Abstract Hacks are one of the most damaging types of cryptocurrency related crime, accounting for billions of dollars in stolen funds since 2009. Professional investigators at Chainalysis have traced these stolen funds from the initial breach on an exchange to off-ramps, i.e. services where criminals are able to convert the stolen funds into fiat or other cryptocurrencies. We analyzed six hack subnetworks of bitcoin transactions known to belong to two prominent hacking groups. We analyze each hack according to eight network features, both static and temporal, and successfully classify each hack to its respective hacking group through our newly proposed method. We find that the static features, such as node balance, in degree, and out degree are not as useful in classifying the hacks into hacking groups as temporal features related to how quickly the criminals cash out. We validate our operating hypothesis that the key distinction between the two hacking groups is the acceleration with which the funds exit through terminal nodes in the subnetworks.
Many real systems can be described by a set of interacting entities forming a complex network. To some surprise, these have been shown to share a number of structural properties regardless of their type or origin. It is thus of vital importance to design simple and intuitive models that can explain their intrinsic structure and dynamics. These can, for instance, be used to study networks analytically or to construct networks not observed in real life. Most models proposed in the literature are of two types. A model can be either static, where edges are added between a fixed set of nodes according to some predefined rule, or evolving, where the number of nodes or edges increases over time. However, some real networks do not grow but rather shrink, meaning that the number of nodes or edges decreases over time. We here propose a simple model of shrinking networks called the war pact model. We show that networks generated in such a way exhibit common structural properties of real networks. Furthermore, compared to classical models, these resemble international trade, correlates of war, Bitcoin transactions and other networks more closely. Network shrinking may therefore represent a reasonable explanation of the evolution of some networks and greater emphasis should be put on such models in the future.
Alexandre Bovet, Carlo Campajola, Francesco Mottes, Valerio Restocchi · 7 authors
Cryptocurrencies (the most paradigmatic blockchain-based systems) are distributed systems that allow to exchange tokens among participants.These cryptocurrencies can also be acquired in exchange markets.The availability of the historical bookkeeping of cryptocurrency transfers in a public ledger opens up the possibility of understanding the relationship between aggregate users' behaviour and the cryptocurrency pricing in exchange markets.This paper analyses the properties of the transaction network of Bitcoin.We consider different representations over a period of nine years since its creation and involving 16 million users and 283 million transactions.Importantly, these transactions do not include orders filled in exchange markets, which are settled outside of the blockchain, and ultimately determine Bitcoin price.By analysing these networks, we show the existence of Granger causal relationships between Bitcoin price movements and changes of its transaction network topology.Our results reveal the interplay between structural quantities, indicative of the collective behaviour of Bitcoin users, and price movements, showing that, during price drops, the system is characterised by a larger heterogeneity of users' activity.
We describe MaGPoS, a novel consensus mechanism which is well suited to decentralized blockchain based protocols. MaGPoS is based on a combination of the well known physics of nano-scale magnetism, and previous implementations of proof of stake. This system has been studied by hundreds of thousands of scientists worldwide for over a hundred years, giving it an extreme level of reliability that is needed for a consensus mechanism. We start by explaining the physics, and study the properties that make it particularly beneficial for use in a consensus mechanism. We then show how to apply the physical model to a decentralized network of nodes, each with their own copy of a blockchain. After this, we describe some example calculations that a node in the decentralized network would make, and provide pseudo code for implementation. Finally, we discuss the how the model achieves all of the important properties that one expects of a consensus mechanism.
Information transfer between time series is calculated using the asymmetric information-theoretic measure known as transfer entropy. Geweke’s autoregressive formulation of Granger causality is used to compute linear transfer entropy, and Schreiber’s general, non-parametric, information-theoretic formulation is used to quantify nonlinear transfer entropy. We first validate these measures against synthetic data. Then we apply these measures to detect statistical causality between social sentiment changes and cryptocurrency returns. We validate results by performing permutation tests by shuffling the time series, and calculate the Z -score. We also investigate different approaches for partitioning in non-parametric density estimation which can improve the significance. Using these techniques on sentiment and price data over a 48-month period to August 2018, for four major cryptocurrencies, namely bitcoin (BTC), ripple (XRP), litecoin (LTC) and ethereum (ETH), we detect significant information transfer, on hourly timescales, with greater net information transfer from sentiment to price for XRP and LTC, and instead from price to sentiment for BTC and ETH. We report the scale of nonlinear statistical causality to be an order of magnitude larger than the linear case.
We study the dependency and causality structure of the cryptocurrency market investigating collective movements of both prices and social sentiment related to almost two thousand cryptocurrencies traded during the first six months of 2018. This is the first study of the whole cryptocurrency market structure. It introduces several rigorous innovative methodologies applicable to this and to several other complex systems where a large number of variables interact in a non-linear way, which is a distinctive feature of the digital economy. The analysis of the dependency structure reveals that prices are significantly correlated with sentiment. The major, most capitalised cryptocurrencies, such as bitcoin, have a central role in the price correlation network but only a marginal role in the sentiment network and in the network describing the interactions between the two. The study of the causality structure reveals a causality network that is consistently related with the correlation structures and shows that both prices cause sentiment and sentiment cause prices across currencies with the latter being stronger in size but smaller in number of significative interactions. Overall our study uncovers a complex and rich structure of interrelations where prices and sentiment influence each other both instantaneously and with lead-lag causal relations. A major finding is that minor currencies, with small capitalisation, play a crucial role in shaping the overall dependency and causality structure. Despite the high level of noise and the short time-series we verified that these networks are significant with all links statistically validated and with a structural organisation consistently reproduced across all networks.
Abeer ElBahrawy, Laura Alessandretti, Andrea Baronchelli
The production and consumption of information about Bitcoin and other digital-, or crypto- , currencies have grown together with their market capitalization. However, a systematic investigation of the relationship between online attention and market dynamics across multiple digital currencies is still lacking. Here, we quantify the interplay between the attention towards digital currencies in Wikipedia and their market performance. We consider the entire edit history of currency-related pages and their view history from July 2015. First, we quantify the evolution of the cryptocurrency presence in Wikipedia by analyzing the editorial activity and the network of co-edited pages. We find that a small community of tightly connected editors is responsible for most of the production of information about cryptocurrencies in Wikipedia. Then, we show that a simple trading strategy informed by Wikipedia views performs better than baseline strategies, in terms of returns on investment, for most of the covered period although the ‘buy and hold strategy’ dominates during the periods of explosive market expansion. Our results contribute to the recent literature on the interplay between online information and investment markets, and we anticipate it will be of interest for researchers as well as investors.
The blockchain technology promises to transform finance, money and even governments. However, analyses of blockchain applicability and robustness typically focus on isolated systems whose actors contribute mainly by running the consensus algorithm. Here, we highlight the importance of considering trustless platforms within the broader ecosystem that includes social and communication networks. As an example, we analyse the flash-crash observed on 21st June 2017 in the Ethereum platform and show that a major phenomenon of social coordination led to a catastrophic cascade of events across several interconnected systems. We propose the concept of ``emergent centralisation'' to describe situations where a single system becomes critically important for the functioning of the whole ecosystem, and argue that such situations are likely to become more and more frequent in interconnected socio-technical systems. We anticipate that the systemic approach we propose will have implications for future assessments of trustless systems and call for the attention of policy-makers on the fragility of our interconnected and rapidly changing world.
Higor Y. D. Sigaki, Matjaž Perc, Haroldo V. Ribeiro
The efficient market hypothesis has far-reaching implications for financial trading and market stability. Whether or not cryptocurrencies are informationally efficient has therefore been the subject of intense recent investigation. Here, we use permutation entropy and statistical complexity over sliding time-windows of price log returns to quantify the dynamic efficiency of more than four hundred cryptocurrencies. We consider that a cryptocurrency is efficient within a time-window when these two complexity measures are statistically indistinguishable from their values obtained on randomly shuffled data. We find that 37% of the cryptocurrencies in our study stay efficient over 80% of the time, whereas 20% are informationally efficient in less than 20% of the time. Our results also show that the efficiency is not correlated with the market capitalization of the cryptocurrencies. A dynamic analysis of informational efficiency over time reveals clustering patterns in which different cryptocurrencies with similar temporal patterns form four clusters, and moreover, younger currencies in each group appear poised to follow the trend of their 'elders'. The cryptocurrency market thus already shows notable adherence to the efficient market hypothesis, although data also reveals that the coming-of-age of digital currencies is in this regard still very much underway.
We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold $\kappa$. We find that the phase transition takes place for $\kappa 0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $\kappa_c$ the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks.
The Lightning Network is a so-called second-layer technology built on top of the Bitcoin blockchain to provide "off-chain" fast payment channels between users, which means that not all transactions are settled and stored on the main blockchain. In this paper, we model the emergence of the Lightning Network as a (bond) percolation process and we explore how the distributional properties of the volume and size of transactions per user may impact its feasibility. The agents are all able to reciprocally transfer Bitcoins using the main blockchain and also - if economically convenient - to open a channel on the Lightning Network and transact "off chain". We base our approach on fitness-dependent network models: as in real life, a Lightning channel is opened with a probability that depends on the "fitness" of the concurring nodes, which in turn depends on wealth and volume of transactions. The emergence of a connected component is studied numerically and analytically as a function of the parameters, and the phase transition separating regions in the phase space where the Lightning Network is sustainable or not is elucidated. We characterize the phase diagram determining the minimal volume of transactions that would make the Lightning Network sustainable for a given level of fees or, alternatively, the maximal cost the Lightning ecosystem may impose for a given average volume of transactions. The model includes parameters that could be in principle estimated from publicly available data once the evolution of the Lighting Network will have reached a stationary operable state, and is fairly robust against different choices of the distributions of parameters and fitness kernels.
The aim of this paper is to propose a theoretical construct, smart network field theory, for the characterization, monitoring, and control of smart network systems. Smart network systems are intelligent autonomously-operating networks, a new form of global computational infrastructure that includes blockchains, deep learning, and autonomous-strike UAVs. These kinds of large-scale networks are a contemporary reality with thousands, millions, and billions of constituent elements, and entail a foundational and theoretically-robust model for their design and operation. Hence this work proposes smart network field theory, drawing from statistical physics, effective field theories, and model systems, for criticality detection and fleet-many item orchestration in smart network systems. Smart network field theory falls within the broader concern of technophysics (the application of physics to the study of technology), in which a key objective is deriving standardized methods for assessing system criticality and phase transition, and defining interim system structure between the levels of microscopic noise and macroscopic labels. The farther implications of this work include the possibility of recasting the P/NP computational complexity schema as one no longer based on traditional time (concurrency) and space constraints, due to the availability of smart network computational resources.
The Bitcoin protocol prevents the occurrence of double-spending (DS), i.e. the utilization of the same currency unit more than once. At the same time a DS attack, where more conflicting transactions are generated, might be performed to defraud a user, e.g. a merchant. Therefore, in this work, we propose a model for detecting the presence of conflicting transactions by means of an 'oracle' that polls a subset of nodes of the Bitcoin network. We assume that the latter has a complex structure. So, we investigate the relation between the topology of several complex networks and the optimal amount, and distribution, of a subset of nodes chosen by the oracle for polling. Results show that small-world networks require to poll a smaller amount of nodes than regular networks. In addition, in random topologies, a small number of polled nodes can make a detection system fast and reliable even if the underlying network grows.
Nino Antulov-Fantulin, Dijana Tolić, Matija Piškorec, Ce Zhang · 5 authors
In this paper, we study the possibility of inferring early warning indicators (EWIs) for periods of extreme bitcoin price volatility using features obtained from Bitcoin daily transaction graphs. We infer the low-dimensional representations of transaction graphs in the time period from 2012 to 2017 using Bitcoin blockchain, and demonstrate how these representations can be used to predict extreme price volatility events. Our EWI, which is obtained with a non-negative decomposition, contains more predictive information than those obtained with singular value decomposition or scalar value of the total Bitcoin transaction volume.
In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and financial herd behavior model. Combining these approaches allows us to propose a model that replicates the long-range memory of absolute returns and trading activity. We compare the statistical properties of the model against the empirical statistical properties of the Bitcoin exchange rates and New York stock exchange tickers. We also show that the fracture in the spectral density of the high-frequency absolute return time series might be related to the mechanism of convergence towards the equilibrium price.
Alexandre Bovet, Carlo Campajola, Jorge F. Lazo, Francesco Mottes · 10 authors
The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science. Here we analyse the evolution of the network of Bitcoin transactions between users. We achieve this by using the complete transaction history from December 5th 2011 to December 23rd 2013. This period includes three bubbles experienced by the Bitcoin price. In particular, we focus on the global and local structural properties of the user network and their variation in relation to the different period of price surge and decline. By analysing the temporal variation of the heterogeneity of the connectivity patterns we gain insights on the different mechanisms that take place during bubbles, and find that hubs (i.e., the most connected nodes) had a fundamental role in triggering the burst of the second bubble. Finally, we examine the local topological structures of interactions between users, we discover that the relative frequency of triadic interactions experiences a strong change before, during and after a bubble, and suggest that the importance of the hubs grows during the bubble. These results provide further evidence that the behaviour of the hubs during bubbles significantly increases the systemic risk of the Bitcoin network, and discuss the implications on public policy interventions.
Tianyu Ray Li, Anup S. Chamrajnagar, Xander R. Fong, Nicholas R. Rizik · 5 authors
In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called \emph{ZClassic}. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to $\sim 400$ data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model'€™s predictive data yielded statistical significance at the $p < 0.0001$ level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or ``alt-coin'', market.
Francesco Parino, Mariano G. Beiró, Laëtitia Gauvin
As the first decentralized digital currency introduced in 2009 together with the blockchain, Bitcoin offers new opportunities both for developed and developing countries. Bitcoin peer-to-peer transactions are independent of the banking system, facilitating foreign exchanges with low transaction fees, such as remittances, and offering a high degree of anonymity. These opportunities together with other key factors led the Bitcoin to become extremely popular and caused its price to skyrocket during 2017 (Henry et al. in J Digit Bank 2(4):311–337, 2018 ). However, while the Bitcoin blockchain attracts a lot of attention, it remains difficult to investigate where this attention comes from, due to the pseudo-anonymity of the system, and consequently to appreciate its social impact. Here we make an attempt to characterize the adoption of the Bitcoin blockchain by country. In the first part of the work we show that information about the number of Bitcoin software client downloads, the IP addresses that act as relays for the transactions, and the Internet searches about Bitcoin provide together a coherent picture of the system evolution in different countries. Using these quantities as a proxy for user adoption, we identify several socio-economic indexes such as the GDP per capita, freedom of trade and the Internet penetration as key variables correlated with the degree of user adoption. In the second part of the work, we build a network of Bitcoin transactions between countries using the IP addresses of nodes relaying transactions and we develop an augmented version of the gravity model of trade in order to identify socio-economic factors linked to the flow of Bitcoin between countries. In a nutshell our study provides a new insight on Bitcoin adoption by country and on the potential socio-economic drivers of the international Bitcoin flow.
Bitcoins and Blockchain technologies are attracting the attention of different scientific communities. In addition, their widespread industrial applications and the continuous introduction of cryptocurrencies are also stimulating the attention of the public opinion. The underlying structure of these technologies constitutes one of their core concepts. In particular, they are based on peer-to-peer networks. Accordingly, all nodes lie at the same level, so that there is no place for privileged actors as, for instance, banking institutions in classical financial networks. In this work, we perform a preliminary investigation on two kinds of network, i.e. the Bitcoin network and the Bitcoin Cash network. Notably, we analyze their global structure and we try to evaluate if they are provided with a small-world behavior. Results suggest that the principle known as 'fittest-gets-richer', combined with a continuous increasing of connections, might constitute the mechanism leading these networks to reach their current structure. Moreover, further observations open the way to new investigations into this direction.
We empirically verify that the market capitalizations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values for the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth and death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's Law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being 'entrenched incumbents' and tokens as an 'explosive immature ecosystem', largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.
Jan 17, 2018·Peter Krafft, Nicolás Della Penna, Alex Pentland. (2018). An Experimental Study of Cryptocurrency Market Dynamics. ACM CHI Conference on Human Factors in Computing Systems (CHI)
P. M. Krafft, Nicolás Della Penna, Alex Sandy Pentland
As cryptocurrencies gain popularity and credibility, marketplaces for cryptocurrencies are growing in importance. Understanding the dynamics of these markets can help to assess how viable the cryptocurrnency ecosystem is and how design choices affect market behavior. One existential threat to cryptocurrencies is dramatic fluctuations in traders' willingness to buy or sell. Using a novel experimental methodology, we conducted an online experiment to study how susceptible traders in these markets are to peer influence from trading behavior. We created bots that executed over one hundred thousand trades costing less than a penny each in 217 cryptocurrencies over the course of six months. We find that individual "buy" actions led to short-term increases in subsequent buy-side activity hundreds of times the size of our interventions. From a design perspective, we note that the design choices of the exchange we study may have promoted this and other peer influence effects, which highlights the potential social and economic impact of HCI in the design of digital institutions.
Large-scale rumor spreading could pose severe social and economic damages. The emergence of online social networks along with the new media can even make rumor spreading more severe. Effective control of rumor spreading is of theoretical and practical significance. This paper takes the first step to understand how the blockchain technology can help limit the spread of rumors. Specifically, we develop a new paradigm for social networks embedded with the blockchain technology, which employs decentralized contracts to motivate trust networks as well as secure information exchange contract. We design a blockchain-based sequential algorithm which utilizes virtual information credits for each peer-to-peer information exchange. We validate the effectiveness of the blockchain-enabled social network on limiting the rumor spreading. Simulation results validate our algorithm design in avoiding rapid and intense rumor spreading, and motivate better mechanism design for trusted social networks.
Ilaria Bertazzi, Sylvie Huet, Guillaume Deffuant, Floriana Gargiulo
Bitcoin-otc is a peer to peer (over-the-counter) marketplace for trading with bit- coin crypto-currency. To mitigate the risks of the p2p unsupervised exchanges, the establishment of a reliable reputation systems is needed: for this reason, a web of trust is implemented on the website. The availability of all the historic of the users interaction data makes this dataset a unique playground for studying reputation dynamics through others evaluations. We analyze the structure and the dynamics of this web of trust with a multilayer network approach distin- guishing the rewarding and the punitive behaviors. We show that the rewarding and the punitive behavior have similar emergent topological properties (apart from the clustering coefficient being higher for the rewarding layer) and that the resultant reputation originates from the complex interaction of the more regular behaviors on the layers. We show which are the behaviors that correlate (i.e. the rewarding activity) or not (i.e. the punitive activity) with reputation. We show that the network activity presents bursty behaviors on both the layers and that the inequality reaches a steady value (higher for the rewarding layer) with the network evolution. Finally, we characterize the reputation trajectories and we identify prototypical behaviors associated to three classes of users: trustworthy, untrusted and controversial.
Marian Gidea, Daniel Goldsmith, Yuri Katz, Pablo Roldan · 5 authors
We analyze the time series of four major cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Ripple) before the digital market crash at the end of 2017 - beginning 2018. We introduce a methodology that combines topological data analysis with a machine learning technique -- $k$-means clustering -- in order to automatically recognize the emerging chaotic regime in a complex system approaching a critical transition. We first test our methodology on the complex system dynamics of a Lorenz-type attractor, and then we apply it to the four major cryptocurrencies. We find early warning signals for critical transitions in the cryptocurrency markets, even though the relevant time series exhibit a highly erratic behavior.