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Subhasis Thakur and John Breslin
Data Science Institute
National University of Ireland Galway
Collusion attack from
hubs in the blockchain
offline channel
network

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“Collusion
practices in a
West of Ireland
livestock mart”
- Curtin & Varley, 1982
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Scalability problem
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Offline channels
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Bitcoin Lightning Network

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Hubs in
Lightning
Network

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Research problem: collusion (eclipse)
attack
● Can a collusion of hubs execute a collusion attack against
another set of hubs?

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Results
● Mathematical model of collusion attack on the channel
network
● Likelihood of collusion attack using Banzhaf indices
● We found that there are 62 nodes who can execute
collusion attacks against 90% of their neighbours in the
Lightning Network
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Model of collusion attack
Neighborhood of Vi
with distance d

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Model of collusion attack
Targets of a collusion attack is a pair
of hubs in its neighborhood

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Model of collusion attack
Vi
forms a collusion to
produce a cut between
hubs V1
and V2
in its
neighborhood

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Model of collusion
attack: how likely
that a hub can orch-
estrate an attack?
Collusion formation as
a cooperative game

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Ability to orchestrate collusion =
Banzhaf index

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Banzhaf index
Banzhaf index = (Number of coalitions where Vi
is a critical
player) / (Number of coalitions where Vi
is a member)

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Banzhaf index (in terms of the ability
to orchestrate collusion)
Banzhaf index = (Number of collusions where Vi
is a critical
player) / (Number of collusions where Vi
is a member)

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Potential of collusion attacks
A high standard deviation would indicate that there are few hubs
who can easily execute a collusion attack while the remaining
hubs are unlikely to execute collusion attack

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● The probability that a hub can successfully execute a
collusion attack increases as its degree increases
● If hubs of the hub network have a uniform degree then,
Banzhaf indices are approximately equal
● Uniform Banzhaf indices may prevent collusion attacks in
the hub network
Method to reduce possibility of
collusion attacks

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Evaluation: data
Bitcoin Lightning Network (1st March 2019)
● # nodes = 2810
● # edges = 22596
● Average degree = 16
● Minimum degree = 1
● Maximum degree = 961

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Evaluation:
algorithm to
compute the
Banzhaf index

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● Relation between the Banzhaf index and the diameter of the network
● The uniformity of Banzhaf increases as the diameter of the network decreases 34

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Vulnerability due to collusion attack
Vulnerability w.r.t. node Vi
= (# of neighbours with a Banzhaf
index less than Vi
) / (Size of neighbourhood of Vi
)

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● There are 62 nodes who can execute collusion attacks against 90% of their
neighbors in the Lightning Network

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Thank you:
any questions?
subhasis.thakur@nuigalway.ie
john.breslin@nuigalway.ie