1 nato-arw, suceava, september 4-8, 2006 1 information security in wireless sensor networks prof....

NATO-ARW, Suceava, September 4-8, 2006 11

Information Security in Wireless Sensor Networks

Prof. Stephan OlariuProf. Stephan Olariu

Sensor Network Research GroupSensor Network Research Group

Old Dominion UniversityOld Dominion University

Norfolk, VA 23529-0162Norfolk, VA 23529-0162

U.S.A.U.S.A.


Conquering scale


How do we conquer scale?

Golden Rule: Divide and Conquer!Golden Rule: Divide and Conquer!

Graft a virtual infrastructure on top of physical Graft a virtual infrastructure on top of physical

networknetwork

How is this done?How is this done? special-purpose: protocol drivenspecial-purpose: protocol driven

general purpose: designed without regard to protocolgeneral purpose: designed without regard to protocol

General-purpose infrastructure should be General-purpose infrastructure should be

leveraged by leveraged by manymany protocols! protocols!


Sensor network topology changes frequentlySensor network topology changes frequently

Self-organization must be adaptive to local Self-organization must be adaptive to local

changeschanges

Global protocols require global information for Global protocols require global information for

making local decisions: making local decisions: global protocols do not global protocols do not

scale!scale!

Localized protocols require Localized protocols require only localonly local information information

for sensor decisionsfor sensor decisions

Maintenance must also remain localMaintenance must also remain local

Localized Localized protocolsprotocols


Components of the virtual infrastructure

Dynamic coordinate system location-based identifiers

coarse-grain location awareness

Clustering scheme cheap scalability

Middleware work model

hierarchical specification of work and QoS

task-based management modellow-level implementation of work model


Remember polar coordinates?

The polar coordinates of a point x in the plane are its polar angle (x), and

its polar distance (x)

This is nice but does not scale


The idea

Instead of a fine-grain location settle for a coarse-Instead of a fine-grain location settle for a coarse-

grain approximationgrain approximation


The dynamic coordinate system

Training performed by AFN

Components: coronas wedges

Individual sensors acquire corona number wedge number

Resulting coordinate

system is dynamic and

does not require sensor IDs

Mine too!Mine too!My coordinates My coordinates are (4,2)are (4,2)


The cluster structure

Cluster: locus of all sensors having the same Cluster: locus of all sensors having the same

coordinatescoordinates

Clustering falls out for free once coordinate Clustering falls out for free once coordinate

system availablesystem available

Accommodates sensors with no IDsAccommodates sensors with no IDs

Clusters can be further subdivided – Clusters can be further subdivided – color graphscolor graphs


Middleware for sensor networks


sensorssensorslocal sink nodelocal sink node

(in(in--network data repositories)network data repositories)

Sink Sink (mobile/airborne)(mobile/airborne)

(connection to outside world)(connection to outside world)

deployment areadeployment area

highhigh--level level

InterestsInterests

(tasks/queries)(tasks/queries)

useruser

ReturnedReturned

resultsresults

Internet/satelliteInternet/satellite LowLow--level level

tasks/queriestasks/queries

Detailed view of sensor network system


Why middleware?

Middleware provides standardized and portable Middleware provides standardized and portable

system abstractionssystem abstractions

Standardizes interface to sensor networksStandardizes interface to sensor networks

Requirements for middleware:Requirements for middleware: negotiate QoS parameters on behalf on networknegotiate QoS parameters on behalf on network

support and coordinate concurrent applicationssupport and coordinate concurrent applications

translate high-level complex goals into low-level taskstranslate high-level complex goals into low-level tasks

coordination among sensorscoordination among sensors

handle heterogeneity of sensorshandle heterogeneity of sensors


The work model

InterestInterest

TaskTask

CapabilityCapability

Primitive operationsPrimitive operations

Application levelApplication level

Network/cluster levelNetwork/cluster level

Sensor levelSensor level


The work model

Application layer

--

Event

Interest Interest Result set, status

(error conditions, etc.)

Clusterr level

Communication

Capability(P-tasks+QoS)

Negotiated QoS

Sink

Sensor Network Layer

Middleware

sensor 1 sensor 2 sensor n

Micro-taskResults, status

CPL CPL CPL


A task-based management scheme


Developing a task-based management scheme

The problem is to develop, based on the work

model, a task-based management scheme that

supports: Automated mapping of application level units of work to

network level units of work subject to the negotiated QoS

constraints

For a network level unit of work, a scalable recruiting

scheme for dynamically assigning sensors to the

workforce performing this unit of work, subject to energy

constraints

Supporting secure group communications among sensors


Task-based management

A task is a tuple T(A,c,S,D,A task is a tuple T(A,c,S,D,,q) where:,q) where:

A – action to be performedA – action to be performed

c – color set to be usedc – color set to be used

S – source clusterS – source cluster

D – destination clusterD – destination cluster

– – routing path from S to Drouting path from S to D

q – desired QoS levelq – desired QoS level


Complexity of collaboration

Sensor limitations make collaboration imperious

Fundamental problems for effective collaboration anonymity

scale

For example, consensus building protocols such as

contention resolution, leader election,

synchronization, invariably assume unique identifiers

Therefore, classical collaboration schemes are not

adequate for sensor networks with anonymous nodes


Information assurance insensor networks


What is information assurance?

Information operations that protect and defend

information and information systems ensuring

their availability, integrity, authentication,

confidentiality, and non repudiation. This

includes providing for restoration of information

systems by incorporating protection, detection,

and reaction capabilities


Key components

Network survivability:Network survivability: ability of the network to ability of the network to function in the wake of failures by minimizing function in the wake of failures by minimizing their impacttheir impact

Information availability (information survivability):Information availability (information survivability): need for a user to have uninterrupted and secure need for a user to have uninterrupted and secure access to information on the network access to information on the network

Network security:Network security: attempts to provide basic attempts to provide basic security services security services

Information security:Information security: an ongoing process that an ongoing process that utilizes software and hardware to help secure utilizes software and hardware to help secure information flow information flow


Thus…

Information assurance is more inclusive than Information assurance is more inclusive than

information security information security

Assurance involves not only Assurance involves not only protectionprotection and and

detection but also detection but also reaction reaction (mainly survivability (mainly survivability

and dependability of the system that has been and dependability of the system that has been

subject to successful attack)subject to successful attack)

It also includes proactive (offensive) information It also includes proactive (offensive) information

operations, termed operations, termed information warfareinformation warfare, against , against

attackersattackers


Information security


What happens in the wired world?

In wired communications signal confined in

copper or optical fiber

Precautions taken to avoid unauthorized access devices are physically protected

cabling is protected from eavesdropping

firewalls are installed

Attacks of interruption and interception of data unlikely

(but possible)

The main thrust is securing the access point rather than

the

application!


What happens in the wireless?

It is not possible to avoid unauthorized devices to reach the network area

Any device within reach of radio-frequency signals can get access to data being transmitted

Thus, attacks of interruption and interception of data are likely What can be done: spread spectrum increases the difficulty for

signal interruption eavesdropping

It is important to understand that wireless communications affect only the physical, data link and network layers of the OSI stack

In particular, all methods of cryptography developed at transport layer and above remain valid: can we afford them??


A taxonomy of security-related problems

Operational security concernsOperational security concerns

Application levelApplication level

the main focus is on techniques that guarantee a the main focus is on techniques that guarantee a

desired application-level functionalitydesired application-level functionality

Network levelNetwork level

the main concern revolves around techniques that the main concern revolves around techniques that

ensure secure communications in sensor networksensure secure communications in sensor networks


Infrastructure security concernsInfrastructure security concerns

Goal: protect the infrastructure throughout the

network lifetime

Problem: develop a scheme to secure infrastructure

against an external adversary such that: the scheme will work uniformly during training (construction

of the infrastructure), and network operation phases

the scheme will work assuming threats to confidentiality,

integrity, availability, as well as threats to the physical layer

(jamming)

A taxonomy of security-related problems


Major insecurities in sensor networks

Problems arising from lack of individual IDs authentication is hard non-repudiation is hard to enforce node impersonation is easy

Problems arising from sleep-awake cycles and system longevity

trust relationships hard to establish

Eavesdropping: may give an adversary access to secret information violating confidentiality

Sensors run the risk of being compromised by infiltration by tampering


Security goals

Availability: ensures the survivability of network

services despite denial-of-service (DoS) attacks Confidentiality: ensures that information is not

disclosed to unauthorized entities Integrity: guarantees that a message being

transferred is never corrupted Authentication: enables a node to ensure the

identity of the peer node with which it

communicates Non-repudiation: ensures that the origin of a

message cannot deny having sent the message Anonymity: hide sources, destinations and routes


A succinct list of attacks

Eavesdropping: an attacker that monitors traffic can read the data transmitted and gather information by examining the source of a packet, its destination, size, number, and time of transmission

Traffic analysis: allows an attacker to determine that there is activity in the network, the location of base stations, and the type of protocol being used in the transmission

Man-in-the-middle: attack establishes a rogue intermediary pretending to be a valid sensor

Tampering: involves compromising data stored inside sensor usually by node capturing

DoS attacks: can be grouped into three categories disabling of service (e.g., sinkhole, HELLO flood attack), exhaustion, and service degradation (e.g., selective forwarding attack)

Can we guard against them?


Philosophy of our solution

““An ounce of prevention An ounce of prevention

is worth is worth

a pound of cure”a pound of cure”


What do we do?

Physical-layer encoding: virtually stamps out

infiltration by the adversary

Also, leverage the virtual infrastructure!

Problems discussedtamper resistanceauthenticationtraffic anonymity


Genetic material

Prior to deployment sensors are injected with the Prior to deployment sensors are injected with the

following following genetic material:genetic material: a public-domain pseudo-random number generatora public-domain pseudo-random number generator

an initial time -- at this point all the sensors are an initial time -- at this point all the sensors are

synchronous to the sinksynchronous to the sink

Each sensor can generate pointers into:Each sensor can generate pointers into: a random sequence a random sequence tt11, t, t22, …, t, …, tii, …, , …, of time epochsof time epochs

a random sequence a random sequence nn11, n, n22, …, n, …, nii, …, , …, of frequency of frequency

channelschannels

for every for every nnii a random hopping sequence a random hopping sequence ffi1i1, f, fi2i2, …, f, …, fipip, …,, …,


Illustrating time epochs, etc


Synchronization – generalities

Synchronization does not scale!Synchronization does not scale! Thus, synchronization must beThus, synchronization must be

short-livedshort-lived task-basedtask-based

Just prior to deployment, the sensors are Just prior to deployment, the sensors are synchronized synchronized

Due to clock drift re-synchronization is necessaryDue to clock drift re-synchronization is necessary Sensors synchronize by following the master Sensors synchronize by following the master

clock running at the sinkclock running at the sink Idea: determine the epoch and the position of Idea: determine the epoch and the position of

the sink in the hopping sequence corresponding the sink in the hopping sequence corresponding to the epoch to the epoch


Synchronization – the details

The sink dwells The sink dwells micro-seconds on each micro-seconds on each frequency in hopping sequencefrequency in hopping sequence

Assume that when a sensor wakes up during its Assume that when a sensor wakes up during its locallocal time epoch time epoch tti i the master clock is in one of the master clock is in one of

the time epochs the time epochs tti-1i-1, t, tii,, or or tti+1i+1

Each sensor knows the Each sensor knows the lastlast frequencies frequencies i-1i-1, , ii,,

and and i+1i+1 on which the sink will dwell in the time on which the sink will dwell in the time

epochs epochs tti-1i-1, t, tii,, and and tti+1i+1

The strategy:The strategy: tune in, cyclically, to tune in, cyclically, to i-1i-1, , ii,, and and i+1i+1

spending time spending time /3/3 units on each of them units on each of them


Synchronization – the details (cont’d)

Assume the sensor meets the sink on frequency Assume the sensor meets the sink on frequency ii in some unknown slot in some unknown slot ss of of tti-1i-1, t, tii,, or or tti+1i+1

To verify the synchronization, the sensor To verify the synchronization, the sensor attempts to meet the sink in slots attempts to meet the sink in slots s+1, s+2s+1, s+2 and and s+3s+3 according to its own frequency hopping for according to its own frequency hopping for epoch epoch tti+1i+1

If a match is found, the sensor declares itself If a match is found, the sensor declares itself synchronizedsynchronized

Otherwise, it will return to scanning frequenciesOtherwise, it will return to scanning frequencies


Making sensors tamper-resistant

Philosophy: no additional hardware! Tampering threat model for sensors

forcing open in-situ removal from the deployment area

Play it safe: if in doubt blank out memory


Using neighborhood signatures

Immediately after deployment each sensor transmits on a specified sets of frequencies, using a special frequency hopping sequence

Each sensor collects an array of signal strengths from the sensors in its locale

NSA – the Neighborhood Signature Array Removal from deployment area changes in the NSA!


NSA-based authentication

Idea: neighbors exchange NSA information, Idea: neighbors exchange NSA information, creating a matrix of signatures creating a matrix of signatures

A sensor that wishes to communicate with a A sensor that wishes to communicate with a neighbor identifies itself with its own NSAneighbor identifies itself with its own NSA

Upon receiving the NSA the sensor checks its Upon receiving the NSA the sensor checks its validityvalidity

Additional twist: store several instances of the Additional twist: store several instances of the matrix of NSAsmatrix of NSAs

Authentication dialogue: “what is your second to Authentication dialogue: “what is your second to the last NSA?”the last NSA?”


Handling DoS attacks

Our physical-layer encoding Our physical-layer encoding

+ Tamper resistance + Tamper resistance

+ Infrastructure anonymity+ Infrastructure anonymity

Make DoS attacks next-to-impossible!Make DoS attacks next-to-impossible!


What is anonymity?

Think of e-voting: the Think of e-voting: the sourcesource of a message must be of a message must be

protectedprotected

Denial of service: the Denial of service: the destinationdestination must be must be

anonymousanonymous

Mutual anonymity: both Mutual anonymity: both sourcesource and and destinationdestination of a of a

communication remain anonymous to each othercommunication remain anonymous to each other

TrafficTraffic anonymity is extremely important! anonymity is extremely important!

StructuralStructural anonymity anonymity


Anonymity in SN

Goal: prevent DoS attacksGoal: prevent DoS attacks data sinksdata sinks traffic patternstraffic patterns communication pathscommunication paths virtual infrastructurevirtual infrastructure

Threat modelThreat model internal adversary – observes local traffic internal adversary – observes local traffic external adversaryexternal adversary – observes the entire network – observes the entire network network has not been infiltratednetwork has not been infiltrated

Strategy: hide source, destination and routing Strategy: hide source, destination and routing pathspaths

Tactics: add noise to trafficTactics: add noise to traffic However, adding noise (spurious traffic) is However, adding noise (spurious traffic) is

expensiveexpensive


An example


Our solution

Randomize destinations Randomize destinations time-dependent destinationstime-dependent destinations

task-dependent destinationstask-dependent destinations

Randomize trafficRandomize traffic stipulating paths in transactionstipulating paths in transaction

computing time-dependent pathscomputing time-dependent paths


Traffic anonymity: centralized solution


Traffic anonymity: distributed solution

Idea: time-dependent routing! Time is rules into epochs t1, t2, … ti … Generic epoch ti has own routing

scheme


Secure group communications in SN

SN environments are inherently collaborative

Groups of sensors need to communicate securely,

e.g. nodes participating in a transaction

nodes collocated in a cluster

Conventional public key cryptography is infeasible

(why?)

Group key management and distribution is one way

to support secure group communications

Group key management challenges in SN include

sensor anonymity, massive large scale, resource

limitations, etc.


A key distribution scheme for secure communications

This scheme supports group key initialization and

subsequent group key management in the trained SN

The scheme draws on Exclusion Basis Systems (EBS), a

combinatorial formulation of the key distribution

problem

The scheme leverages the infrastructure in two ways: it leverages the training protocol for the purpose of group key

initialization, and

it leverages the coordinate system during network operation

for mapping a particular node, using its location as hash key,

to the set of EBS keys the node currently holds


Major highlights of EBS

In EBS systems, each group member is assigned a In EBS systems, each group member is assigned a

unique subset of keys from a key pool unique subset of keys from a key pool

Specifically, an EBS is defined as a collection Specifically, an EBS is defined as a collection of of

subsets of the set of memberssubsets of the set of members

Each subset corresponds to a key and the elements Each subset corresponds to a key and the elements

of a subset are the sensors that have that key of a subset are the sensors that have that key

An EBS is characterized by the triple E(An EBS is characterized by the triple E(n,k,m), ),

wherewhere n is number of members numbered 1 to n is number of members numbered 1 to n

k is size of the subset of keys each member holds, and is size of the subset of keys each member holds, and

m is the number of re-key messages needed to evict any is the number of re-key messages needed to evict any

member (and re-key the systemmember (and re-key the system))


Major highlights of EBS (cont’d)

To construct EBS(n,k,m) for feasible n,k, and m, we employ a canonical enumeration of all possible ways of forming k-subsets of objects from a set of k+m objects

Canonical matrix for EBS(10,3,2)Canonical matrix for EBS(10,3,2)

Rows correspond to keys in the key pool (not shaded), and session key

(shaded)

Columns correspond to members

M0 M1 M2 M3 M4 M5 M6 M7 M8 M9 K1 1 1 1 1 1 1 0 0 0 0 K2 1 1 1 0 0 0 1 1 1 0 K3 1 0 0 1 1 0 1 1 0 1 K4 0 1 0 1 0 1 1 0 1 1 K5 0 0 1 0 1 1 0 1 1 1 T 1 0 0 0 0 1 0 0 1 0 S 1 1 0 0 0 1 1 0 0 0 U 1 1 1 1 1 1 1 1 0 0


EBS at work: key initialization

Let the EBS system in use be EBS(Let the EBS system in use be EBS(n,k,mn,k,m)) At pre-deployment each node is loaded with At pre-deployment each node is loaded with k, mk, m and the and the

set {set {kk11,k,k22, …,k, …,kk+mk+m} that represent the EBS key pool, in } that represent the EBS key pool, in

addition to the state loaded for training purposesaddition to the state loaded for training purposes Each node Each node xx computes independently the set of keys computes independently the set of keys

assigned to it as follows:assigned to it as follows:

do the training protocol (node side)do the training protocol (node side)

hash key = Calculate the unique cluster Id(C(x),W(x))hash key = Calculate the unique cluster Id(C(x),W(x))

Corona(x), Wedge(x)Corona(x), Wedge(x)

myK-subset = Hash(Canonical matrix of EBS(n,k,m) hash key) myK-subset = Hash(Canonical matrix of EBS(n,k,m) hash key)

stopstop

startstart

Calculate sub-cluster IdCalculate sub-cluster Id

and use that as hash keyand use that as hash key


Key initialization – an example

Assume EBS(32,3,4), and a coordinate system Assume EBS(32,3,4), and a coordinate system

with 2 coronas and 8 wedgeswith 2 coronas and 8 wedges

Also, assume that the population in each cluster Also, assume that the population in each cluster

is to be divided to 2 sub-clustersis to be divided to 2 sub-clusters

the details of the sub-clustering scheme are the details of the sub-clustering scheme are

omitted here: each node places itself in a omitted here: each node places itself in a

sub-cluster in its own clustersub-cluster in its own cluster

Suppose Corona(x)= 1 and Wedge(x)=4Suppose Corona(x)= 1 and Wedge(x)=4

Node Node xx computes the set of keys assigned to it computes the set of keys assigned to it


Key initialization – an example (cont’d)

[0,1][0,1]

[2,3][2,3][4,5][4,5]

[6,7][6,7][14,15][14,15]

[12,13][12,13][10,11][10,11]

[8,9][8,9]

[16,17][16,17]

[18,19][18,19][20,21][20,21]

[22,23][22,23]

[24,25][24,25]

[26,27][26,27] [28,29][28,29]

[30,31][30,31]

[0,1][0,1]

[2,3][2,3][4,5][4,5]

[6,7][6,7][14,15][14,15]

[12,13][12,13][10,11][10,11]

[8,9][8,9]

[16,17][16,17]

[18,19][18,19][20,21][20,21]

[22,23][22,23]

[24,25][24,25]

[26,27][26,27] [28,29][28,29]

[30,31][30,31]

(0,0)(0,0)

(0,1)(0,1)(0,2)(0,2)

(0,3)(0,3)(0,7)(0,7)

(0,6)(0,6)(0,5)(0,5)

(0,4)(0,4)

(1,0)(1,0)

(1,1)(1,1)(1,2)(1,2)

(1,3)(1,3)

(1,4)(1,4)

(1,5)(1,5) (1,6)(1,6)

(1,7)(1,7)

(0,0)(0,0)

(0,1)(0,1)(0,2)(0,2)

(0,3)(0,3)(0,7)(0,7)

(0,6)(0,6)(0,5)(0,5)

(0,4)(0,4)

(1,0)(1,0)

(1,1)(1,1)(1,2)(1,2)

(1,3)(1,3)

(1,4)(1,4)

(1,5)(1,5) (1,6)(1,6)

(1,7)(1,7)

The coordinate systemThe coordinate system

A map of all sub-clustersA map of all sub-clusters

1. 1. Choose at random a sub cluster (say Choose at random a sub cluster (say 0)0)

2. Compute the globally unique sub-2. Compute the globally unique sub-cluster ID (24)cluster ID (24)

3. Derive the hash key (24+1)3. Derive the hash key (24+1)

4. Hash in to Canonical(32,3,4)4. Hash in to Canonical(32,3,4)

5. The bit string 0100011 5. The bit string 0100011 corresponding to keys Kcorresponding to keys K22,k,k66,k,k7 7 is is

returned returned


To sum up

Wireless sensor networks – the next paradigm shiftWireless sensor networks – the next paradigm shift

Sensors: “smart dust” – like entitiesSensors: “smart dust” – like entities

Virtual infrastructure – general-purposeVirtual infrastructure – general-purpose

Can be leveraged for all sorts of applicationsCan be leveraged for all sorts of applications

Research in its infancyResearch in its infancy

Stay tuned for more…Stay tuned for more…


Lightweight MAC and data aggregation

Idea: use collisions to advantage

Use collisions for data aggregation fault tolerance

Assume that results of sensed data for task T can be partitioned into 2k disjoint groups

Each sensor encodes its data in a string of k bits

Since the sensors are synchronous, they transmit data bit-by-bit left-to-right:

0 is not transmitted 1 is transmitted

Clearly, the logical OR is received


Routing – centralized


Routing – distributed


A second-generation sensor architecture

sensorsensor ADCADCprocessorprocessor

storagestoragetransceivertransceiver

MobilizerMobilizerLocation finding systemLocation finding system

Power generatorPower generator

Sensing UnitSensing Unit Processing UnitProcessing Unit

Power UnitPower Unit

core componentscore components

optional componentsoptional components


A few examples…


Secure routing in SN


Solutions out there…

Hierarchical routingHierarchical routing

use clusters to aid routinguse clusters to aid routing

Security can be achieved by having cluster head Security can be achieved by having cluster head

as key generatoras key generator

Problem: what happens if the cluster head is Problem: what happens if the cluster head is

compromised?compromised?

Possible solution: multiple cluster heads for each Possible solution: multiple cluster heads for each

clustercluster


Directed diffusion

The query is flooded throughout the network or in targeted area

Events start from some specific points and move outwards to reach the requesting node

A small number of nodes can be reinforced to prevent further flooding

This type of data collection does not fully exploit the feature of SN that adjacent nodes have similar data (unless aggregation done at some nodes: which ones?)


Distributed routing


Goal: mm3 devices!

MICA mote (1MICA mote (1stst generation sensor node) generation sensor node) Specs (2Specs (2ndnd generationgeneration sensor node) sensor node)

Size Size 2mm x 2.5mm2mm x 2.5mm Processor/Memory Processor/Memory AVR-like RISC processor, 3K of memory, 8 bit on-chip ADC, AVR-like RISC processor, 3K of memory, 8 bit on-chip ADC,

paged memory system, 32 KHz oscillatorpaged memory system, 32 KHz oscillatorRadioRadio:: FSK radio transmitter, FSK radio transmitter,OtherOther: : Programming interface, RS232 compatible UART, 4-bit Programming interface, RS232 compatible UART, 4-bit input port, 4-bit output port, encrypted communication input port, 4-bit output port, encrypted communication

hardware supporthardware supportCostCost less than $1.00 (in quantity) less than $1.00 (in quantity)What can it do?What can it do? Communicate 40+ feet indoors (walls), 19,200Kbps, frequency Communicate 40+ feet indoors (walls), 19,200Kbps, frequency separation 180KHzseparation 180KHz


Wireless networks 101

Infrastructure-based networks cellular networks

satellite networks

Rapidly-deployable networks ad-hoc networks

sensor networks

heterogeneous networks

Hybrid networks wireless Internet


Interfacing SNs

sink sinksink


What are color graphs?

Simple way to enrich Simple way to enrich

hierarchyhierarchy

Clusters are furtherClusters are further

subdivided into subdivided into pp color color

sets sets

What result are What result are pp

(global) color graphs(global) color graphs


What’s so nice about color graphs?

Very robust: each color graph is connected with high probability

Thus, can serve for routing!

They are (rich) cousins of circular arc graphs: vast body of knowledge to tap into for protocol design!

Graceful degradation as energy budget depleted

1 nato-arw, suceava, september 4-8, 2006 1 information security in wireless sensor networks prof....

Documents

conquering scale slide

sensor networks requirements

wireless sensor networks

sensor decisions maintenance

polar coordinates

local localized protocols

local information

system available