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Consider a Secure Overlay

Services (SOS) system with a

total of 12 nodes. The system

uses three consistent hashingfunctions (i.e., there are three

beacon nodes). Two nodes

(distinct from the beacon

nodes) are selected to serve as

secret servlets and three other

distinct nodes are used as

access nodes.

Consider a DoS attack that

cripples m random nodes of the

SOS system.

Problem 1

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Problem 1

a) Let m=2 and consider a single

user of class 1, say user U1. What

is the probability that U1 is

prevented by the DoS attack from

accessing the target?

b) Let m=2. What is the probability

that the DoS attack cripples all

communications destined to thetarget from all users?

c) Repeat part (b) assuming the

system has been compromised and

the IP address of beacon node B3became known to the attacker. So

the attacker always attacks B3.

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Problem 1.a- Solution

++=

2

12/)11011(

N=12

Explanation

For m=2, there are 11 ways to attack A1 andone other node including S1.

There are 10 ways to attack S1 and one other

node excluding A1.

There is a single way to attack both B1 and B2.

=

=

==

+

+

==

=

2

12

02

102

2

2)1

1

11

1

1(

11

111

1

1

m

N

m

N

m

N

10

10=

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Problem 1.b- Solution

b) Pr(disrupting all user communications}

= Pr{S1S2 or S1B3 or S1A3}

N=12

=

=

+

+

=

2

12

0

10

2

2

0

10

2

2

0

10

2

2

m

N

= 3/66 = 0.045

2/11*12

111

2

12

2

2

2

2

2

2

++=

+

+

=

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Problem 1.c- Solution

c) If identity of beacon node B3 is compromised, the attacker

always launches attack on B3. So if m=2, the attacker always

attacks B3 and another random node.

Pr(disrupting all user communications}

= Pr{attacking S1 in addition to the default attack on B3}

=

=

1

11/1

1

1/

0

10

1

1

m

N

N=12

= 1/11 = 0.0909