ArticlePDF Available

Analyzing hack subnetworks in the bitcoin transaction graph


Abstract and Figures

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.
This content is subject to copyright. Terms and conditions apply.
Applied Network Science
Goldsmith et al. Applied Network Science (2020) 5:22
RESEARCH Open Access
Analyzing hack subnetworks in the
bitcoin transaction graph
Daniel Goldsmith*, Kim Grauer and Yonah Shmalo
Chainalysis, New York, USA
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.
Keywords: Cybercrime, Network analysis, Complex networks, Hacks, Crytocurrency,
Bitcoin, Cybersecurity, Temporal networks, Sociotechnical systems
The Bitcoin network is a distributed, public ledger, secured through blockchain technol-
ogy. All transactions occur between two distinct public addresses and are permanently
recorded on the specific blockchain built for bitcoin. The process of securing these trans-
actions is handled by bitcoin miners, who use their computing power to solve complex
cryptographic problems and in the process verify blocks and transactions (Nakomoto
Anyone can create a bitcoin address to receive funds through a variety of software
projects such as (BLOCKCHAIN LUXEMBOURG S.A 2011)orElectrum
wallets (Electrum 2011). Additionally, there is no limit to the number of bitcoin addresses
that any individual or organization can make. There are also no requirements for verifying
your identity in the process of address creation. It is completely free to make an address,
however, it costs money to transfer money on the network by paying transaction fees.
Because of the ease of transactions between pseudonymous addresses, cryptocurren-
cies, and bitcoin in particular have been especially attractive to criminals who both exploit
© The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate
credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were
made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless
indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your
intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly
from the copyright holder. To view a copy of this licence, visit
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 2 of 20
technological vulnerabilities and prefer to move funds through the pseudonymous bit-
coin transaction network to avoid detection by law enforcement (Huang and et al. 2018).
Indeed, the amount of cybercrime involving cryptocurrencies has grown via ransomware
(Huang and et al. 2018), scamming activity, phishing scams, and hacking of exchanges
or wallets (Chainalysis 2019). There have been several attempts to quantify the scale of
criminal activity as well (Yin and et al. 2017).
Notably, exchange hacks are one of the most costly types of cryptocurrency related
crime. Hackers have stolen $1.7 billion dollars worth of cryptocurrency from exchanges
since 2011 (Chainalysis 2019). Tracing stolen funds in order to freeze the assets of the per-
petrators is one of the most effective ways of safeguarding against future attacks, as this
method removes bad actors from the ecosystem and disincentivizes similar activity from
other actors. Typically, either government or private cyberinvestigators, take up the task
of tracing stolen cryptocurrency funds. Their investigations begin with a known address
that has been hacked. They then follow the funds through up to thousands of different
addresses until the funds hit a service (an off-ramp), i.e. an alternative means of cash-
ing out the stolen bitcoin. Ideally, an investigator will trace funds to a service so that a
subpoena can be issued to the service to unmask the identity of the criminal. These inves-
tigations result in traced out subnetworks representing the flow of stolen bitcoin from the
point of breech on an exchange through exit ramps.
We obtained six subnetworks from investigators at Chainalysis, a firm specializing in
blockchain investigations. These were investigations carried out over several months, and
which effectively trace all of the stolen funds through the entire bitcoin transaction graph.
Each edge is a transfer of the stolen money to a node which is controlled by the hacker.
The size and complexity of these graphs vary according to the amount of effort the hacker
used to move funds and that hacker’s level of technological sophistication.
Similar subnetworks can be collectively generated by the community of users that
trace funds on the public Bitcoin ledger and often does occur after a criminal steals
cryptocurrency on a public ledger (ErgoBTC 2019).
We present research to algorithmically visualize and analyze hack cash out subnetworks
that capture the temporal behavior of hackers and locate the stolen funds. We then build
similarity matrices based on eight graph features, run community detection over those
matrices, and successfully classify certain hacks to the known hacking organization to
have carried out the attack. We find that temporal features, such as the rate at which
the hackers send funds to exit ramps, are the most effective features to use for grouping
specific hacks together and classifying them to their hacking groups.
We find that this method might prove useful as a component of some automated classi-
fication system designed for anti-money laundering or anti-fraud detection of transaction
ledgers, not only for the specific use case that we describe in the work below as specific
to these investigations, Chainalysis, or even bitcoin as a whole.
Algorithmically traversing hack subnetworks and its limitations
We investigate bitcoin hacks by traversing subnetworks of nodes that have been built out
by professional crime investigators. These hack subnetworks are comprised of nodes that
have either directly or indirectly received hacked funds, see Fig. 1for visualization.
We then create visualizations to identify trends in the hack and to better under-
stand the time patterns specific to each hack as the stolen bitcoin flows to the
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 3 of 20
Fig. 1 Sample Hack Subnetwork, Hack A3
boundary of the networks generated, see Fig. 2. In some cases, when the level of
obfuscation is minimal, investigations tracking stolen funds often terminate at ser-
vices (see Methodology section on identifying services), simply because criminals want
to change their stolen bitcoin for fiat currency, or at least convert it to a another
Fig. 2 Amount in Play over Time
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 4 of 20
Yet cryptocurrency investigations are usually much more complex then this (Nouh and
et al. 2019). Often, the investigator may not know if a node belongs to a service, par-
ticularly in the case of a mixing service. Furthermore, stolen bitcoin from some of the
largest hacks may utilize laundering mechanisms in which OTC brokers act as third
party sellers allowing for a change of hands to an entity that is no longer behind the
hack. This activity can not be detected through blockchain analytics unless their is a
source of ground truth confirming the funds passing through on OTC broker. Without
this confirmation, the funds would appear to move from one pseudonymous node to
Sometimes the investigations are so complex that the investigator simply cannot go
through the process of tracing every single stolen bitcoin to an cash out point. In this case,
the investigator may choose to chase particularly promising leads, rather then spend the
time to analyze every single transaction that occurred. At any given time, stolen funds
may be sitting idly in non-service clusters for extended periods of time. In practice, it is
common for funds to slowly leak out of these “holding” clusters (Chainalysis 2019).
Generally, as networks are built out manually by subject matter experts, methods
such as the one proposed below can help ensure that the proper classifications of these
networks have been achieved.
1. We first gather subnetworks of known hacks that have been built out by
professional investigators.
Due to the sensitivity of this data and relative infrequency of hack events, the
result of this process provided a small set of anonymized, curated subnetworks
that trace stolen funds from the origin of the hacks to all end points of interest.
It is at this point that we introduce a new tool for analyzing these subnetworks
for additional insights that we can eventually return to the investigators and
compliance officers at exchanges.
2. We traverse these subnetworks from the starting clusters through the boundary of
the subnetwork.
An element of complexity emerges in this analysis that requires additional
attention, namely that the terminal nodes require a more rigorous definition
than any cluster sitting on the outskirts of the subnetwork since many of these
terminal nodes act as sinks but still slowly leak funds despite maintaining
control over the majority of their hacked balance. This definition will be
fleshed out in the subsection “Defining Terminal Nodes.” Additionally, as seen
in Table 1, the simple static network characteristics demonstrate that the data
is tree like, with low average degrees (in- and out-degrees are equivalent on
average) and low clustering coefficients. Yet the complexity due to the
temporal nature of the subnetworks as well as the nature of these terminal
nodes require additional features to be defined before information can be
meaningfully extracted from the data, since it is not always the leaves of these
tree-like subnetworks that play important roles, either from the temporally -
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 5 of 20
Table 1 Summary Statistics for Each Hack
Hack Txs Nodes Avg In-Deg Clust. Coeff
A1 1,981 1,257 1.02 0.001
A2 421 55 1.11 0.041
A3 607 218 1.05 0.008
B1 190 176 1.01 0.000
B2 374 335 1.06 0.002
B3 57,299 174 1.62 0.068
in that they arrive latest - or topologically - they sit farthest in the transaction
3. Next, to better visualize the temporal activity in the hacks, we create two time
series that display the activity of the hacked funds.
First, we measure how active the hackers are over time by computing the
number of transfers the hackers make each day, as seen in Fig. 3.
Second, we measure the funds traced as they move to terminal nodes, as seen
in Fig. 2. As the funds move through terminal nodes, the share of funds still
Fig. 3 Transactions over Time
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 6 of 20
held by hackers decreases. A fully tracked hack subnetwork would be visualized
by the funds decreasing from 100% to 0% of funds still held by the hacker over
the number of days that it takes to fully exit the funds through terminal nodes.
4. We then generate distributions for the following features for each hack subnetwork:
Logarithm of Hack balance of all nodes, see Fig. 4.
Weighted In-degree of all nodes, see Fig. 5.
Weighted out-degree of all nodes, see Fig. 6.
Average number of transactions to terminal nodes per day, across all ρvalues,
derived from data shown in Fig. 3.
Terminal Nodes as a function of ρ, see Fig. 7.
Logarithmic difference of the average percent of funds still in play, across all ρ
values, derived from data shown in Fig. 2.
Second difference of the average percent of funds still in play, across all ρ
values, derived from data shown in Fig. 2.
Logarithmic difference of the standard deviation of the percent of funds still in
play, across all ρvalues, derived from data shown in Fig. 8.
Fig. 4 Distribution of Log Balance
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 7 of 20
Fig. 5 Distribution of In Degree
5. Afterwards, we create similarity matrices corresponding to each distribution,
whose elements are the pairwise similarities of the distributions corresponding to
each of the hack subnetworks via the 1-Dimensional Wasserstein Distance, i.e. the
Earthmover Distance (Villani 2003;).
6. We run two community detection algorithms, Modularity Optimization (Clauset
and et al. 2004) and Walktrap (Pons and et al. 2013). We compare the output of the
overall approach across the similarity matrices for all the distributions against our
ground truth attribution of the two underlying hacking groups and demonstrate
the potential for such a method by properly reattributing the hack networks to
their respective groups. Both this step and the previous step are motivated by the
idea that relational data is best analyzed using the tools of network science and the
similarity of the distributions between the hacks in question fall into relational
data. For a larger range of approaches utilizing complex networks for more general
data clustering see (de Arruda and et al. 2012). The reason we employ purely
topological distance here, rather than the exponent of a related distance as
suggested in de Arruda and et al. (2012), is due to the inherent assumption that the
behavior of the underlying hacking groups are similar to the point of minor
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 8 of 20
Fig. 6 Distribution of Out Degree
perturbations in the underlying distributions of activity, which we believe the
Earthmover Distance is particularly well suited to detect.
7. Lastly, we review the output communities and test our hypothesis that the features
relating to the hack dynamics are more informative in classifying the hacking
groups than the static network features.
Identifying services
A typical service can control thousands of addresses, while larger services can even man-
age into the millions. We identify services by exploiting features unique to the Bitcoin
blockchain. There are many different approaches that blockchains employ to crypto-
graphically verify transactions, but the Bitcoin blockchain relies on Unspent Transaction
Outputs (UTXO’s) to record all transactions. A UTXO is the unspent output of a pre-
vious transaction that a user is entitled to transfer to another bitcoin address. Every
wallet that holds a positive bitcoin balance is in possession of at least one UTXO. When
multiple UTXO’s are held by a single user and spent together in a transaction, it then
becomes possible to definitively ascribe common ownership to all of the UTXO’s that
were spent together. This concept of a cospend is the basis of the clustering activity used
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 9 of 20
Fig. 7 Number of Terminal Nodes as function of ρ,TvR
by blockchain analysis firms such as Chainalysis to identify clusters of addresses con-
trolled by a single entity. The network then becomes comprised of cospend clusters, i.e.
nodes, composed of multiple addresses rather than long chains of single-use addresses
(Meiklejohn and et al. 2013; Akcora and et al. 2019).
Once addresses have been mapped to a node through cospending activity, the node
can be mapped to a named entity by interacting directly with it. For the example of an
exchange, this process can occur by visiting an exchange’s website, depositing funds on
the exchange, and tracing that transaction via a block explorer (BLOCKCHAIN LUX-
EMBOURG S.A 2011). Only services with publicly available address information can be
identified in this way.
When stolen funds arrive at a known service, such as a an exchange, we can assume that
the hackers have attempted to cash out their funds. Professional investigators trace funds
through these nodes to create hack subnetworks that capture as much of the meaningful
movement of the stolen funds as possible.
Defining terminal nodes
There are two types of terminal nodes discussed in this paper. 1) A known service terminal
node that is a confirmed service through the process mentioned above of pairing ground
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 10 of 20
Fig. 8 Standard Deviation of Amount in Play over Time
truth knowledge with cospending activity. These services can be exchanges, mixers, gam-
bling sites, merchant service platforms, or any exit ramp through which a criminal can
off-load stolen bitcoin to an institutional cryptocurrency player. 2) An unknown service
node, where the investigator has reason to believe a node is behaving like a service and
will therefore terminate the investigation at that point.
One problem may arise when the investigator simply chooses to stop pursuing a lead.
At this point, the boundary of their investigated subnetwork might resemble a terminal
node. This limitation should be further investigated in future work. In the cases of the
subnetworks chosen for this research, the investigators followed all leads, which limited
the terminal nodes to those described above.
By default, terminal nodes are the edges of the graph subnetwork. Ideally, a subnetwork
of a hack would track 100% of the funds from the point of a hack through all exit ramps.
This would allow us to set ρ=0.00, as the terminal nodes would simply be all the natural
edges of the graph. In this case, the investigator would trace funds to a service, whether
it be an exchange, mixing site, gambling site, etc. ρ=0.00 indicates that a node has only
ever received funds within the subnetwork.
We focus on the ratio rather than the difference of funds sent to received because
we want to maximize the number of meaningful leads for investigators rather than raw
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 11 of 20
amount due to hacked funds. By returning this normalized list of terminal nodes and
resulting charts, we find all partial sinks “of interest” in the subnetwork that may facil-
itate the issuance of subpoenas or other leads, as well as wallets to watch because they
still contain funds, large or small. As a secondary filter, we can sort by balance due to the
hack, but this feature is only relevant in the operational stage for investigators, not when
conducting our analysis.
We de fine ρas:
ρ=weighted in-degree
weighted out-degree ,
i.e. the ratio for a given node of the total amount of funds it sent to the total amount of
funds it received.
Others have proposed using ratios of the in/out degrees when studying the Bitcoin
Transaction Graph, but in different contexts and not as a node-level feature (Bovet and et
al. 2018). We introduce this ratio as a means of classifying individual nodes based on fea-
tures specific to networks of financial transactions. This is particularly important when
trying to capture the underlying behavior of the nodes over time, as value flows in the
temporal network that they collectively compose.
Subnetworks that vary over time, such as hack investigations, generate terminal nodes
throughout the duration of the network’s activity. Terminal nodes with high ρvalues
should represent an optimal list of possible leads for an investigation, since they represent
sinks of value in the transaction graph and are therefore plausibly operated by the true
perpetrator of the hack or another entity of interest.
Figure 9shows the spectrum of ρvalues and their subsequent interpretation.
Visualizing temporal behavior in the hack subnetworks
The temporal visualizations are shown in Figs. 3and 2.Figure3shows the number of
transfers over time within the hack subnetwork so that the investigator can get a sense of
how active the hackers are over time. They can answer questions such as: does the hacking
group consistently make transactions over time, or do they tend to move funds according
to a temporal pattern. A pattern may be indicative of an algorithm moving the funds, as
opposed to actual individuals approving the transactions.
Figure 2shows how the funds exit over time through terminal nodes. It allows an inves-
tigator to see the exiting strategy of the hacking group in time. For example, do the hackers
exit the funds in one period of time, or consistently over a longer duration of time? Each of
these strategies has implications for how the investigator profiles the hacking group over-
all. For example, a hacking group that exits all the funds through one exchange in one day
Fig. 9 Spectrum of rho values and their significance
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 12 of 20
may be less organized and less well-funded than a hacking group that gradually, through
thousands of strategic transactions, exits the funds over a long period of time.
The trends are made visible by restructuring the hack subnetworks into time series.
Figure 3demonstrates how active the hackers are by using the number of transactions
they carry out as proxies.
Figure 3allows us to see the way the hackers utilize terminal nodes. Hacking group
alpha (A1) is much more active, slowly moving funds through terminal nodes over a
shorter period. Hacking group beta (B1) utilizes fewer transactions in general, but tends
to send all of their transfers to terminal nodes in a short period of time. In the case of
chart B1 in Fig. 3, the hackers sat on their funds for a long period of time before abruptly
exiting over 70% of the funds through a few exit ramps within a one week period.
To test the hypothesis that the hackers are best classified using temporal features such
as the rate at which funds cash out at terminal nodes, we vary ρin the following sensitivity
analysis section to observe stolen bitcoin exiting through terminal nodes under a range of
Sensitivity analysis of ρ
We allowed ρto range from 0.02 to 0.98 to test the implications of gradually change the ρ
parameter. A cluster with a very low ρvalue, e.g. ρ=0.1, would have to hold on to more
90% of the funds it received to be considered a terminal node. On the other hand, a very
high ρvalue, e.g. ρ=0.9, allows a cluster to retain only 10% of the funds it received from
the hack in order for it to be considered a terminal node. A higher ρwill capture many
more terminal nodes, as it is an easier condition for nodes to meet.
A lower ρvalue means that the there are fewer terminal nodes picked up in the graph,
and the criteria for being “of interest” to an investigator is extremely high. A very low ρ
specifies that wallets of interested are those which may only hold small amounts of the
total funds that it received. A node holding over 90% of the funds might be a holding
wallet gradually leaking out funds, it might be a consolidation wallet for a criminal ring,
a wallet associated with other types of criminal activity, or even a point of conversion to
another cryptocurrency if, for example, the wallet is an Exodus wallet, which allows for
wallet level cryptocurrency conversions.
Choosing the right value for ρallows us to optimally grow the hack subnetwork such
that it would include the paths of interest without becoming too large to meaningfully
analyze. We found that setting the ratio too high resulted in a less meaningful yet larger
hack subnetwork, where the terminal nodes did not adequately capture dynamics of inter-
est, and setting the ratio to be too low did not include clusters that likely should have been
Applying a range of ρfrom ρ=0.02 through ρ=0.98, in increments of 0.02, had
very large implications for the amount of funds considered to be tracked. While chang-
ing ρtypically revealed how much of the funds the investigator tracked, at the same
time, changing the ρvalue does not impact the overall cash out trend witnessed by the
These results indicate that varying ρmay not be useful for understanding the behaviors
of the hacker, but is a useful tool for identifying nodes of interest that could be possible
leads to the investigator. Indeed the variance in the ρparameter proved one of the most
useful tools for running community detection.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 13 of 20
We finally then needed to handle the introduction of funds at a time later than the hack
by either the same or different user. To account for this, we either add these new flows to
the funds at the start and work with the new total as our amount of hacked funds, or we
incorporate these flows into our ρdefinition, by stating a further constraint that if ρ>1,
then it is a terminal node and we do not follow its flows forward in time. In the case of the
former, we can track all funds engaged in clearly illicit activity, regardless of source, while
in the case of the latter, we are actively restricting the subnetwork to funds that explicitly
originated from the source of the hack.
Feature definitions
The goal when selecting which distributions to analyze was to capture the behavior of
movement of the hacked funds in a precise way. To confirm the hypothesis that the two
hacking groups exhibit different cashout strategies, we decided to consider the empirical
distributions of 8 different features, as mentioned in Step 4 of the Pipeline.
In the following definitions, the expectations are defined over the nodes of the subnet-
works (and terminal nodes in the case of Transactions). Additionally, the time units are
discretized at the daily level. Lastly, the Initial Hack Amount is the value stolen from the
exchange by the hacking group which was the source of the investigated subnetworks.
We define several of the features in our analysis as follows:
1. Amount in Play.
AIP =Initial Hack Amount terminalnodes weighted in degree
2. Hack balance of all nodes.
Bal =log(weighted in degree weighted out degree)
3. Logarithmic first difference of the average,
, percent of amounts still in play,
LDA =log E[AIP(t+1)]
4. Second difference of AIP, across all ρvalues.
Second Diff (AIP)=LDA(t+1)LDA(t)
5. Logarithmic difference of the standard deviation,
=log E[(AIP(t+1)E[AIP(t+1)])2]
6. Average number of transactions to terminal nodes,
per day, across all ρvalues.
Transactions =E[TTN]
Similarity matrices
Once all of the normalized histograms were generated, we measure the pair-wise simi-
larity between them, per variable, via the 1-Dimensional Wasserstein Distance, a.k.a. the
Earthmover Distance or L1Norm. Generally, the LpNorm is defined as:
where Fand Gare empirical distribution functions with generalized inverses, F1and
G1(Villani 2003;).
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 14 of 20
Community detection
After the similarity matrices are computed for the distributions of interest, the goal
becomes differentiating between the two hacking groups. We propose a method of rep-
resenting the similarity matrices as networks and searching for two distinct communities
via both Modularity Optimization and Walktrap and comparing the results.
Modularity Optimization (Clauset and et al. 2004) consists of finding a near maximal
value for Modularity, Q, returned from the communities applied to some null model of
network formation, typically a Random Network.
vw Avw kvkw
where misthenumberofedgesinthenetwork,Avw is 1 when nodes vand ware con-
nected and 0 otherwise, kvis the sum of Avw over w,andδ(i,j)is 1 when iand jare equal
and 0 otherwise.
Walktrap (Pons and et al. 2013) operates similarly, also attempting to optimize the same
modularity, but with a focus on short random walks exiting communities as the explicit
motivation and approach.
Both algorithms are built for analyzing large networks, and their true modularity
optimization functions are not explicitly the Qwritten above, but a derived form.
We utilized both methods as independent confirmation rather than any benefits from
their relative optimizations. As the resulting networks are small, with one node cor-
responding to each hack, are eight distributions analyzed, and two applications of
community detection, any conclusions drawn from our method are only tentative since
no conclusive results can be drawn from such small amounts of data. Nevertheless, we
propose the full method as technically sound and a novel tool in the analysis of hack
subnetworks in the bitcoin blockchain.
As discussed in the Methodology, the communities shown in Fig. 10 correspond to those
identified by two clustering algorithms with the first two rows being Walktrap’s output
communities on each distribution’s similarity network as seen in Fig. 11,andthesecond
two rows being the results obtained via Modality Optimization. As can be seen, similarity
matrices derived from different distribution comparisons, whether analyzed by the same
or different algorithm lead to different observed communities. Though they are often
different, the communities do share some common characteristics with each other. For
example, for all but the clustering of Balance similarity and TvR, nodes {B1, B2, B3}are
always clustered together. Furthermore, 9 out of the 16 clusters have at least two members
of group A together.
To better quantify consensus among the results in Fig. 10,wefirstfindonenodeN
which remains in the same group through all of the methods (we chose node B6) so as to
establish a common group naming (in other words, it is no longer the case that a node is
either in the blue or the red group seen in Fig. 10, rather that each node is either in the
same group as our fixed node or in the opposite group), and then we generate a number
ni,jassociated to each node iand community j,withj∈{1, 2, 3, ...,16}, setting ni,j=1
if iis in the same group as Nand ni,j=0 otherwise. We then compute the probability
of node ibeing in the same group as Nwith p=16
16 . Finally we bisect the vector of
values to along its median and obtain the grouping {A1, A2, A3},{B1, B2, B3}.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 15 of 20
Fig. 10 Communities for all features’ similarity matrices - First by Walktrap then Modularity Optimization
Fig. 11 Similarity Matrices of Feature Distributions for Hacking Groups A and B
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 16 of 20
This process was repeated using two feature set combinations. The first set contained
all 8 features, and its resulting vector was (0.625, 0.5, 0.1875, 0.8125, 1, 1). The second
set included only temporal features, namely: LDA, Second Diff(AIP), LDST, and ATVR
and had a resulting vector of (0.25, 0.5, 0, 1, 1, 1). Note, that the ground-truth vector is
simply (0, 0, 0, 1, 1, 1). In both cases, the bisection works to successfully find the two
communities. In the case of only temporal features, the results are even more compelling
We ran this analysis on historical hacks curated by Chainalysis investigators. The 6 hacks
analyzed were carried out by 2 distinct and well-known hacking groups that have been
active for the past several years. Each hack was manually classified by the investigators
into one of the two groups, which we take as ground truth. We did not include images of
these investigations because they visually did not contribute towards understanding the
hacking methods.
Analyzing the subnetworks using our proposed methodology allowed investigators to
observe the cash out methods for the different hacking groups. Furthermore, the analy-
sis of each subnetwork based on the features above facilitated greater understanding of
each specific hack and hacking group, as well as the ability to successfully classify the
subnetworks into their respective hacking groups via our pipeline.
Hacking group alpha
We analyzed three distinct hacks carried out by hacking group alpha. Hacking group
alpha is a large, well-funded organization. The hacks analyzed in this paper reveal that
the subnetworks tracing funds stolen by hacking group alpha are highly complex, with
the stolen funds moving through many nodes. The stolen bitcoins are slowly cashed out
through terminal nodes overtime. Investigators confirmed this trend.
Funds flowing to terminal nodes from the three hacks visualized in Fig. 2further con-
firm this trend. Stolen bitcoin being moved by hacking group alpha appear to slowly leak
out of possession of the hackers through terminal nodes. Taking both the first and second
differences for the amount in play visualized in Fig. 2demonstrates that the acceleration
at which stolen funds exit through terminal nodes is a significant means of clustering the
graphs. Just taking first differences successfully clusters hack A3 and hack A1 together.
Visually, A1 and A3 are more similar. Looking at the second differences, i.e. the accelera-
tion, for the amount in play visualized in Fig. 2is most successful at finding communities
of hacks. Running community detection on the similarity matrices for the second differ-
ences of the amount in play successfully identifies that A1, A2, and A3 belong in the same
The number of transfers that the hackers use to move the funds has also proven sig-
nificant for helping to effectively classify the hacks according to their hacking groups. As
shown in Fig. 3, hack A2 and A3 appear to have similar trends in terms of the number of
transfers made each day following the hack. The community detection that we ran on the
hacks classified these two hacks together when looking only at trends in the frequency of
transactions sent to terminal nodes.
Analysing the variance in the ρparameter, as visualized by Fig. 8captures how the
share of funds exiting through terminal nodes changes as ρapproaches 1. The standard
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 17 of 20
deviation for the ρparameter as ρapproaches 1 approximates the variety in behavior for
terminal nodes. Using the log difference in standard deviation across the amount in play
by varying ρallows us to classify hacks A3 and A1 together. Both these hacks had similar
changes in the amount in play for each ρover time, whereas A2 had some uncharacteristic
behavior for hacking group alpha around day 250. A2 was a much smaller sized subnet-
work, with only 55 nodes, than A1 and A3, with 1257 and 218 respectively. This made
the standard deviation of the amount exiting through terminal node more sensitive as ρ
We investigated whether the distribution of balances across all the nodes in the hack
would be a useful indicator to help classify hacks. This was one of the weakest features
used to classify the hacks into hacking groups. As shown in Fig. 4there is a wide vari-
ety in the distribution across all the nodes in the graph based on their hack balances.
Hack A3’s distribution, for example, had a higher peak, meaning many of the hacks in A3
held a similar balance. Yet A2 had much more variety across the nodes within the graph
in terms of how much stolen bitcoins each node ended up holding. Using the distribu-
tion of the log balance by nodes was not useful on its own to help classify hacks, and
caused one of the few instances of mistakenly grouping hacks A3 and B4 together as seen
in Fig. 10.
Hacking group beta
We then analyzed three hacks carried out by the second hacking organization referred to
here as hacking group beta. When visualizing the hack subnetworks for hacking group
beta, there are striking differences in the cash out mechanisms. Hacking group beta
tends to send a majority of its funds through terminal nodes over a short period of time.
They tend to sit on their funds quietly, sometimes moving some funds through wallets of
interest, but have a characteristically abrupt cash out pattern.
This pattern is visualized in Fig. 2, where hacks B1, B2 and B3 all have notable vertical
drops, representing abrupt moments of cashing out through terminal nodes. Running
our community detection algorithms on the first differences of this activity successfully
classified all B hacks as belonging together, see Fig. 10, yet also identified hack A2 as
fitting a similar pattern. The second differences for the amount in play chart is the best at
predicting the proper community assignment. Its top performance can be attributed to its
correctly capturing the acceleration of the funds exiting through terminal nodes, which
confirms the hypothesis put forward by investigators about temporal trends in exiting
All of the hacks from hacking group beta have a large variance for ρas ρapproaches one,
which can also be visualized in 2. This signifies a large range in sending versus receiving
behavior for the nodes within the hacking group beta hacks. Funds are exiting through
a wide variety of nodes, and not simply hitting one exit point which only ever received
Looking at the distribution of balances held by the nodes within the subnetwork demon-
strates the variety of node behaviors present. However, this was again a weak feature when
it came to classifying the hacks through community detection. Hack B1 had many nodes
that passed through mixing services which were unclustered in the subnetwork. The mix-
ers would siphon off parts of the stolen funds into consolidator wallets in similar patterns.
The investigator only tracked the fattest paths, leaving many of the known nodes passing
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 18 of 20
through mixers with a similar balance. Using balance distribution when the graph is not
fully built out was shown not to be useful for community detection.
We next looked at the variation in the AIP over all ρas visualized in Fig. 8.Theshape
of this graph visualizes how ρaffects the share of funds exiting through terminal nodes.
Almost all of hack B1’s funds exit through a wide variety of terminal nodes on the first day.
The standard deviation peaks at this point, followed by a long period of no fund move-
ments. We successfully classified hacks B1, B2, and B3 together using our community
detection algorithms, but hack A2 was mistakenly grouped in when using this feature, as
shown in Fig. 10.
We then analyzed the number of transactions going to terminal nodes in Fig. 3.The
number of transactions showed no clear visible pattern to help classify the hacks into
hacking groups. While the community detection algorithms successfully classified all
three hacks from hacking group beta together, it also picked up hack A1.
Key takeaways
We began this analysis by talking with Chainalysis investigators about what they knew
about the hacking groups. They indicated that the key differentiation between the two
groups, is the pattern by which they hold funds and the subsequent rate at which they
cash them out. Our analysis confirms this hypothesis.
We conclude that static features of the charts, such as balance distributions, in degrees,
and out degrees are not useful features for classifying the hacks into hacking groups.
There are many limitations to these static features. To start, they likely require a fully built
out, comprehensive graph. Many of the graphs we chose to analyze were incomplete from
the start. This means the takeaways from the static features of the charts were also fun-
damentally incomplete. Table 1contains general summary statistics that further reinforce
the relative scarcity of meaningful information from the static features for the hacks.
More importantly, our hypothesis of focusing on the temporal features of the subnet-
works, rather than the static features was validated. The results indicate that the patterns
by which the subnetworks evolve over time serve as useful features for optimal clas-
sification based on the method described in this paper. The optimal classifications in
Fig. 10, specifically the second difference - or acceleration - of AIP, are most charac-
teristic of the subnetworks temporal nature. Varying ρto alter our level of resolution
into terminal nodes also plays a role in the usefulness of our temporal features and
the resulting classifications. The correct classifications were obtained when similarity
matrices were built from these temporal features and the community detection algo-
rithms was subsequently run to differentiate the hacking groups based on these features
Hacks represent an important challenge for law enforcement, the Bitcoin community, and
financial institutions. There is opportunity for an algorithmically informed approach to
analysis of existing hacks as well as real time monitoring of hacks. This research rep-
resents an attempt at building a more rigorous framework for such an approach via
an analysis of both the static and temporal features of hack subnetworks and suggests
that the temporal features represent an important avenue of exploration for a deeper
understanding of the hack subnetworks.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 19 of 20
Future work
In this paper, we have described our proposed approach for analyzing characteristics
of the hack subnetworks within the broader bitcoin transaction graph as a means of
classifying specific hacks to their respective perpetrating hacking groups. We find that
specifically, the temporal characteristics are the most effective for allowing this catego-
rization to occur. Our methods, however, can also be used in other contexts. Open source
investigations, for example, can exploit these methods to more effectively track stolen
funds from the breach point on the exchange that has been hacked.
This technique also, for example, could be used even in fiat systems such as the swift
network. For example, once a potential fraud flag is raised on an account, this method
could be used to learn from the behavior of the fraudulent actors. There are, however,
limitations to extending this method to the fiat system. One key distinction between our
use case and the fiat example stems from how we knew the hack was initiated by either of
only two actors. If however one considers a much larger system with many more potential
criminal actors, it might take many ground truth examples and a more robust learning
algorithm to distinguish between the broader scope of potential illicit actors.
AIP: Amount in Play; Bal: Balance; LDA: Logarithmic first difference of the average; TvR: Number of Terminal Nodes vs ρ;
UTXO: Unspent Transaction Output
We thank the Chainalysis investigators for their collaboration.
Authors’ contributions
DG, KG, and YS designed research, performed research, and wrote the paper. All authors read and approved the final
This research was funded by Chainalysis.
Availability of data and materials
Due to the sensitivity of the underlying data, we cannot currently release our dataset.
Competing interests
The authors declare that they have no competing interests.
Received: 18 October 2019 Accepted: 4 March 2020
Akcora CG, et al. (2019) BitcoinHeist: Topological Data Analysis for Ransomware Detection on the Bitcoin Blockchain
BLOCKCHAIN LUXEMBOURG S.A (2011) Block Explorer. Accessed 12
Dec 2019
Bovet A, et al. (2018) Network-based indicators of Bitcoin bubbles
Chainalysis (2019) Chainalysis Cryptocrime Report 2019.
cryptocrime-review. Accessed 12 Dec 2019
Clauset A, et al. (2004) Finding community structure in very large networks. Phys Rev E 70:66–111
de Arruda GF, et al. (2012) A complex networks approach for data clustering. Phys A 391:6174–6183
Electrum (2011) Electrum Wallet. Accessed 12 Dec 2019
ErgoBTC (2019) Tracking Plustoken Funds. plustoken-
whale-attempted- bitcoin-laundering-and- its-impact- on-wasabi-wallet-
787c0d240192. Accessed 12 Dec 2019
Huang DY, et al. (2018) Tracking Ransomware End-to-end. In: 2018 IEEE Symposium on Security and Privacy (SP): 20-24
May 2018. IEEE, San Francisco. pp 618–631
Meiklejohn S, et al. (2013) A fistful of bitcoins: characterizing payments among men with no names. In: IMC ’13
Proceedings of the 2013 conference on Internet measurement conference: 23 - 25 October 2013. ACM, Barcelona.
pp 127–140
Nakomoto S (2009) Bitcoin: A Peer-to-Peer Electronic Cash System.
paper. Accessed 12 Dec 2019
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Goldsmith et al. Applied Network Science (2020) 5:22 Page 20 of 20
Nouh M, et al. (2019) Cybercrime Investigators are Users Too! Understanding the Socio-Tehnical Challenges Faced by
Law Enforcement. In: Proceedings of the 2019 Workshop on Usable Security (USEC) at the Network and Distributed
System Security Symposium (NDSS), 24-27 February 2019. ACM, San Diego
Pons P, et al. (2013) Computing communities in large networks using random walks. In: IMC ’13 Proceedings of the 2013
conference on Internet measurement conference: 23 - 25 October 2013. ACM, Barcelona. pp 127–140
Villani C (2003) Topics in Optimal Transportation, Graduate Studies in Mathematics. Am Math Soc.
Villani C Optimal Transport: Old and New. Springer
Yin S, et al. (2017) A first estimation of the proportion of cybercrminal entities in the bitcoin ecosystem using supervised
machine learning. In: 2017 IEEE International Conference on Big Data (Big Data). p 17504747.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Terms and Conditions
Springer Nature journal content, brought to you courtesy of Springer Nature Customer Service Center GmbH (“Springer Nature”).
Springer Nature supports a reasonable amount of sharing of research papers by authors, subscribers and authorised users (“Users”), for small-
scale personal, non-commercial use provided that all copyright, trade and service marks and other proprietary notices are maintained. By
accessing, sharing, receiving or otherwise using the Springer Nature journal content you agree to these terms of use (“Terms”). For these
purposes, Springer Nature considers academic use (by researchers and students) to be non-commercial.
These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal
subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription
(to the extent of the conflict or ambiguity only). For Creative Commons-licensed articles, the terms of the Creative Commons license used will
We collect and use personal data to provide access to the Springer Nature journal content. We may also use these personal data internally within
ResearchGate and Springer Nature and as agreed share it, in an anonymised way, for purposes of tracking, analysis and reporting. We will not
otherwise disclose your personal data outside the ResearchGate or the Springer Nature group of companies unless we have your permission as
detailed in the Privacy Policy.
While Users may use the Springer Nature journal content for small scale, personal non-commercial use, it is important to note that Users may
use such content for the purpose of providing other users with access on a regular or large scale basis or as a means to circumvent access
use such content where to do so would be considered a criminal or statutory offence in any jurisdiction, or gives rise to civil liability, or is
otherwise unlawful;
falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association unless explicitly agreed to by Springer Nature in
use bots or other automated methods to access the content or redirect messages
override any security feature or exclusionary protocol; or
share the content in order to create substitute for Springer Nature products or services or a systematic database of Springer Nature journal
In line with the restriction against commercial use, Springer Nature does not permit the creation of a product or service that creates revenue,
royalties, rent or income from our content or its inclusion as part of a paid for service or for other commercial gain. Springer Nature journal
content cannot be used for inter-library loans and librarians may not upload Springer Nature journal content on a large scale into their, or any
other, institutional repository.
These terms of use are reviewed regularly and may be amended at any time. Springer Nature is not obligated to publish any information or
content on this website and may remove it or features or functionality at our sole discretion, at any time with or without notice. Springer Nature
may revoke this licence to you at any time and remove access to any copies of the Springer Nature journal content which have been saved.
To the fullest extent permitted by law, Springer Nature makes no warranties, representations or guarantees to Users, either express or implied
with respect to the Springer nature journal content and all parties disclaim and waive any implied warranties or warranties imposed by law,
including merchantability or fitness for any particular purpose.
Please note that these rights do not automatically extend to content, data or other material published by Springer Nature that may be licensed
from third parties.
If you would like to use or distribute our Springer Nature journal content to a wider audience or on a regular basis or in any other manner not
expressly permitted by these Terms, please contact Springer Nature at
... Entity Graph), (iv) Transaction and Address Graph, and (v) Hypergraph. Our literature review includes the following references (Ober et al., 2013;Ron and Shamir, 2013;Zhao and Guan, 2015;Battista et al., 2015;Fleder et al., 2015;Maesa et al., 2017;Haslhofer et al., 2017;Akcora et al., 2018;Phetsouvanh et al., 2018;Maesa et al., 2018;Gaihre et al., 2018;Goldsmith et al., 2019;Pontiveros et al., 2019;Maesa et al., 2019;Sharma and Bhatia, 2020;Lv et al., 2020). ...
... They also perform a temporal analysis, studying how the different components change over time. (Goldsmith et al., 2019) Authors analyze six hack subnetworks of bitcoin transactions known to belong to two prominent hacking groups (Pontiveros et al., 2019) Authors propose propose a new centrality measure named mint centrality. The measure uses the inherent tree structure of transactions in bitcoin and their relation to the corresponding set of coinbase transactions (Sharma and Bhatia, 2020) Authors analyze payments to Ransomware. ...
Full-text available
Bitcoin is the most well-known cryptocurrency. It was first released in 2009 by Satoshi Nakamoto. Bitcoin serves as a decentralized medium of digital exchange, with transactions verified and recorded in the blockchain. The latter is a public immutable distributed ledger that operates without the need of a trusted record keeping authority or a central intermediary. It provides OLTP capabilities with both atomic transactions and data durability guarantees for blockchain transactions. Blockchain ledgers were not designed to perform analytics questions. The availability of the entire bitcoin transaction history, stored in its public blockchain, offers interesting opportunities for analyzing the transactions to obtain insights on users/entities patterns and transactions patterns. For these purposes, the authors need to store and analyze cryptocurrency transactions in a data warehouse. In this chapter, they investigate public blockchain datasets, and they overview different data models for setting up a data warehouse appliance of cryptocurrencies.
... In 2018, based on previous research, Matzutt [10] identified blockchain fund transfers and uploaded illegal content and found that in more than 1600 documents, most of them were text or images, and these documents had obvious illegal content. In 2020, Goldsmith [11] identified and analyzed the blockchain hacker subnetwork and found that hackers would change BTC into certain specific funds. In addition, according to the network characteristics, hackers were classified into different hacker groups. ...
Full-text available
Malicious users can upload illegal data to the blockchain to spread it, resulting in serious threats due to the tamper-proof characteristics of the blockchain. However, the existing methods for uploading illegal data identification cannot select trust nodes and ensure the credibility of the identification results, leading to a decrease in the credibility of the methods. To solve the problem, this paper proposes a blockchain-based trust model for uploading illegal data identification. The trust model mainly has the following two core modules: Reputation-based random selection algorithm (RBRSA) and incentive mechanism. By assigning reputation attributes to nodes, the proposed RBRSA will select nodes according to reputation values. RBRSA favors the nodes with high reputation value to ensure the randomness and credibility of the identification nodes. The incentive mechanism is designed to ensure the credibility of the identification results through the credibility analysis of the model based on game theory and Nash equilibrium. Identification nodes that identify illegal data correctly will obtain incentives. In order to obtain a higher income, the identification nodes must identify illegal data correctly. Credibility analysis and comparative experiments show that the probability of selecting credible nodes by RBRSA is up to 23% higher than the random selection algorithm. The probability of selecting the nodes with a reputation value of 20 by RBRSA is 27% lower than the random selection algorithm; that is, the probability that RBRSA selects untrusted nodes is lower. Therefore, the nodes selected by RBRSA have superior credibility compared with other methods. In terms of the effect of the incentive mechanism, the incentive mechanism can encourage nodes to identify data credibly and improve the credibility of identification results. All in all, the trusted model has higher credibility than other methods.
... Our dataset has been pre-processed by Chainalysis Inc following approaches as in [73,74,75]. This process uses established heuristics [76,77,78,79,80] in order to map addresses into entities. ...
Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyze two datasets containing 245M transactions (16B USD) that took place on online marketplaces between 2010 and 2021. The data cover 28 dark web marketplaces, i.e., unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, lifetimes available products, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylized facts of the data. Our findings have implications for understanding market power on online marketplaces as well as inter-marketplace competition.
... This dataset has been made public by the original researchers who worked on the Bitcoin Heist for ransomware detection on the Bitcoin Blockchain [8]. An analysis study of the hack subnetworks in the Bitcoin graph has been conducted by Chainalysis based on time series, nodes traveled, and Unspent Transaction Outputs (UTO) to cite a few of the features [9]. However, due to the sensitivity of the underlying data, these researchers have not made their specific dataset public. ...
Ransomware attacks are on the rise and attackers are hijacking valuable information from different critical infrastructures and businesses requiring ransom payments to release the encrypted files. Payments in cryptocurrencies are designed to evade tracing the transactions and the recipients. With anonymity being paramount, tracing cryptocurrencies payments due to malicious activity and criminal transactions is a complicated process. Therefore, the need to identify these transactions and label them is crucial to categorize them as legitimate digital currency trade and exchange or malicious activity operations. Machine learning techniques are utilized to train the machine to recognize specific transactions and trace them back to malicious transactions or benign ones. I propose to work on the Bitcoin Heist data set to classify the different malicious transactions. The different transactions features are analyzed to predict a classifier label among the classifiers that have been identified as ransomware or associated with malicious activity. I use decision tree classifiers and ensemble learning to implement a random forest classifier. Results are assessed to evaluate accuracy, precision, and recall. I limit the study design to known ransomware identified previously and made available under the Bitcoin transaction graph from January 2009 to December 2018.
... Community detection is one of the earliest and still most actively developing areas in complex network analysis, attempting to shed an important light into intrinsic network organization. While the first methods for network community detection go back to Kernighan and Lin (1970), Tarjan (1971), Bron and Kerbosch (1973), and Zachary (1977), nowadays the area continues to attract the attention of researchers and data scientists in a broad range of disciplines, from monitoring pre-election political communication, racial protest rhetoric on Twitter, and hidden trendsetters in online media (Helal et al., 2017;Matuszewski & Szab o, 2019;Tien et al., 2020;Weaver et al., 2018) to identifying parts of the brain potentially affected by marijuana use (Brumback et al., 2016;Filbey et al., 2014;Hurd et al., 2019), to tracking whale clubs, and grouping malicious addresses on blockchain (Akcora, Li, et al., 2020;Goldsmith et al., 2020). Such a very diverse set of methods and applications of network community detection has resulted in a wide variety of surveys, with some providing a broader overview while others focusing on a particular discipline, for example, social sciences or physics (see Table 1). ...
Full-text available
Identifying and tracking community structures in complex networks are one of the cornerstones of network studies, spanning multiple disciplines, from statistics to machine learning to social sciences, and involving even a broader range of application areas, from biology to politics to blockchain. This survey paper aims to provide an overview of some most popular approaches in statistical network community detection as well as the newly emerging research directions such as community extraction with higher-order features and community discovery in multilayer and multiscale networks. Our goal is to offer a unified view at methodological interconnections and the wide spectrum of interdisciplinary data science applications of network community analysis. This article is categorized under: • Data: Types and Structure > Graph and Network Data • Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification Abstract Community detection in power grid networks for system resilience analysis.
... In addition to other challenges, the lack of privacy also makes it easier for third parties to front-run a user's trades [DGK + 20, TCS21]. Another such problem is the ability for attackers to deanonymize agents by doing basic statistical analyses of public trades performed on DEXs [GGS20,Cha20]. In contrast, centralized brokers and exchanges preserve user privacy, but agents are required to trust that the exchange won't leak sensitive trade data. ...
Constant function market makers (CFMMs) such as Uniswap, Balancer, Curve, and mStable, among many others, make up some of the largest decentralized exchanges on Ethereum and other blockchains. Because all transactions are public in current implementations, a natural next question is if there exist similar decentralized exchanges which are privacy-preserving; i.e., if a transaction's quantities are hidden from the public view, then an adversary cannot correctly reconstruct the traded quantities from other public information. In this note, we show that privacy is impossible with the usual implementations of CFMMs under most reasonable models of an adversary and provide some mitigating strategies.
... They were able to correctly identify malicious accounts involved in gambling. In another study (Goldsmith et al. 2020), the authors analysed transfer of funds within a sub-network and used temporal feature such as how quickly funds are cashed. ...
Full-text available
Directed Graph based models of a blockchain that capture accounts as nodes and transactions as edges, evolve over time. This temporal nature of a blockchain model enables us to understand the behavior (malicious or benign) of the accounts. Predictive classification of accounts as malicious or benign could help users of the permissionless blockchain platforms to operate in a secure manner. Motivated by this, we introduce temporal features such as burst and attractiveness on top of several already used graph properties such as the node degree and clustering coefficient. Using identified features, we train various Machine Learning (ML) models and identify the algorithm that performs the best in detecting malicious accounts. We then study the behavior of the accounts over different temporal granularities of the dataset before assigning them malicious tags. For the Ethereum blockchain, we identify that for the entire dataset—the ExtraTreesClassifier performs the best among supervised ML algorithms. On the other hand, using cosine similarity on top of the results provided by unsupervised ML algorithms such as K-Means on the entire dataset, we were able to detect 554 more suspicious accounts. Further, using behavior change analysis for accounts, we identify 814 unique suspicious accounts across different temporal granularities.
... Despite these positive leading indicators, one must not become complacent and overly reliant on well-established instruments within the cryptographic asset sphere. There are two main reasons for such caution: (a) the ever-present, and actively evolving, risk of as yet unforeseen security breaches and exploits; and (b) traditionally described blockchain system vulnerabilities that are inherent to the consensus mechanisms operations (e.g., the "51% attack" and related concepts) [52][53][54][55][56]. ...
Technical Report
Full-text available
Since its inception, the cryptographic asset sector (CAS) has experienced an impressive amount of growth, including a series of market bubble events. Inspired by the success of early entrants into the CAS, a vast number of alternative cryptocurrencies (or 'altcoins') emerged. While many altcoins have been-and continue to be-successful, it must be noted that majority have done poorly. In fact, it has been estimated that more than 1,100 cryptocurrency projects have failed during the past 5 years. At some point, each failed project featured a community of users, many of whom believed that a particular developer or team had the-winning formula‖ to succeed in this increasingly crowded and competitive space. Unfortunately, many such communities have been deeply disappointed, yet continue to hope for a sustainable solution for asset/value recovery despite all evidence pointing to the contrary. For the purposes of this White Paper, we shall call such projects 'non-viable endeavors' or NVEs. Our group - InfiniLooP Initiative Developers (ILID) - set out to conduct a comprehensive market analysis in the area of NVEs. Our primary objective was to determine factors related to user and community perception of NVEs, including a set of value-based considerations related to willingness to swap NVE coins/tokens for coins originating from a new and viable project. Our secondary objective was to elucidate the most preferred type of replacement cryptocurrency asset (RCA) in accordance to its technical and social/community characteristics. Here, we present the findings of a comprehensive, 18-month survey of NVE communities, conducted by the ILID group. Primary outcome results of our survey show that approximately one-third of NVE owners would consider swapping their defunct assets for a new asset, preferably meeting a specific set of optimized conditions. Moreover, our data indicate that majority of those willing to proceed with an asset swap would favor a replacement asset that is a 'staking' or an 'interest-paying' alternative, and that an asset with an original/unique blockchain is preferred over a digitally-issued token. Based on the above data, our team implemented InfiniLooP - a staking asset with its own blockchain - as a simple and practical answer to the challenges faced by NVE cryptocurrency communities.
Bitcoin is the first and most widely used cryptocurrency in the world. It provides a pseudonym identity to its users that is established using the user’s public key, which leads to preserving the user’s privacy. Each transfer of bitcoin cryptocurrency among the users makes a transaction. The pseudonym identities are considered as transaction end-points. These transactions are recorded on an immutable public ledger called Blockchain which is an append-only data structure. The popularity of Bitcoin has increased unreasonably. The general trend shows a positive response from the common masses indicating an increase in trust and privacy concerns which makes an interesting use case from the analysis point of view. Moreover, since the blockchain is publicly available and up-to-date, any analysis would provide a live insight into the usage patterns which ultimately would be useful for making a number of inferences by law-enforcement agencies, economists, tech-enthusiasts, etc. In this paper, we study various applications and techniques of performing data analytics over Bitcoin blockchain from a graph theoretic perspective. We also propose a framework for performing such data analytics and explored a couple of use cases using the proposed framework.
Full-text available
The pronounced multi-domain technologicalization specific to the last decades has had a significant impact on all areas of activity, including the financial one. The use of cyberspace to facilitate the actions undertaken in the monetary activity has generated the development of this field to the point where virtual currencies have been created and new technologies have been developed to support their use. Like any emerging domain, the cryptocurrency field and the related technology are in a relatively early stage and exclusively imply operating in cyberspace, thus generating security risks in the event of the involvement of malicious entities in illicit activities. In this context, it is worth analyzing how the improper use of the crypto domain can lead to various risks to national security.
Conference Paper
Full-text available
Cybercrime investigators face numerous challenges when policing online crimes. Firstly, the methods and processes they use when dealing with traditional crimes do not necessarily apply in the cyber-world. Additionally, cyber criminals are usually technologically-aware and constantly adapting and developing new tools that allow them to stay ahead of law enforcement investigations. In order to provide adequate support for cybercrime investigators, there needs to be a better understanding of the challenges they face at both technical and socio-technical levels. In this paper, we investigate this problem through an analysis of current practices and workflows of investigators. We use interviews with experts from government and private sectors who investigate cybercrimes as our main data gathering process. From an analysis of the collected data, we identify several outstanding challenges faced by investigators. These pertain to practical, technical, and social issues such as systems availability, usability, and in computer-supported collaborative work. Importantly, we use our findings to highlight research areas where user-centric workflows and tools are desirable. We also define a set of recommendations that can aid in providing a better foundation for future research in the field and allow more effective combating of cybercrimes.
Full-text available
Bitcoin is a purely online virtual currency, unbacked by either physical commodities or sovereign obligation; instead, it relies on a combination of cryptographic protection and a peer-to-peer protocol for witnessing settlements. Consequently, Bitcoin has the unintuitive property that while the ownership of money is implicitly anonymous, its flow is globally visible. In this paper we explore this unique characteristic further, using heuristic clustering to group Bitcoin wallets based on evidence of shared authority, and then using re-identification attacks (i.e., empirical purchasing of goods and services) to classify the operators of those clusters. From this analysis, we consider the challenges for those seeking to use Bitcoin for criminal or fraudulent purposes at scale.
Conference Paper
Full-text available
Bitcoin is a purely online virtual currency, unbacked by either physical commodities or sovereign obligation; instead, it relies on a combination of cryptographic protection and a peer-to-peer protocol for witnessing settlements. Consequently, Bitcoin has the unintuitive property that while the ownership of money is implicitly anonymous, its flow is globally visible. In this paper we explore this unique characteristic further, using heuristic clustering to group Bitcoin wallets based on evidence of shared authority, and then using re-identification attacks (i.e., empirical purchasing of goods and services) to classify the operators of those clusters. From this analysis, we characterize longitudinal changes in the Bitcoin market, the stresses these changes are placing on the system, and the challenges for those seeking to use Bitcoin for criminal or fraudulent purposes at scale.
Full-text available
Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a similarity measure, and partitioned using spectral methods. However, these methods are not accurate when the clusters are not well separated. In addition, it is not possible to automatically determine the number of clusters. These limitations can be overcome by taking into account network community identification algorithms. In this work, we propose a methodology for data clustering based on complex networks theory. We compare different metrics for quantifying the similarity between objects and take into account three community finding techniques. This approach is applied to two real-world databases and to two sets of artificially generated data. By comparing our method with traditional clustering approaches, we verify that the proximity measures given by the Chebyshev and Manhattan distances are the most suitable metrics to quantify the similarity between objects. In addition, the community identification method based on the greedy optimization provides the smallest misclassification rates.
Introduction The Kantorovich duality Geometry of optimal transportation Brenier's polar factorization theorem The Monge-Ampere equation Displacement interpolation and displacement convexity Geometric and Gaussian inequalities The metric side of optimal transportation A differential point of view on optimal transportation Entropy production and transportation inequalities Problems Bibliography Table of short statements Index.
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, which runs in time O(mn^2) and space O(n^2) in the worst case, and in time O(n^2log n) and space O(n^2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.
The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.