The 1st International Conference on Mathematical Research for Blockchain Economy / Fira, Santorini / 9th May 2019

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

2. “Collusion
practices in a
West of Ireland
livestock mart”
- Curtin & Varley, 1982
2

3. Scalability problem
3

4. Offline channels
4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. 14

15. 15

16. 16

17. 17

18. 18

19. 19
Bitcoin Lightning Network

20. 20
Hubs in
Lightning
Network

21. 21
Research problem: collusion (eclipse)
attack
● Can a collusion of hubs execute a collusion attack against
another set of hubs?

22. 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
22

23. 23
Model of collusion attack
Neighborhood of Vi
with distance d

24. 24
Model of collusion attack
Targets of a collusion attack is a pair
of hubs in its neighborhood

25. 25
Model of collusion attack
Vi
forms a collusion to
produce a cut between
hubs V1
and V2
in its
neighborhood

26. 26
Model of collusion
attack: how likely
that a hub can orch-
estrate an attack?
Collusion formation as
a cooperative game

27. 27
Ability to orchestrate collusion =
Banzhaf index

28. 28
Banzhaf index
Banzhaf index = (Number of coalitions where Vi
is a critical
player) / (Number of coalitions where Vi
is a member)

29. 29
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)

30. 30
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

31. 31
● 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

32. 32
Evaluation: data
Bitcoin Lightning Network (1st March 2019)
● # nodes = 2810
● # edges = 22596
● Average degree = 16
● Minimum degree = 1
● Maximum degree = 961

33. 33
Evaluation:
algorithm to
compute the
Banzhaf index

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

35. 35
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
)

36. 36
● There are 62 nodes who can execute collusion attacks against 90% of their
neighbors in the Lightning Network

37. 37
Thank you:
any questions?
subhasis.thakur@nuigalway.ie
john.breslin@nuigalway.ie