We call this quantity unique IP and, as explained in the following section, this can be used as a proxy to study the adoption in different countries. In Fig. We limit the interval of analysis regarding relay node IP to the period beginning from March to May , because there is some uncertainty on the reliability of the data outside this interval. The level of the signal after May becomes too low and there is little information to extract.
Map representing the number of new IP addresses appeared in the Bitcoin system by country in the time interval from to , for the countries selected for our study see the list in Table 9. Countries have been selected based on the activity IP and clients as explained in Sect. To better assess the Bitcoin uptake we also consider the number of Bitcoin Client downloads. Generally speaking, a Bitcoin client is a software used to manage and store Bitcoin addresses and make transactions on the Bitcoin network. The official Bitcoin client is called Bitcoin Core , and it was available from sourceforge.
SourceForge provides some statistics about the downloads, including the total number of downloads, daily aggregated by country, as shown in Fig. As other clients exist and some users perform transactions through web-based services, the data from Bitcoin Core does not involve all the Bitcoin users. However, as explained in Sect. We limit the interval of analysis on the number of client downloads to the period from the beginning of up to May Evolution of the number of Bitcoin clients downloaded.
World trends, and country-level trends for 2 of the main countries in term of number of downloads. Here we use Google Trends as a proxy for the collective attention on the subject, a method already proposed in [ 25 ]. Although the time series experience a similar drop as the other two Fig. Summary plots of proxies. Time evolution of the number of Bitcoin client downloads, the number of new IP appearing in the Bitcoin system and Google Trends searches on Bitcoin at the worldwide level.
The vertical black line marks the limit of database usage. With the aim of exploring the relationship between some socio-economic indexes and the Bitcoin adoption, we gathered some datasets at country level as summarized in Table 3. We mainly focused on indexes that can distinguish the most developed, richest and wealthiest countries from developing countries. We want to underline that the country development cannot be summarized into a one dimensional economic indicator indeed there is no criterion that is generally accepted [ 26 ]. With the goal of appreciating Bitcoin adoption at the country level, we have identified Bitcoin client downloads, IP of relay nodes and Google Trends as possible sources of information.
Here, we show that these quantities provide a similar and consistent picture of users. Then, we show how countries with different developing indexes have different trends of adoption and lastly, we explore how country socio-economic indexes are linked to Bitcoin adoption. The numbers of relay node IP and client downloads are directly related to the blockchain, so both of them give a direct information of Bitcoin usage even if none of them can provide a complete picture of the users.
In particular, the number of IP addresses does not consider users that do not run a node, and thus do not appear as an IP in the network. On the other side, the number of client downloads provides only information about users using this specific client. Because of these limitations, we cannot identify the exact number of users per country but a trend of evolution. To compare the information given by the numbers of IP addresses and client downloads, we first select countries whose activity level permits the analysis.
For each one year moving windows with one-month step from to , we repeatedly filter out countries for which the number of unique IP addresses or client downloads, is lower than the respective medians. At the end of the filtering process, we select a group of 72 countries, listed in Table 9. A degree of uncertainty exists about the possibility to obtain information about the users from IP addresses and Bitcoin client downloads. Indeed, the first IP address is a noisy identification of the origin of the transaction, while Bitcoin Core is not the only Bitcoin client in use and might give a partial picture of overall Bitcoin adoption.
In order to check if they give a consistent picture of Bitcoin adoption, we study the correlation between the two time series and after removing small fluctuations by applying a moving window average window length: 1 month, offset: 1 day , we indeed measure a high correlation Table 4.
The fact that they correlate positively even though they potentially concern different users encourages the use of these data sources as proxy for the distribution of users among countries. Additionally, we compute the Spearman correlation coefficient between the ranking of countries given by IP addresses and client downloads in three different years, arriving to the same conclusion.
We also confronted the Google Trends time series with the numbers of unique IPs and client downloads computing the pairwise Pearson correlations. Given the high correlations as shown in Table 4 , we conclude that the Google Trends time series may also be used as an indicator of the country Bitcoin adoption. We suppose that this assumption holds for the whole Google Trends data collection period that is longer than for other data sources.
This allows us to discuss long term adoption trends of the selected countries. To assess the relevance of the use of Bitcoin search time series for comparing country adoption, we also measured the Spearman correlation between the pairwise rankings of countries by Bitcoin searches, number of Bitcoin clients downloaded and new IPs appearing.
How does Bitcoin work? - Bitcoin
Correlations are also high, apart for the year where the signal about Bitcoin searches is too low for allowing comparison between countries. Moreover the country ranking based on Google queries heavily depends on Google usage by country, which can be very heterogeneous. As there is no trivial normalization to compensate the heterogeneity of Google usage within countries we will not use the rank provided by sorting Google Trends by countries.
Using the data from Google Trends we studied the evolution of the collective attention by country from to early As we are interested in the long term trends, we smoothed the Bitcoin search time series by country using a low-pass filter to focus on variation on a time scale of 3 years. Applying such approximation, each country Bitcoin search time series can be represented as a linear combination of k components, stored as the rows of matrix H , and with the coefficients stored in W. The left-hand side of Fig. On Fig. The shape of the 4 principal components are shown in Fig. We can see a trend of adoption with a high increase only starting from the middle of The other three components instead fluctuate over time and represent trends of attention that were already notable in the early years of Bitcoin.
Looking at the coefficient matrix, W , we separated the countries in 2 groups. Those having the increasing component as highest coefficient, that we call growing countries, and the others whose main components are the fluctuating components, that we call fluctuating countries. As shown in Table 5 , grouping countries by development indexes we observed that most of the developed countries are among the fluctuating countries.
On the other hand, a large part of the developing countries show a recent high interest in Bitcoin.
Got a tip?
The picture that emerges from this analysis is that at the beginning, attention towards Bitcoin comes only from the developed countries, while starting from we can see interest picking up in the developing countries. Output of the factorization of the matrix representing the Bitcoin search time series. The reconstruction error is given by the Frobenius norm of the matrix difference between the original and the approximated matrices.
The growing component red represents the trend of the new adopters. The other 3 components are the fluctuating ones, and mostly represent what we call the early adopters. Google Trends time series, original, filtered and reconstructed for 6 countries. For each country we plot: the raw values from Google Trends green , the filtered trend red , and the reconstructed trend after the NMF blue. In the first row we show 2 examples of high developed countries H with fluctuating trends. In the second and third row we report examples of countries with upper middle UM and lower middle LM development index and a growing trend of adoption.
The blue line is present but hidden under the red one due to the goodness of the approximation.
Going down the rabbit hole
As measured by the socio-economic indexes, the countries we are analyzing are very heterogeneous. Here we attempt to link the different socio-economic indexes with the different trends of adoption. Focusing on a time interval of one year, we compute the Spearman correlation coefficient between the rank of countries according to the number of client downloads or number of unique IP addresses normalized by population and the ranking according to different socio-economic indexes. The general picture that emerges is that socio-economic welfare—as present in most developed countries— appears to have stimulated the Bitcoin adoption, at least for the years , , and for which we could carry out this analysis.
Beside some expected correlations, like the one regarding the Internet penetration that represents an essential condition to participate in the Bitcoin network, the results obtained for the overall freedom and trade freedom are especially interesting. The two indexes provide a measure of the economic freedom. Trade freedom measures the presence of barriers that affect imports and exports of goods and services, it is measured starting from the average tariff that affect imports and exports of goods and services, and a penalty score that quantifies other type of trade regulation.
It combines measures for four broad categories: rule of law property rights, judicial effectiveness, government integrity ; Government size tax burden, government spending, and fiscal health ; regulatory efficiency business freedom, labor freedom, and monetary freedom and market openness trade freedom, investment freedom, and financial freedom. The correlations show a positive association between Bitcoin adoption and policies promoting economic freedom, which is somewhat contrary to the common notion that Bitcoin adoption could be driven by overly restrictive legislation.
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In this second section, we attempt to identify the key socio-economic indexes related to the international Bitcoin flow. The process that leads to the estimation of the Bitcoin flow network consists first of all in a clustering of Bitcoin addresses into users, through a deanonymization process, then in a mapping that assigns users to countries. Bitcoin transactions are made between Bitcoin addresses, which are the result of applying a hash function to some input string. Moreover users can create new Bitcoin addresses without limitation in order to hold, receive and send Bitcoin; this is computationally cheap and has no cost for them.
However, a partial deanonymization method exists and it permits to reveal the group of Bitcoin addresses likely owned by a single user. This additional step is essential for us to make hypothesis on the destination country of transactions, as the IP proxy gives information only on the sender of a transaction. Moreover this process is useful to remove the self change addresses and the related transactions as explained below. This method is based on two heuristics that take inspiration from the underlying functioning of the Bitcoin transaction [ 21 , 28 — 32 ].
The creator of the Bitcoin suggests, in his original paper, the first heuristic that deals with input addresses [ 33 ]. Users who hold more than one Bitcoin address can provide a certain number of input addresses in order to reach the desired amount he wants to spend.
Analysis of the Bitcoin blockchain: socio-economic factors behind the adoption
Due to this functioning, the same user might hold all the input addresses of a transaction. This observation is used to create the first heuristic. If two or more Bitcoin addresses are inputs to the same transaction, they are controlled by the same user. The sum of the Bitcoin contained in the input addresses has to be entirely spent. As a consequence, the part of the amount that exceeds the value that the sender wants to spend is usually sent to a new Bitcoin address.
The latter is called a shadow change address, it is created by the sender with the only purpose to collect back the change. For each transaction, one of the output addresses might be a shadow address.
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There is not an explicit self shadow addresses, in the sense that there is no Bitcoin address that is present both as an input and output of the same transaction. After applying the two heuristics, we do not have directly clusters of users, but we only have a partial aggregation at the transaction level.
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This process of grouping turns out to be computationally challenging for our large dataset. The heuristics are applied to each transaction and generate a large number of groups of addresses, of which we have to check all intersections to decide whether to group them. However this problem can be mapped onto the problem of finding the connected components in a network. We built a network in which Bitcoin addresses represented the nodes and they were linked together if they belonged to the same partial group.
We then extracted the connected components of this network. The whole deanonymization process is highly sensitive to any imperfection of the heuristics. The potential effect of a heuristic error is to infer a wrong grouping from some transaction, it could lead to collapse Bitcoin addresses of different users onto a single entity, with the risk of creating users that seem to control a huge number of Bitcoin addresses. Being aware of this problem, we tried to use the safest heuristics possible, even at the expense of discarding some true linking between Bitcoin addresses.
As some false linking could anyway occurs, the timespan we use for the deanonymization starts to play a key role; the longer the period of analysis, the bigger the probability that errors can cause the appearance of big clusters of Bitcoin addresses. Reducing the interval of the analysis might lead to the identification of a large number of small groups of addresses, in other terms the same user might still be split in several group of addresses.