrates of Selfish Mining strategies using only elementary probabilities and combinatorics, more precisely, Dyck words. We can avoid computing stationary probabilities on Markov chain, nor stopping times for Poisson processes as in previous analysis. We do apply these techniques to other block withholding strategies in Bitcoin, and then, we consider also selfish mining in Ethereum.
Mining pools, the main components of the Bitcoin network, dominate the computing resources and play essential roles in network security and performance aspects. Although many existing measurements of the Bitcoin network are available, little is known about the details of mining pool behaviors (e.g., empty blocks, mining revenue and transaction collection strategies) and their effects on the Bitcoin end users (e.g., transaction fees, transaction delay and transaction acceptance rate). This paper aims to fill this gap with a systematic study of mining pools. We traced over 1.56 hundred thousand …
The mining of bitcoin is modeled using system dynamics, showing that the past evolution of the network hash rate can be explained to a large extent by an efficient market hypothesis applied to the mining of blocks. The possibility of a decrease in the network hash rate from the next halving event (May 2020) is exposed, implying that the network may be close to 'peak hash', if the price of bitcoin and the revenues from transaction fees will remain at approximately the present level.
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…
Bitcoin is a decentralized crypto-currency, and an accompanying protocol, created in 2008. Bitcoin nodes continuously generate and propagate blocks---collections of newly approved transactions that are added to Bitcoin's ledger. Block creation requires nodes to invest computational resources, but also carries a reward in the form of bitcoins that are paid to the creator. While the protocol requires nodes to quickly distribute newly created blocks, strong nodes can in fact gain higher payoffs by withholding blocks they create and selectively postponing their publication. The existence of such s…
Grover's algorithm confers on quantum computers a quadratic advantage over classical computers for searching in an arbitrary data set, a scenario that describes Bitcoin mining. It has previously been argued that the only side-effect of quantum mining would be an increased difficulty. In this work, we argue that a crucial argument in the analysis of Bitcoin security breaks down when quantum mining is performed. Classically, a Bitcoin fork occurs rarely, i.e., when two miners find a block almost simultaneously, due to propagation time effects. The situation differs dramatically when quantum mine…
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…
Bitcoin is the most secure blockchain in the world, supported by the immense hash power of its Proof-of-Work miners, but consumes huge amount of energy. Proof-of-Stake chains are energy-efficient, have fast finality and accountability, but face several fundamental security issues: susceptibility to non-slashable long-range safety attacks, non-slashable transaction censorship and stalling attacks and difficulty to bootstrap new PoS chains from low token valuation. We propose Babylon, a blockchain platform which combines the best of both worlds by reusing the immense Bitcoin hash power to enhanc…
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 …
The Bitcoin cryptocurrency has received much attention recently. In the network of Bitcoin, transactions are recorded in a ledger. In this network, the process of recording transactions depends on some nodes called miners that execute a protocol known as mining protocol. One of the significant aspects of mining protocol is incentive compatibility. However, literature has shown that Bitcoin mining's protocol is not incentive-compatible. Some nodes with high computational power can obtain more revenue than their fair share by adopting a type of attack called the selfish mining attack. In this pa…
We describe and analyze perishing mining, a novel block-withholding mining strategy that lures profit-driven miners away from doing useful work on the public chain by releasing block headers from a privately maintained chain. We then introduce the dual private chain (DPC) attack, where an adversary that aims at double spending increases its success rate by intermittently dedicating part of its hash power to perishing mining. We detail the DPC attack's Markov decision process, evaluate its double spending success rate using Monte Carlo simulations. We show that the DPC attack lowers Bitcoin's s…
Our aim is to determine conditions for quantum computing technology to give rise to security risks associated with quantum Bitcoin mining. Specifically, we determine the speed and energy efficiency a quantum computer needs to offer an advantage over classical mining. We analyze the setting in which the Bitcoin network is entirely classical except for a single quantum miner who has small hash rate compared to that of the network. We develop a closed-form approximation for the probability that the quantum miner successfully mines a block, with this probability dependent on the number of Grover i…
A blockchain, such as Bitcoin, is an append-only, secure, transparent, distributed ledger. A fair blockchain is expected to have healthy metrics; high honest mining power, low processing latency, i.e., low wait times for transactions and stable price of consumption, i.e., the minimum transaction fee required to have a transaction processed. As Bitcoin matures, the influx of transactions increases and the block rewards become insignificant. We show that under these conditions, it becomes hard to maintain the health of the blockchain. In Bitcoin, under these mature operating conditions (MOC), th…
Many of the recent works on the profitability of rogue mining strategies hinge on a parameter called $γ$ that measures the proportion of the honest network attracted by the attacker to mine on top of his fork. These works, see arXiv:1808.01041 and arXiv.1805.08281, have surmised conclusions based on premises that erroneously treat $γ$ to be constant. In this paper, we treat $γ$ as a stochastic process and attempt to find its distribution through a Markov analysis. We begin by making strong assumptions on gamma's behaviour and proceed to translate them mathematically in order to apply them in a…
This paper presents a new blockchain network simulator that uses bitcoin's original reference implementation as its main application. The proposed simulator leverages the use of lightweight virtualization technology to build a fine tuned local testing network. To enable fast simulation of a large scale network without disabling mining service, the simulator can adjust the bitcoin mining difficulty level to below the default minimum value. In order to assess the performance of blockchain under different network conditions, the simulator allows to define different network topologies, and integra…
Bitcoin is a "crypto currency", a decentralized electronic payment scheme based on cryptography which has recently gained excessive popularity. Scientific research on bitcoin is less abundant. A paper at Financial Cryptography 2012 conference explains that it is a system which "uses no fancy cryptography", and is "by no means perfect". It depends on a well-known cryptographic standard SHA-256. In this paper we revisit the cryptographic process which allows one to make money by producing bitcoins. We reformulate this problem as a Constrained Input Small Output (CISO) hashing problem and reduce …
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 …
Mining is the important part of the blockchain used the proof of work (PoW) on its consensus, looking for the matching block through testing a number of hash calculations. In order to attract more hash computing power, the miner who finds the proper block can obtain some rewards. Actually, these hash calculations ensure that the data of the blockchain is not easily tampered. Thus, the incentive mechanism for mining affects the security of the blockchain directly. This paper presents an approach to attack against the difficulty adjustment algorithm (abbreviated as DAA) used in blockchain mining…
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 …
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…
Bitcoin is a decentralised digital currency that relies on cryptography rather than trusted third parties such as central banks for its security. Underpinning the operation of the currency is a peer-to-peer (P2P) network that facilitates the execution of transactions by end users, as well as the transaction confirmation process known as bitcoin mining. The security of this P2P network is vital for the currency to function and subversion of the underlying network can lead to attacks on bitcoin users including theft of bitcoins, manipulation of the mining process and denial of service (DoS). As …
As the most successful cryptocurrency to date, Bitcoin constitutes a target of choice for attackers. While many attack vectors have already been uncovered, one important vector has been left out though: attacking the currency via the Internet routing infrastructure itself. Indeed, by manipulating routing advertisements (BGP hijacks) or by naturally intercepting traffic, Autonomous Systems (ASes) can intercept and manipulate a large fraction of Bitcoin traffic. This paper presents the first taxonomy of routing attacks and their impact on Bitcoin, considering both small-scale attacks, targeting …
We analyze Bitcoin mining from the perspective of a game and propose an optimal mining model that maximizes profits of pools and miners. The model is a two-stage Stackelberg game in which each stage forms a sub-game. In stage I, pools are the leaders who assign a computing power to be consumed by miners. In stage II, miners decide of their power consumption and distribution. They find themselves in a social dilemma in which they must choose between mining in solo, therefore prioritizing their individual preferences, and participating in a pool for the collective interest. The model relies on a…
Bitcoin-NG is among the first blockchain protocols to approach the \emph{near-optimal} throughput by decoupling blockchain operation into two planes: leader election and transaction serialization. Its decoupling idea has inspired a new generation of high-performance blockchain protocols. However, the existing incentive analysis of Bitcoin-NG has several limitations. First, the impact of network capacity is ignored. Second, an integrated incentive analysis that jointly considers both key blocks and microblocks is still missing. In this paper, we aim to address these two limitations. First, we p…
As the second largest cryptocurrency by market capitalization and today's biggest decentralized platform that runs smart contracts, Ethereum has received much attention from both industry and academia. Nevertheless, there exist very few studies about the security of its mining strategies, especially from the selfish mining perspective. In this paper, we aim to fill this research gap by analyzing selfish mining in Ethereum and understanding its potential threat. First, we introduce a 2-dimensional Markov process to model the behavior of a selfish mining strategy inspired by a Bitcoin mining str…
We compute and compare profitabilities of stubborn mining strategies that are variations of selfish mining. These are deviant mining strategies violating Bitcoin's network protocol rules. We apply the foundational set-up from our previous companion article on the profitability of selfish mining, and the new martingale techniques to get a closed-form computation for the revenue ratio, which is the correct benchmark for profitability. Catalan numbers and Catalan distributions appear in the closed-form computations. This marks the first appearance of Catalan numbers in the Mathematics of the Bitc…
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…
We calculate the probability of success of block-hiding mining strategies in Bitcoin-like networks. These strategies involve building a secret branch of the block-tree and publishing it opportunistically, aiming to replace the top of the main branch and rip the reward associated with the secretly mined blocks. We identify two types of block-hiding strategies and chart the parameter space where those are more beneficial than the standard mining strategy described in Nakamoto's paper. Our analysis suggests a generalization of the notion of the relative hashing power as a measure for a miner's in…
Cryptocurrencies have garnered a lot of attention by governments and internet enthusiasts over the past three years. These currencies are celebrated for their security and speedy transactions in a modern era of digital commerce. Bitcoin was the first of these currencies to gain a large advantage over subsequent iterations. Bitcoin was first conceived by Satoshi Nakamoto who mentioned the concept of a cryptocurrency in his paper titled Bitcoin. It featured new concepts such as proof of work and transactions which utilized hash based encryption. One particular alternative cryptocurrency is known…
We review the so called selfish mining strategy in the Bitcoin network and compare its profitability to honest mining.We build a rigorous profitability model for repetition games. The time analysis of the attack has been ignored in the previous literature based on a Markov model,but is critical. Using martingale's techniques and Doob Stopping Time Theorem we compute the expected duration of attack cycles. We discover a remarkable property of the bitcoin network: no strategy is more profitable than the honest strategy before a difficulty adjustment. So selfish mining can only become profitable …
Simple closed-form upper and lower bounds are developed for the security of the Nakamoto consensus as a function of the confirmation depth, the honest and adversarial block mining rates, and an upper bound on the block propagation delay. The bounds are exponential in the confirmation depth and apply regardless of the adversary's attack strategy. The gap between the upper and lower bounds is small for Bitcoin's parameters. For example, assuming an average block interval of 10 minutes, a network delay bound of ten seconds, and 10% adversarial mining power, the widely used 6-block confirmation ru…
Blockchain technology is ushering in another break-out year, the challenge of blockchain still remains to be solved. This paper analyzes the features of Bitcoin and Bitcoin-NG system based on blockchain, proposes an improved method of implementing blockchain systems by replacing the structure of the original chain with the graph data structure. It was named GraphChain. Each block represents a transaction and contains the balance status of the traders. Additionally, as everyone knows all the transactions in Bitcoin system will be baled by only one miner that will result in a lot of wasted effor…
We study selfish mining in Ethereum. The problem is combinatorially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula. Equivalent strategies in Bitcoin do have different profitabilities in Ethereum. The attacker can either broadcast his fork one block by one, or keep them secret as long as possible and publish them all at once at the end of an attack cycle. The first strategy is damaging for substantial hashrates, and we show that the second strategy is even worse. This confirms what we already proved for Bitcoin: Selfi…
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…
