Download Analyzing the Vulnerability of Superpeer Networks

Analyzing the
Vulnerability of Superpeer
Networks Against Attack
Niloy Ganguly
Department of Computer Science & Engineering
Indian Institute of Technology, Kharagpur
Kharagpur 721302
Co-authors
Bivas Mitra, Fernando Peruani, Sujoy Ghose
Peer to Peer architecture
Node
Node
Node
Internet
Node

All peers act as both clients and servers i.e. Servent (SERVer+cliENT)



Provide and consume data
Any node can initiate a connection
No centralized data source


Node
“The ultimate form of democracy on the Internet”
File sharing and other applications like IP telephony, distributed
storage, publish subscribe system etc
Department of Computer Science, IIT Kharagpur, India
Peer to peer and overlay network
 An overlay network is built on
top of physical network
 Nodes are connected by virtual
or logical links
Underlying physical network
becomes unimportant
Interested in the complex graph
structure of overlay
Department of Computer Science, IIT Kharagpur, India
Dynamicity of overlay networks


Peers in the p2p system leave network randomly
without any central coordination
Important peers are targeted for attack

DoS attack drown important nodes in fastidious
computation


Fail to provide services to other peers
Importance of a node is defined by centrality measures

Like degree centrality, betweenness centraliy etc
Department of Computer Science, IIT Kharagpur, India
Dynamicity of overlay networks


Peers in the p2p system leave network randomly
without any central coordination
Important peers are targeted for attack
 Makes overlay structures highly dynamic in
nature
 Frequently it partitions the network into smaller
fragments
 Communication between peers become
impossible
Department of Computer Science, IIT Kharagpur, India
Problem definition

Investigating stability of the networks against the churn and
attack
Network Topology + Attack


= How (long) stable
Developing an analytical framework
Examining the impact of different structural parameters upon
stability



Peer contribution
degree of peers, superpeers
their individual fractions
Department of Computer Science, IIT Kharagpur, India
Steps followed to analyze

Modeling of

Overlay topologies


pure p2p networks, superpeer networks, hybrid networks
Various kinds of attacks

Defining stability metric

Developing the analytical framework

Validation through simulation

Understanding impact of structural parameters
Department of Computer Science, IIT Kharagpur, India
Modeling: Superpeer networks


Topology of the overlay networks are modeled by degree
distribution pk
 pk specifies the fraction of nodes having degree k
Superpeer network (KaZaA, Skype) - small fraction of
nodes are superpeers and rest are peers

Modeled using bimodal degree distribution





r
kl
km
p kl
p km
=
=
=
=
=
fraction of peers
peerpdegree
k  kl , k m
k 0
degree
psuperpeer
0
k
r
(1-r)
Department of Computer Science, IIT Kharagpur, India
Modeling: Attack


qk probability of survival of a node of degree k
after the disrupting event
Deterministic attack
qk 
0 high degrees are progressively removed
 Nodes
having




qk=00when
 qk k>kmax
1
0< qk< 1 when k=kmax
qk  1
qk=1 when k<kmax
Degree dependent attack

Nodes having high degrees are likely to be removed

Probability of removal of node having degree k
f k  1  qk  k 
Department of Computer Science, IIT Kharagpur, India
Stability Metric:
Percolation Threshold
Initially all the nodes in the
network are connected
Forms a single giant component
Size of the giant component is the
order of the network size
Nodes in the network
are connected and
form a single
component
Giant component carries the
structural properties of the entire
network
Department of Computer Science, IIT Kharagpur, India
Stability Metric:
Percolation Threshold
f fraction of
nodes
removed
Initial single
connected
component
Giant component
still exists
Department of Computer Science, IIT Kharagpur, India
Stability Metric:
Percolation Threshold
f fraction of
nodes
removed
Initial single
connected
component
fc fraction
of nodes
removed
Giant component
still exists
The entire graph
breaks into smaller
fragments
Therefore fc =1-qc becomes the percolation threshold
Department of Computer Science, IIT Kharagpur, India
Development of the analytical
framework

Generating function:

Formal power series whose coefficients encode information
P ( x )  a0  a1 x  a2 x
Here



(a0 , a1 , a2 ,.....)
2
 a3 x  ......... 
3

a
k 0
k
xk
encode information about a sequence
Used to understand different properties of the graph


degrees.
G0 ( x ) 
k 0
pk x k
Average degree
generates probability distribution of the vertex
z   k   G0 ' (1)
Department of Computer Science, IIT Kharagpur, India
Development of the analytical
framework

pk .qk
specifies the probability of a node having degree k to be present
k
in the network after (1-qk) fraction of nodes removed.


F0 ( x)   pk qk x k becomes the corresponding generating function.
k 0
pk
(1-qk)
fraction of nodes
removed
Department of Computer Science, IIT Kharagpur, India
pk .qk
Development of the analytical
framework
 pk .qk
specifies the probability of a node having degree k to
k be
present in the network after (1-qk) fraction of nodes removed.


F0 ( x)   pk qk x k becomes the corresponding generating function.
k 0

Distribution of the outgoing edges of first neighbor of a randomly chosen
node
pk  kp q x
F1 ( x) 
k
k
k
 kp
k
k 1

pk .qk

F0 ( x)
z
k
Department of Computer Science, IIT Kharagpur, India
Random
node
First
neighbor
Development of the analytical
framework


H1(x) generates the distribution of the size of the components that
are reached through random edge
H1(x) satisfies the following condition
Department of Computer Science, IIT Kharagpur, India
Development of the analytical
framework

H 0 ( x) generates distribution for the component size to which a
randomly selected node belongs to

Average size of the components


F0 (1) F1 (1)
H 0 (1)  F0 (1) 

1  F1 (1)

Average component size becomes infinity when
Department of Computer Science, IIT Kharagpur, India
1  F1(1)  0
Development of the analytical
framework
1  F1(1)  0

Average component size becomes infinity when

With the help of generating function, we derive the following critical
condition for the stability of giant component

 kp
k 0
Degree distribution

k
( kqk  qk  1)  0
Peer dynamics
The critical condition is applicable

For any kind of topology (modeled by pk)

Undergoing any kind of dynamics (modeled by 1-qk)
Department of Computer Science, IIT Kharagpur, India
Stability metric: simulation


The theory is developed based on the concept of
infinite graph
At percolation point


In practice we work on finite graph


theoretically ‘infinite’ size graph reduces to the ‘finite’ size
components
cannot simulate the phenomenon directly
We approximate the percolation phenomenon on
finite graph with the help of condensation theory
Department of Computer Science, IIT Kharagpur, India
How to determine percolation
point during simulation?




Let s denotes the size of a component and ns determines the
number of components of size s at time t
At each timestep t a fraction of nodes is removed from the network
sns
Calculate component size distribution
CSt ( s) 
 sn
s
If CSt (s ) becomes monotonically decreasing function at the time t
 t becomes percolation point
Initial condition (t=1)
s
Intermediate condition (t=5)
Department of Computer Science, IIT Kharagpur, India
Percolation point (t=10)
Peer Movement : Churn and attack

Degree independent node failure


Probability of removal of a node is constant & degree
independent
 qk=q
Deterministic attack

Nodes having high degrees are progressively removed
 qk=0 when k>kmax
 0< qk< 1 when k=kmax
 qk=1 when k<kmax
Department of Computer Science, IIT Kharagpur, India
Stability of superpeer networks
against deterministic attack


Removal of a fraction of high
degree nodes are sufficient to
breakdown the network
Case 2:
1
0.9
ft (Percolation threshold)
Two different cases may arise
 Case 1:
0.8
0.7
Theoretical model (Case 1)
Theoretical model (Case 2)
Simulation results
Average degree k=10
Superpeer degree k =50
m
0.6
0.5
0.4
0.3
0.2


Removal of all the high degree
0.1
nodes are not sufficient
to

 k   kl (kl 001)r  2

f tar the
(1 network
r )1 
breakdown
 km (ofkm  1)(1  r ) 
Have to remove a fraction
low degree nodes
Department of Computer Science, IIT Kharagpur, India
4
6
kl (Peer degree)
8
10
Stability of superpeer networks
against deterministic attack


Removal of a fraction of high
degree nodes are sufficient to
breakdown the network
Case 2:
1
0.9
ft (Percolation threshold)
Two different cases may arise
 Case 1:
0.8
0.7
Theoretical model (Case 1)
Theoretical model (Case 2)
Simulation results
Average degree k=10
Superpeer degree k =50
m
0.6
0.5
0.4
0.3
0.2
Removal of all the high degree
0.1
nodes are not sufficient
to

 k   kl (kl 001)r  2
4
6


f

(
1

r
)
1

breakdown
tar the network
 k (k  1)(1  r )  kl (Peer degree)
m
m



Have to
remove a in
fraction
 Interesting
observation
case 1of
low degree nodes
 Stability decreases with increasing value of peers –
counterintuitive

Department of Computer Science, IIT Kharagpur, India
8
10
Peer contribution

Controls the total bandwidth contributed by the
peers

Determines the amount of influence superpeer nodes exert
on the network
Peer contribution
where
is the average degree
 We investigate the impact of peer contribution
upon the stability of the network

Department of Computer Science, IIT Kharagpur, India
Impact of peer contribution for
deterministic attack
• The influence of high degree peers increases with the
increase of peer contribution
• This becomes more eminent as peer contribution
Department of Computer Science, IIT Kharagpur, India
Impact of peer contribution for
deterministic attack
• Stability of the networks ( ) having peer contribution
primarily depends upon the stability of peer ( )
Department of Computer Science, IIT Kharagpur, India
Impact of peer contribution for
deterministic attack


Stability of the network increases with peer contribution for
peer degree kl=3,5
Gradually reduces with peer contribution for peer degree kl=1
Department of Computer Science, IIT Kharagpur, India
Stability of superpeer networks against
degree dependent attack

Probability of removal of a node is directly
fk  k 
proportional to its degree

Hence
C  km

 Calculation of normalizing constant C
k
 Minimum value f k 
C
 This yields an inequality
rkl
 1
(kl 1)  (1  r )km
 1

(km 1)  km (k (km  kl )  km  2k )

 k    k m pk
m
k 0
Department of Computer Science, IIT Kharagpur, India
Stability of superpeer networks against
degree dependent attack

Probability of removal of a node is directly
fk  k 
proportional to its degree

Hence C  km
 Calculation of normalizing constant C
k
 Minimum value
fk 
C
 The solution set of the above inequality can be


either bounded
or unbounded
(0   c   c )
bd
(0   c )

 k    k m pk
m
k 0
Department of Computer Science, IIT Kharagpur, India
Degree dependent attack:
Impact of solution set
Three situations may arise



Removal of all the superpeers along with a
fraction of peers – Case 2 of deterministic attack
Removal of only a fraction of superpeer – Case 1
of deterministic attack
Removal of some fraction of peers and
superpeers
Department of Computer Science, IIT Kharagpur, India
Degree dependent attack:
Impact of solution set
Three situations may arise

Case 2 of deterministic attack



c  c
c
sp
fp 
c
l
c
C c
Case 1 of deterministic attack



Networks having bounded solution set (0     bd )
c
c

If
bd ,
k

f  1
Networks having unbounded solution set
c
If
,
c
0

f
fp 0
 c 
sp  1
(0   c )
Degree Dependent attack is a generalized case of
deterministic attack
Department of Computer Science, IIT Kharagpur, India
Impact of critical exponent c Validation through
simulation
Bounded solution set with
 cbd  1.17
Removal of any combination of
where
disintegrates the network

 At
superpeer need to be removed
 cbd ,all
1.17
along with a fraction of peers
Performed simulation
on graphs with N=5000
and 500 cases
 Good agreement between theoretical and
simulation results

Case Study :
Superpeer network with
kl=3, km=25, k=5
Department of Computer Science, IIT Kharagpur, India
Summarization of the results

In deterministic attack, networks having small
peer degrees are very much vulnerable

Increase in peer degree improves stability


Superpeer degree is less important here!
In degree dependent attack,

Stability condition provides the critical exponent


Amount of peers and superpeers required to be
removed is dependent upon
More general kind of attack
Department of Computer Science, IIT Kharagpur, India
Conclusion
Contribution of our work
Development of general framework to analyze the stability of
superpeer networks
Modeling the dynamic behavior of the peers using degree
independent failure as well as attack.
Comparative study between theoretical and simulation results to
show the effectiveness of our theoretical model.
Future work
Perform the experiments and analysis on more realistic network
Department of Computer Science, IIT Kharagpur, India
Thank you
Department of Computer Science, IIT Kharagpur, India