Download On the Optimal Allocation of Adversarial Resources Stylianos

ON THE OPTIMAL ALLOCATION OF
ADVERSARIAL RESOURCES
STYLIANOS GISDAKIS, PANOS PAPADIMITRATOS
Adviser: Frank,Yeong-Sung Lin
Present by Chris Chang
AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

INTRODUCTION
Wireless sensor networks cover a broad range of
mission-critical applications
 The nature of these applications, often operating
in hostile and adverse environments, makes
security indispensable.
 There has been a wide gamut of security schemes
for wireless sensor networks, for example:

managing cryptographic keys
 securing communication
 detecting faulty data aggregation
 detecting sybil attacks

INTRODUCTION
When the adversary compromises multiple
sensor nodes; that is, controls their operation,
and extracts their private/secret cryptographic
material and such an adversary can replicate
such cryptographic keys and insert her own
misbehaving nodes at will.
 Clearly, the more numerous the cryptographic
keys and the nodes under the control of the
adversary are, the higher her strength is.

INTRODUCTION
Assuming that security mechanisms are put in
place and considering the above-mentioned
strong adversary, taking over a significant
fraction of the system nodes.
 Where and how should the adversary hit, or
equivalently how should the adversary allocate
her resources in order to distort the most of the
data collected by the victim network?

INTRODUCTION
In this paper, the most important thing is when
the entire or a large part of the network is of
interest for an adversary that does not have
overwhelming power.
 We model the mission critical network as a set of
parts where the adversary can attack.
 The better the choice of attack points, that is,
network parts where the attack is mounted, the
higher the impact and thus the “gain” of the
adversary

INTRODUCTION
In this paper, we do not venture to reveal
vulnerabilities of this WSN.
 Rather, we analyze the tactics of the adversary,
exactly to shed light on how vulnerable a
mission-critical sensor network can be as a
function of the adversarial strength.
 We see that the problem of identifying an optimal
attack, is computationally hard. Thus, we develop
an efficient heuristic approach to determine a
close-to-optimal attack tactic.

AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

SYSTEM AND ADVERSARIAL MODEL

System and adversarial model
1.
2.
3.
System Model
Adversarial Model
Problem Statement
SYSTEM AND ADVERSARIAL MODEL
(SYSTEM MODEL)
We model a wireless sensor network (WSN) as a
set, S, of n clusters S = {C 1 , C 2 , ..., C N }.
 We do not dwell on the cluster formation, e.g., the
communication topology formation. (clusters are
formed according to the requirements of the
supported application)
 The number of benign nodes within a cluster C i
is defined by a function F ben (C i ) : S → N .

SYSTEM AND ADVERSARIAL MODEL
(SYSTEM MODEL)
The valuations of all the clusters of the network
are encoded as a vector V = {V 1 , V 2 , ..., V N }.
 These values of are either proportional to the
number of benign nodes within the specific
cluster or context specific.
 We term U total to be the utility gained by the
adversary by controlling the whole network so
that
.

SYSTEM AND ADVERSARIAL MODEL
(SYSTEM MODEL)

Nodes are equipped with a set of cryptographic
keys used to ensure the confidentiality, the
integrity and the authenticity of the
communications among nodes and the sink.
SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)

We assume that adversarial resources fall into
two categories :
1.
2.
physical devices (R Phy )
cryptographic keys (R Crypto)
R Phy is the number of sensor nodes the
adversary controls, either by having introduced
them to the system or by having compromised
formerly deployed benign nodes.
 R Phy << n, not a large fraction of the total
number of sensor nodes

SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)
R Crypto is the cryptographic keys that attacker
possesses result from benign node compromised.
 R Phy ≤ R Crypto (which means that a compromised
node can have more than one cryptographic key.)
 we require that one single key cannot be used
by more than one node simultaneously in
order to not trigger sybil detection schemes.

SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)
In our model, the adversary is aware of the
allocation of benign nodes within each cluster (i.e
knows F ben (C i )).
 Function F val : [0, n] → R+ maps cluster C i to its
value.
 The attacker is aware of F val, and as a result can
quantify the utility gained by controlling each
cluster.

SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)
We consider data manipulation, so that the view
of the data the WSN user gets is not the actual
one but the one the adversary wishes for it.
 This attack can be launched against each and
any of the clusters. If the manipulation takes
place, arbitrarily or within a level wished by the
adversary, then we say the adversary won over
the cluster.
 We term the utility of the adversary as U mal .

SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)

Considering two generic types of attack to
control a cluster and to manipulate the produced
measurements :
1.
2.

Local Majority Attack
Stealthy Data Attack:
Local Majority Attack :
 The
adversary controls the majority of the nodes in the cluster
and she can impair or affect any data collection process.
 With
the help of a smaller fraction of nodes an attacker can
still affect data collection.
 Deviations
can be products of false measurements injected by
the malicious nodes.
SYSTEM AND ADVERSARIAL MODEL
(ADVERSARIAL MODEL)

Stealthy Data Attack :

To remain undetected in case misbehavior detection
mechanisms are in place, adversary controlled nodes
report data that differ no more than δ from the
measurements reported by benign cluster members.
SYSTEM AND ADVERSARIAL MODEL
(PROBLEM STATEMENT)
The adversary can choose which clusters to
attack, and this means, in our model, to choose
which clusters she will deploy adversarial nodes
(out of the available R Phy ).
 Then, for each of the nodes allocated, the
adversary can choose how many keys to equip
each of those nodes with (out of the R Crypto ).
 Our goal is to identify the optimal allocation
of resources that maximizes her U mal given
the deployment of the benign nodes of the WSN.

AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

ADVERSARIAL TACTICS
First, the adversary decides on the subset M of
clusters, which when controlled will maximize
U mal.
 In order to attack a cluster she must allocate at
least one physical device into each of the
clusters of M.  |M| ≤ R Phy

ADVERSARIAL TACTICS
Since each cluster has a value, the problem
becomes the definition of the subset of clusters
that will yield a U mal as close to U total as
possible, but does not exceed a predefined
value termed as target.
 This is equivalent to the Subset Sum S(V, U
total ) that is an NP-Complete combinatorial
optimization problem.

ADVERSARIAL TACTICS
To calculate the U mal for a given subset M the
attacker should define the optimal distribution of
R Crypto among the clusters in the subset.
 Besides, R Crypto doesn’t allow the attacker to
control all of the clusters of a subset M, and
the problem is equivalent to the 0-1 Knapsack
Problem of combinatorial optimization.

ADVERSARIAL TACTICS

Adversarial tactics
1.
2.
Cluster Selection
Resource Allocation per Selected Clusters
ADVERSARIAL TACTICS
(CLUSTER SELECTION)
In this paper, we use Genetic Algorithms (GAs)
whose main algorithmic structure is termed a
Chromosome to help us to solve the subset sum
problem.
 A chromosome : a candidate solution to the
optimization problem.
 Two basic operators of genetic algorithms are

Mutation
 Cross-Over

ADVERSARIAL TACTICS
(CLUSTER SELECTION)
We apply this Genetic Algorithm as a heuristic
for the Cluster Selection problem.
 Chromosomes whose number of genes is equal to
R Phy (the adversary is physically constrained to
R Phy .)

ADVERSARIAL TACTICS
(CLUSTER SELECTION)
Each gene includes an integer value that
represents the index or an identifier of some
cluster.
 For example, consider chromosome {C 1 , C 5 , C 8 ,
C 20 } :

This candidate solution (chromosome) describes a
scenario with an adversary constrained to R Phy = 4
 Attacking clusters C 1 , C 5 , C 8 , and C 20.

ADVERSARIAL TACTICS
(CLUSTER SELECTION)
In each evolution of the genetic algorithm,
chromosomes are evaluated based on the
maximum utility they can achieve.
 After a defined number of iterations (evolutions
of the algorithm), the GA converges to an optimal
(or near optimal in case of large scale networks)
resource allocation of both R Crypto and R Phy .

ADVERSARIAL TACTICS
(RESOURCE ALLOCATION PER SELECTED
CLUSTERS)


F cost : [0, Max] → N : the function that assigns a
cost to each cluster.
To launch a majority attack against a cluster C i


The function of cost is : F cost (C i ) = F ben (C i ) + 1
To launch attacks against data aggregation
The function of cost is : F cost (C i , Δ, δ) → N
 This function is the amount of malicious nodes
required in order to produce a deviation from the
average aggregate equal to Δ by reporting values that
are a percentage δ of the average value produced by
the rest of the nodes in the cluster.

ADVERSARIAL TACTICS
(RESOURCE ALLOCATION PER SELECTED
CLUSTERS)

For a chromosome with N genes the problem of
optimal allocation of R Crypto is formulated as
follows:
ADVERSARIAL TACTICS
(RESOURCE ALLOCATION PER SELECTED
CLUSTERS)



This maximization program is in fact the formal
definition of the 0-1 Knapsack Problem.
In the paper, we use Dynamic Programming to
solve the 0-1 Knapsack Problem .
The output of this algorithm is a vector ,which
defines which clusters of the chromosome under
evaluation should be selected in order to achieve
maximum utility within the resource constraints
set by R Crypto .
AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

ANALYSIS
1.
2.
Simulation Setup
Results
ANALYSIS (SIMULATION SETUP)
We implemented our model using the JGAP [5]
genetic algorithm package.
 For the dynamic programming part of the model
we implemented a basic dynamic programming
algorithm.
 The setup of the experiments included
configurations with clusters assigned a number of
benign sensor nodes.
 In every simulation, the attacker was provided
with a number of compromised nodes and a
number of cryptographic resources.

ANALYSIS (SIMULATION SETUP)
ANALYSIS (RESULTS)
ANALYSIS (RESULTS)
ANALYSIS (RESULTS)
ANALYSIS (RESULTS)
AGENDA
Introduction
 System and adversarial model
 Adversarial tactics
 Analysis
 Conclusion and future work

CONCLUSION AND FUTURE WORK
We consider resilience in the presence of strong
and intelligent adversaries which cannot in
principle have overwhelming power.
 It is necessary for the attacker to know where
and how to attack the victim network to
maximize the impact of her exploit.

CONCLUSION AND FUTURE WORK
we develop an efficient and effective heuristic
that can guide the adversary, notably the
allocation of the adversary’s resources, to solve
this computationally hard problem, and we also
find that our approximate solution is nearoptimal.
 We will expand our investigation to make it a
two-sided one, to cover both the attacker and the
system security designer. The latter is in fact our
ultimate target.

Thanks for your listening