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Security in Wireless Sensor Networks: Key Management Approaches

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Security in Wireless Sensor Networks: Key Management Approaches

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Security in Wireless Sensor Networks: Key Management Approaches. Vasyl A. Radzevych and Sunu Mathew. Overview. Wireless Sensor Networks (WSN) Security issues in WSN Key management approaches in WSN: Overview Pre-Deployed Keying Key pre-deployment Key derivation information pre-deployment

Security in Wireless Sensor Networks: Key Management Approaches

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Security in Wireless Sensor Networks:Key Management Approaches

Vasyl A. Radzevych and Sunu Mathew

- Wireless Sensor Networks (WSN)
- Security issues in WSN
- Key management approaches in WSN:
- Overview
- Pre-Deployed Keying
- Key pre-deployment
- Key derivation information pre-deployment
- Location aware pre-deployed keying
- Random Key Pre-deployment (P-RKP)
- Key derivation information pre-deployment

- Autonomous protocols
- Pairwise asymmetric (public key)

- Arbitrated protocols
- Identity based group keying

- Conclusions

- Sensor network is composed of a large number of sensor nodes
- Sensor nodes are small, low-cost, low-power devices that have following functionality:
- communicate on short distances
- sense environmental data
- perform limited data processing

- Network usually also contains “sink” node which connects it to the outside world

- WSN can be used to monitor the conditions of various objects / processes. Some examples:
- Military: friendly forces monitoring, battlefield surveillance, biological attack detection, targeting, battle damage assessment
- Ecological: fire detection, flood detection, agricultural uses
- Health related: human physiological data monitoring
- Miscellaneous: car theft detection, inventory control, habitat monitoring, home applications

- Sensors are densely deployed either inside or very close to the monitored object / process

- The discussed applications require communication in WSN to be highly secure
- Main security threats in WSN are:
- Radio links are insecure – eavesdropping / injecting faulty information is possible
- Sensor nodes are not temper resistant – if it is compromised attacker obtains all security information

- Attacker types:
- Mote-class: attacker has access to some number of nodes with similar characteristics / laptop-class: attacker has access to more powerful devices
- Outside (discussed above) / inside: attacker compromised some number of nodes in the network

- Main types of attacks on WSN are:
- spoofed, altered, or replayed routing information
- selective forwarding
- sinkhole attack
- sybil attack
- wormholes
- HELLO flood attacks
- acknowledgment spoofing

B

A1

A2

A3

A4

- Injecting fake routing control packets into the network, examples: attract / repeal traffic, generate false error messages
- Consequences: routing loops, increased latency, decreased lifetime of the network, low reliability

Example: captured node attracts traffic by advertising shortest path to sink, high battery power, etc

- Multi hop paradigm is prevalent in WSN
- It is assumed that nodes faithfully forward received messages
- Compromised node might refuse to forward packets, however neighbors might start using another route
- More dangerous: compromised node forwards selected packets

- Sinkhole attack:
- Idea: attacker creates metaphorical sinkhole by advertising for example high quality route to a base station
- Laptop class attacker can actually provide this kind of route connecting all nodes to real sink and then selectively drop packets
- Almost all traffic is directed to the fake sinkhole
- WSN are highly susceptible to this kind of attack because of the communication pattern: most of the traffic is directed towards sink – single point of failure

- Sybil attack:
- Idea: a single node pretends to be present in different parts of the network.
- Mostly affects geographical routing protocols

- Idea: tunnel packets received on one part of the network to another
- Well placed wormhole can completely disorder routing
- Wormholes may convince distant nodes that they are close to sink. This may lead to sinkhole if node on the other end advertises high-quality route to sink

- Wormholes can exploit routing race conditions which happens when node takes routing decisions based on the first route advertisement
- Attacker may influence network topology by delivering routing information to the nodes before it would really reach them by multi hop routing
- Even encryption can not prevent this attack
- Wormholes may convince two nodes that they are neighbors when on fact they are far away from each other
- Wormholes may be used in conjunction with sybil attack

- Many WSN routing protocols require nodes to broadcast HELLO packets after deployment, which is a sort of neighbor discovery based on radio range of the node
- Laptop class attacker can broadcast HELLO message to nodes and then advertises high-quality route to sink

- Some routing protocols use link layer acknowledgments
- Attacker may spoof acks
- Goals: convince that weak link is strong or that dead node is alive.
- Consequently weak link may be selected for routing; packets send trough that link may be lost or corrupted

- Link layer encryption prevents majority of attacks: bogus routing information, Sybil attacks, acknowledgment spoofing, etc.
- This makes the development of an appropriate key management architecture a task of a great importance
- Wormhole attack, HELLO flood attacks and some others are still possible: attacker can tunnel legitimate packets to the other part of the network or broadcast large number of HELLO packets
- Multi path routing, bidirectional link verification can also be used to prevent particular types of attacks like selective forwarding, HELLO flood

- The protocol must establish a key between all sensor nodes that must exchange data securely
- Node addition / deletion should be supported
- It should work in undefined deployment environment
- Unauthorized nodes should not be allowed to establish communication with network nodes

- Sensor node constraints:
- Battery power
- Computational energy consumption
- Communication energy consumption

- Transmission range
- Memory
- Temper protection
- Sleep pattern

- Battery power
- Network constraints:
- Ad-hoc network nature
- Packet size

- Resilience against node capture: how many node are to be compromised in order to affect traffic of not compromised nodes?
- Addition: how complicated is dynamic node addition?
- Revocation: how complicated is dynamically node revocation?
- Supported network size: what is the maximum possible size of the network?
- Note: since WSN can be used in a lot of different ways it is not reasonable to look for one key management approach to suite all needs: 20 000 node network deployed from the airplane over a battle field has quite different requirements from 10 node network installed to guard the perimeter of the house

- Pre-deployed keying:
- Key pre-deployment
- Straightforward approaches
- Eschenauer / Gligor random key pre-deployment
- Chan / Perrig q-composite approach
- Zhu / Xu approach
- DiPietro smart attacker model and PRK protocol

- Key derivation information pre-deployment
- Liu / Ning polynomial pre-deployment

- Key pre-deployment
- Self-enforcing autonomous approaches
- Pairwise asymmetric (public key)

- Arbitrated protocols
- Identity based hierarchical keying

- Single mission key is obviously unacceptable
- Pairwise private key sharing between every two nodes is impractical because of the following reasons:
- it requires pre-distribution and storage of n-1 keys in each node which is n(n-1)/2 per WSN.
- most of the keys would be unusable since direct communication is possible only in the nodes neighborhood
- addition / deletion of the node and re-keying are complex

- Due to Eschenauer and Gligor
- Relies on probabilistic key sharing among nodes of WSN
- Uses simple shared-key discovery protocol for key distribution, revocation and node re-keying
- Three phases are involved: key pre-distribution, shared-key discovery, path-key establishment

- Generate a large key pool P (217-220 keys) and corresponding key identifiers
- Create n key rings by randomly selecting k keys from P
- Load key rings into nodes memory
- Save key identifiers of a key ring and associated node identifier on a controller
- For each node load a key which it shares with a base station

- Takes place during initialization phase after WSN deployment. Each node discovers its neighbor in communication range with which it shares at least one key
- Nodes can exchange ids of keys that they poses and in this way discover a common key
- A more secure approach would involve broadcasting a challenge for each key in the key ring such that each challenge is encrypted with some particular key. The decryption of a challenge is possible only if a shared key exists

- During the path-key establishment phase path-keys are assigned to selected pairs of sensor nodes that are within communication range of each other, but do not share a key
- Node may broadcast the message with its id, id of intended node and some key that it posses but not currently uses, to all nodes with which it currently has an established link. Those nodes rebroadcast the message to their neighbors
- Once this message reaches the intended node (possible through a long path) this node contacts the initiator of path key establishment
- Analysis shows that after the shared-key discovery phase a number of keys on a key ring are left unused

1000 nodes, 40 nodes neighborhood, P=10000

number of hops

Path length to neighbors

- Key revocation is accomplished in the following way: a controller node that has all keys and ids in its memory, broadcasts a message containing a list of k key identifiers for the key ring to be revoked
- This message is signed with signature key which is encrypted and unicasted to all nodes prior revocation. This encryption is done using individually shared between node and controller keys
- After obtaining a signature key, each node locate received identifiers in its key ring and removes the corresponding keys if they are present
- Since some links might disappear they should be reestablished using keys that are left in the key ring

- More robust then approaches that use single mission key
- In case node is captured k<<n keys are obtained
- This means that the attacker has a probability of k/P to attack successfully any other WSN link

- Two nodes are connected if they share a key
- Full connectivity of WSN is not required because of the limited communication capabilities of the sensor nodes
- Two important questions:
- What should be the expected degree of a node so that WSN is connected?
- Given expected degree of a node what values should the key ring size, k, and pool, P, have for a network of size n so that WSN is connected?

- Random-graph theory helps in answering the first question

- A random graph G(n,p) is a graph of n nodes for which the probability that a link between any two nodes exists is p
- Question: what value should p have so that it is “almost certainly true” that graph G(p,n) is connected?
- Pc is a desired probability for the graph connectivity
- Based on the formulas above p and d=p(n-1) can be found (d-expected degree of a node)

Erdos-Renyi formula:

(1)

(2)

Expected degree of node vs. number of nodes, where

Pc=Pr[G(n,p) is connected]

- Due to the limited communication capabilities a number of nodes with which a particular node can communicate is n’<<n
- This means that the probability of two nodes sharing at least one key in their key rings of size k is p’=d/(n’-1)>>p
- Key pool size P can be derived as a function of k:

Probability of sharing at least one key when two nodes

choose k keys from a pool of size P

- WSN contains n=10000 nodes, desired probability of network connectivity is Pc=0.99999, communication range supports 40 nodes neighborhoods
- According to the formula (1) c=11.5, therefore p=2*10-3
d=2*10-3*9999=20

- This means that if each node can communicate with on average 20 other nodes the network will be connected
- p’=20/(40-1)=0.5
- According to formula (3) k can be set to 250 and P can be set to 100000

- Enhancement of the basic probabilistic approach
- Idea: nodes should share q keys instead of only one
- Approach:
- Key pool P is an ordered set
- During initialization phase nodes broadcast ids of keys that they have
- After discovery each nodes identifies the neighbor with which it share at least q keys
- Communication key is computed as a hash of all shared keys
- Keys appear in hash in the same order as in key pool

- q-composite approach has greater resiliency to node capture than the basic approach if small number of nodes were captured
- Simulations show that for q=2, the amount of additional communications compromised when 50 nodes (out of 10000) have been compromised is 4.74%, as opposed to 9.52% in the basic scheme
- However if large number of nodes have been compromised q-composite scheme exposes larger portion of network than the basic approach
- The larger q is the harder it is to obtain initial information
- Parameter q can be customized to achieve required balance for a particular network

- Another modification of the basic probabilistic approach
- Major enhancement:
- Pseudorandom number generator is used to improve security of key discovery algorithm
- Also uses secret sharing which jointly with logical paths allows nodes toestablish a pairwise key that is exclusively known to the two nodes (in contrast to basic probabilistic approach, where other nodes might also know some particular key)

- Background: a pseudo-random number generator, or PRNG, is a random number generator that produces a sequence of values based on a seed and a current state. Given the same seed, a PRNG will always output the same sequence of values.
- Key pool P of size l is generated
- For each node u, pseudorandom number generator is used to generate the set of m distinct integers between 1 and l (key ids). Nodes unique id u is used as a seed for the generator
- Each node is loaded with key ring of size m
- Keys for the key rings are selected from key pool P in correspondence with integers (key ids) generated for a particular node by pseudorandom number generator
- This allows any node u that knows another nodes v id to determine the set of ids of keys that v poses

- The established on previous step keys are not exclusive and consequently not secure enough, however they can be used to establish exclusive key
- During the network initialization phase, nodes discover so called logical paths
- Nodes can establish a direct path in case they share a common key on their key rings
- This can easily be accomplished as was described in the previous slide by discovering common key id
- In case nodes do not share a key authors propose a path-key establishment algorithm similar to one in basic probabilistic approach, the difference is that nodes try to establish several logical paths, which later should help in establishing a pairwise key

- The next step of network initialization is pairwise key establishment
- A sender node randomly generates a secret key ks
- Then derives n-1 random strings sk1, sk2,…, skn-1
- skn is computed as follows: skn = ks XOR sk1XOR sk2 XOR,…, XOR skn-1
- This way a recipient has to receive all n shares in order to derive a secret key ks
- After secret shares are computed, each of them is send to the recipient using different logical path
- Once all shares are received the recipient can confirm the establishment of pairwise key by sending a HELLO message encoded with a new key
- Authors provide a framework according to which number of shares and the way they are send is decided

- So far all the discussed approaches have used one of the following algorithms for shared-key discovery:
- Key id notification
- Challenge response
- Pseudorandom key id generation

- Those algorithms work well against so called “oblivious” attacker, the one that randomly selects next sensor to compromise
- What if attacker selects nodes that will allow him to compromise the network faster, based on already obtained information (key ids)?
- This is the case of so called “smart” attacker

- More precisely smart attacker can be defined as follows:
- at each step of the attack sequence, the next sensor to tamper is sensor s, where s maximizes E[G(s)| I(s)], the expectation of the key information gain G(s) given the information I(s) the attacker knows on sensor s key-ring

- Simulations show that Key id notification and pseudorandom key id generationcan be easily beaten by the smart attacker
- Challenge response performs better

Experimental results on id notification and pseudorandom key id generation: Number of sensors to corrupt in order to compromise an arbitrary channel.

Experimental results on challenge response:

Number of sensors to corrupt in order to compromise an arbitrary channel.

- Why not using challenge response? Inefficient
- The goal is to define a key pre-deployment scheme that supports an efficient and secure key discovery phase, as efficient as pseudorandom key id generation (no message exchange) and as secure as challenge response
- DiPietro et al. suggested a new algorithm that achieves the above described requirements

- Key pre-distribution
- For each sensor sa
- For all keys vPi of the pool P, compute z=fy(a || vPi)
- Iff z≡0 mod (P/K), then put vPi into the key ring Va of sensor sa

- Assumption P/K divides by 2h, where h is the size of the input

- For each sensor sa
- Key discovery
- In case sensor sb wants to establish a secure channel with sensor sa it has to perform the following calculations:
- For each key vbj in its key ring sensor sb computes z=fy(a||vbj)
- If z≡0 mod (P/K), sensor sa also has key sb

- In case sensor sb wants to establish a secure channel with sensor sa it has to perform the following calculations:

- Benefits:
- Complexity is comparable to pseudo-random index transformation: no message exchange and K applications of the pseudo-random function.
- Only who already knows key vPi can know whether sensor sa has that key or not by computing z=fy(a||vbj) and checking out if
z≡0 mod( P/K ). All other entities gets no information from z. This is exactly the same information revealed by challenge response

- Drawbacks:
- Not enough control of key ring size: it is possible that applying the formula to sensor id and key in a key pool will yield key ring that is
- too large - larger than sensor memory
- too small – not enough for the network to be connected

- In either case node id a should be regenerated
- Authors prove that it is feasible to regenerate sensor ids to achieve required properties

- Not enough control of key ring size: it is possible that applying the formula to sensor id and key in a key pool will yield key ring that is

Experimental results on PRK algorithm: number of sensors to corrupt in order to compromise an arbitrary channel. The PRK algorithm is as secure as challenge response and in the same time as efficient as pseudorandom key id generation

- Polynomial based key pre-distribution scheme reduces the amount of pre-distributed information still allowing each pair of nodes to compute a shared key
- Polynomial based key pre-distribution is λ-collusion resistant, meaning that as long as λ or less nodes are compromised the rest of the network is secure
- Utilizes polynomial shares

- Special case: λ=1
- Each node has an id rU which is unique and is a member of finite field Zp
- Three elements a, b, c are chosen from Zp
- Polynomial f(x,y) = (a + b(x + y) + cxy) mod p is generated
- For each node polynomial share gu(x) = (an+ bnx) mod p
where an= (a + brU) mod p and bn= (b + crU) mod p is formed and pre-distributed

- In order for node U to be able to communicate with node V the following computations have to be performed:
- Ku,v= Kv,u= f(ru,rv) = (a + b(ru+rv) + crurv )mod p
- U computes Ku,v= gu(rv)
- V computes Kv,u= gv(ru)

- Example:
- 3 nodes: U, V, W, with the following id’s 12, 7, 1 respectively
- p=17 (chosen parameter)
- a=8, b=7, c=2 (chosen parameters)
- Polynomial f(x,y) = 8+7(x+y)+2xy
- g polynomials are gu(x) = 7 + 14x, gv(x) = 6 + 4x,
gw(x) = 15+9x

- Keys are Ku,v=3, Ku,v=4, Ku,v=10
- U computes Ku,v= gu(rv) = 7+14*7mod17 = 3
- V computes Kv,u= gv(ru) = 6+4*12mod17 = 3

- Polynomial based key pre-distribution scheme can be generalized to any λ by changing polynomials in the following way:
- is a randomly generated, bivariate λ-degree, symmetric polynomial over finite field Zp, p≥n is prime

- Combination of polynomial-based key pre-distribution and the key pool idea discussed above
- Increases network resilience to node capture
- Can tolerate no more than λ compromised nodes, where λ is constrained by the size of memory of a node
- Idea: use a pool of randomly generated polynomials
- When pool contains only one polynomial the approach degenerates to basic polynomial based key pre-distribution scheme
- When all polynomials are of degree 0 the approach degenerates to key pool approach
- Three phases are involved: setup, direct key establishment, path key establishment

- Set F of bivariate λ-degree polynomials over finite field Fq is generated
- Each polynomial is assigned a unique id
- For each sensor node a subset of s’ polynomial is randomly chosen from F
- For each polynomial in the chosen subset a polynomial share is loaded into nodes memory

- During this phase all possible direct links are established
- A node can establish a direct link with another node if they both share a polynomial share of a particular polynomial
- How to find common polynomial? Use above discussed approaches

- If direct connection establishment fails nodes have to start path key establishment phase
- Nodes need to find a path such that each intermediate nodes share a common key
- Node may broadcast the message with polynomials ids that it posses to all nodes with which it currently has an established link
- Once this message reaches the intended node (possible through a long path) this node computes a key and contacts the initiator of path key establishment
- Drawback: may introduce considerable communication overhead

The probability p that 2 sensors share a polynomial vs

size s of the polynomial pool (s’ – number of polynomial

shares in each sensor)

Fraction of compromised links between non compromised nodes

vs number of compromised nodes

(20000 nodes, nodes can store equivalent of 200 keys)

- Instance of general framework discussed above
- Benefits:
- Guarantees that any two nodes can establish a pairwise key, if no nodes were compromised
- Allows sensors to directly determine whether it can establish a pairwise key with another node and which polynomial to use in case of positive answer

- 2m λ-degree polynomials are generated
, where

and N is the size of the network

- Each row of the grid is associated with polynomial
and each column is associated with polynomial

- For each sensor an unoccupied intersection (i, j) of the grid is selected and assigned to the node

- The id of the node is created by concatenation of binary representations of i and j. ID=< ib:: jb >
- Intersections should be densely selected within a rectangle area of the grid
- Polynomial shares of corresponding (row / column) polynomials together with id are pre-distributed to each node

Node assignment in the grid

- To establish a pairwise key with node j, node i checks whether ci=cj or ri=rj
- If either of conditions hold, nodes have a polynomial share of the same polynomial, consequently they can compute a common key directly
- Otherwise nodes have to go through path discovery

- Idea: nodes can use intermediate nodes to help in establishing a common key
- The intermediate node should be located in either the same row / column as first node or same column / row as a second node
- This way intermediate node definitely share a polynomial with both nodes
- Note: there are only two of such intermediate nodes for each pair of nodes
- What if both if them are compromised / unreachable?
- The path through the grid should be established
- Authors developed an efficient protocol to accomplish this
- The main idea of the protocol is that intermediate nodes try to forward the request to the node that is located in the same row / column as a destination

Establishing a path through the grid

- The limited computation and power resources of sensor nodes often makes it undesirable to use existing public-key algorithms, such as Diffie-Hellman key agreement or RSA signatures

- Is it possible to develop a public key infrastructure suitable for wireless sensor networks?
- Recent studies show that it is still possible to utilize public key ideas for the purposes of securing WSN
- Gaubatz et al. developed an ultra low power implementation of Rabin's Scheme and NtruEncrypt Algorithm
- Authors have demonstrated that it is possible to design public key encryption architectures with power consumption of less than 20 mW using the right selection of algorithms and associated parameters, optimization and low power techniques
- The details of solutions will not be discussed, since it mainly involves VLSI / circuit design

- According to the model, network consists of three types of nodes: command node, gateways and regular sensor nodes
- Gateways partition the network into distinct clusters as follows

- Sensor nodes
- Are equipped with GPS modules and can determine its location during bootstrapping
- Remain stationary

- Gateways
- Can unicast / broadcast information to other gateways on the network
- Can establish the group key using a group key agreement protocols

- Command node
- is assumed to be secure and is trusted by all of the nodes in the sensor network

- Description of the initialization phase:
- Prior deployment each gateway is assigned |S|/|G| keys, where |S| is the number of sensors on the network and |G| is the number of gateways
- Each sensor is preloaded with id if the gateway with which it share a key
- After deployment each gateway forms a cluster using cluster formation algorithm and acquires the keys of the sensors in its cluster from the other gateways
- After key exchange is performed gateways erases key of sensors that do not belong to its cluster

- Each sensor Si broadcasts its id (idSi) and id (idGj) of the gateway with which it shares a key

- Clustering process is performed

- After clustering gateways identify set of sensors that
- belong to its cluster {id}i andbroadcasts it to other gateways

- Each gateway Gj replies to Gi with the set of keys and corresponding sensor ids {(KSk,Gj, idSk)}i

- On the last step, each sensor receives a message that assigns
- it to the gateway

- Each new sensor is preloaded with two keys as other sensors
- Command node transmits the list of (identifier, key) pairs to a randomly selected gateway Gh, which becomes the gateway that shares the keys of the new sensors:

- Each added node broadcasts a hello message (same as on
- initialization phase)

- Clustering mechanisms adjusts itself
- Each gateway broadcasts the sensors in its range to the gateways in G, requesting the keys for those sensors

- Gh responds to those requests

- Each new sensor Si is assigned to the gateway Gi

- If a group of sensors are compromised, they can be trivially evicted from the command node’s sensor list by the command node, as well as from their cluster by the gateway.
- Gateway revocation is slightly more complicated
- Command node evicts gateway G from the list of gateways and chooses a head gateway Gh randomly
- Command node sends the identifiers of each sensor and their new gateway Gi to Gh
- Also the new keys that sensors share with Gi are sent

- Clustering process takes place
- Second and third parts of the message is sent to Gi
- Gi notifies each sensor on its cluster about new shared key

Distribution of sensor energy consumption with our

approach.

- Benefits:
- Low energy consumption
- Low communication overhead for key establishment
- Low memory requirements for sensor nodes
- Good resilience against sensor capture

- Drawbacks:
- Specific network model requirements
- Sensors have to be equipped with GPS modules
- Efficient clustering algorithm is required

- Problem:
- How to pick a large key pool while still maintaining high connectivity? (i.e maintain resilience while ensuring connectivity) (e.g. 100,000 vs 200)

- Solution:
- Exploit Location information (Deployment Knowledge)
- Du et. al. Infocom 2004. Exploit Location Knowledge for P-RKP
- Huang et. Al. SASN 2004. Exploit Location Knowledge for SK-RKP

- Exploit Location information (Deployment Knowledge)

- Du et. al (IEEE Infocom 2004)
- Improves Random Key Predistribution (Eschenauer and Gligor) by exploiting Location Information.
- Studies a Gaussian distribution for deployment of Sensor nodes to improve security and memory usage.

- Rectangular Deployment area (X x Y)
- General Deployment Model (Individual)
- Current predeployment schemes assume pdf for location f(x,y) as 1/XY.
- Group based Deployment Model.

- Group based Deployment Model:
- N sensor nodes divided into t x n equal size groups. Group G(i,j) has deployment point x(i,j).
- Deployment points arranged in a grid
- Resident points of node k follow pdf

- Groups select from key group S (i,j)
- Probability node is in a certain group is (1 / tn).

- Key sharing graphs used to enable connectivity
- Use flooding to find secure path (Limit to 3 hops)
- Setting up the key pools
- Two horizontally or vertically neighboring pools share a|Sc| keys where 0<= a <= 0.25
- Two diagonally neighboring key pools share b|Sc| keys, where 0<=b<=0.25
- Two non-neighboring key pools share no keys.
- Overlapping factors - a,b

- Key Assignment for Key Pools
- For group , select keys from the global key pool S, then remove these keys from S.
- For group , select a. keys from pool , then select keys from global pool S
- For group select a. from each of the key pools , and if they exist; select b. Keys from each of the key pools and if they exist; then select w keys from the global key pool S, and remove these w keys from S.

- Detemining |Sc|
- When |S| = 100,000, t = n = 10, a = 0.167, b = 0.083
|Sc| = 1770

- When |S| = 100,000, t = n = 10, a = 0.167, b = 0.083

- Performance Evaluation
- Evaluation Metrics
- Connectivity (Local and Global)
- Communication overhead
- Resilience against node capture

- Evaluation Metrics
- System configuration
- |S| = 100,000. N = 10,000.
- Deployment area = 1000m x 1000m
- T =n =10m. Each grid is 100m x 100m.
- Center of grid is deployment point. Wireless communication range is 40m.

- Local Connectivity
- Plocal = Pr((B(n1,n2)|A(n1,n2))

- Probability node is in a certain group is (1 / tn)
- Probability that nodes i and j have local connectivity) is 1)Probability that and share a key (p-lambda) *
2)Probability that resides around the point Z(x,y) *

3)Probability that is a neighbor of

Plocal is the average of this value across the whole region

- Performance – Local connectivity
- With 100 keys, location management improves local connectivity from 0.095 to 0.687

- Global connectivity
- Only simulation results are available

- Effects of the Overlapping Factors (a,b)

- Communication overhead
- Path needed when two neighbours cannot find a common key.
- ph(i) is the probability that the smallest number of hops needed to connect two neighbouring nodes is i. i is at most 3.

- Resilience against node capture
- Fraction of additional communication (among uncaptured nodes) that can be compromised based on capture of x nodes.
- Location of the x captured nodes affects results.
- Assume random location of x nodes (unrealistic)
- Location knowledge significantly improves network resilience
- 1 – (1 – m/|S|)^x

- Huang et. al. (SASN 2004)
- Claims random node capture assumption too weak (selective capture possible)
- Grid–group deployment scheme.
- Introduces the node fabrication attack
- Uses location based information and a structured key pool
- Claims fewer number of keys and resilience to selective node capture and node fabrication attacks

- P-RKP vs SK-RKP
- Robustness of both weakened by selective node capture attack

- Both are also weakened by node fabrication attack
- P-RKP – By capturing two nodes, attacker can fabricate and deploy (2m new nodes.
- SK-RKP is harder to compromise (still possible)
- Grid-Group Deployment Scheme
- Partition N sensors into i.j groups with sensors in each group
- Assign the identifier [(i,j),b] to each sensor in the G(i,j) where b= 1,….N
- Assign m keys to each sensor in group G(i,j)
- Uniformly distribute the sensors for the group G(i,j) in zone Z(i,j)

- Divide key poll P into L x M sub-key pools (P(i,j), i = 1….L,j = 1…M)). Each sub-key pool is divided into w sub-key spaces. A sub-key space is a N x ( +1) key matrix A, where each element of A is a unique key)
- Divide the N sensors into L x M groups (a group is represented by G(i,j) where i = 1,….L, j = 1,…M)
- Assign unique identifiers to the sensors. For each sensor, assign id = [(i,j),b], where (i,j) is the group id and b = 1,….N
- For sensor [(i,j),b], randomly select T sub-key spaces in P(i,j) making sure the selected sub-key space is not already selected times. Load sensor with the bth row of matrix A for each sub key space selected

- For each sensor in group G(i,j), randomly select one sensor, say j, from a neighbouring group, say G(i2,j2).
- Install duple < , > in i and duple < , > in j, where key is unique and , are the node ids.
Once a peer node is selected, it cannot select another node in the same group

- If all sensors have selected a node in each of its neighboring groups, stop, otherwise go to the first step

- Key establishment within the same zone
- Each sensor, say [(i,j),b], broadcasts identifier [(i,j),b] and key space identifiers [ , ]
- For each neighbor, sensor adds a link in key-graph if they share a key .
- Sensor broadcasts list of neighbors who share key-space with it. Uses similar messages from others to expand key-graph.
- Source routing to to request and establish pairwise keys with all its neighbors.

- Each sensor, broadcasts desired node list (of nodes in the adjacent zone)
- A neighbor of the requestor within the same zone who already shares a key with the nodes For each neighbor, sensor adds a link in key-graph if they share a key
- Sensor broadcasts list of neighbors who share key-space with it. Uses similar messages from others to expand key-graph.
- Source routing to request and establish pairwise keys with all its neighbors.

- Memory overhead
- For p = 0.5238, m = 68 (similar to Du et. Al.)

- Security Analysis
- Secure against Random Node capture, Selective Node capture and Node Fabrication attacks

- Robust security mechanisms are vital to the wide acceptance and use of sensor networks for many applications
- Key management in turns is one the most important aspects in any security architecture
- Various peculiarities of Wireless Sensor Networks make the development of good key management scheme a challenging task
- We have discussed several approaches to key management in WSN
- All of them have strong and weak points
- The diverse nature of WSN usage makes it not reasonable to look for some particular approach that would be suitable for all cases

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- W. Du, J. Deng, Y. Han, S. Chen, P. Varshney. A Key Management Scheme for Wireless Sensor Networks Using Deployment Knowledge. IEEE Infocom 2004.
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