1 Computer Science CSC/ECE 774 – Advanced Network Se Topic 5. Wireless Sensor Network Security Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 1 Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 2 Wireless Sensor Networks sensor Communication and processing module 1. Network protocol (e.g., routing) 2. Data management (e.g., aggregation) 3. Localization and time synchronization 4. Energy management, robustness,etc. 5. Security Node to node Node to sink Group communication a. Key management b. Broadcast authentication Location? c. Security of fundamental services d. Detection of attacks, etc. Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 3 Wireless Sensor Networks (Cont’d) • Composed of – Low cost, low power, and multifunctional nodes – Wireless communication in short distances • Sensor node – Sensing – Data processing – Communication – Unattended
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Computer Science
CSC/ECE 774 – Advanced Network Security
Topic 5. Wireless Sensor Network Security
Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 1
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 2
Wireless Sensor Networks
sensor
Communication and processing
module
1. Network protocol (e.g., routing) 2. Data management (e.g., aggregation) 3. Localization and time synchronization 4. Energy management, robustness,etc. 5. Security
Node to node
Node to sink Group communication
a. Key management b. Broadcast authentication
Location?
c. Security of fundamental services d. Detection of attacks, etc.
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 3
Wireless Sensor Networks (Cont’d)
• Composed of – Low cost, low power, and multifunctional nodes – Wireless communication in short distances
• Sensor node – Sensing – Data processing – Communication – Unattended
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 4
• For each key on a key ring, each node broadcasts a list – α, EKi(α), i= 1, …, k, where α is a challenge
• If a node receives this list, it tries to decrypt each cipher-text with every key it has
• The node establishes a shared key if it can successfully decrypt a cipher-text
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 16
Probabilistic Key Pre-Distribution (Cont’d)
• Path-key establishment – Assign a path-key to selected pairs of nodes that
• Are in wireless communication range • Do not share a common key • But are connected by two or more links at the end of
shared-key discovery
– Established through those links
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 17
Probabilistic Key Pre-Distribution (Cont’d)
• Revocation – Revoke the entire key ring of a compromised node – A controller node broadcasts a single revocation
message containing a signed list of key ids for the revoked key ring
• The controller generates a signature key Ke, and unicasts it to each node by encrypting it with the key they share.
– Each node verifies the signed list of key ids, and removes those keys from its key ring
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 18
Probabilistic Key Pre-Distribution (Cont’d)
• Re-keying – Restart shared-key discovery and path-key
discovery
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 19
Analysis
• Model a sensor network as a random graph – All the sensor nodes are the vertices in the graph – There is an edge between two vertices if the corresponding
nodes share a common key
• Analysis questions – What should be the expected degree (d) of a node so that a
sensor network with n nodes is connected? – Given d and the size of a neighborhood (n’), what should be
the key ring size (k) and key pool size (P) for a network with n nodes?
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 20
Analysis (Cont’d) • What should be the expected degree (d) of a node so that a
sensor network with n nodes is connected? – Answered by random graph theory – G(n, p): a graph of n nodes for which the probability that a link exists
between two nodes is p. – d = p * (n-1): expected degree of a node (i.e. the average number of
edges connecting that node with its neighbors). • Erdös and Rényi’s Equation:
– Given a desired probability Pc for graph connectivity and number of nodes, n, the threshold function p is defined by:
– where
€
Pc = limn→∞
Pr[G(n, p) is connect] = e−e− c
€
p =ln(n)n
+cn
and c is any real constant.
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 21
Analysis (Cont’d)
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 22
Analysis (Cont’d)
• Given d and the size of a neighborhood (n’), what should be the key ring size (k) and key pool size (P) for a network with n nodes? – p’: probability of sharing a key between any two nodes in a
neighborhood (p’=d/(n’-1)) – p’ = 1 - Pr[two nodes do not share any key]
• Simplify with Stirling’s approximation €
p'=1− ((P − k)!)2
(P − 2k)!P!
€
n!≈ 2π nn+12e−n
€
p'=1−(1− k P)
2(P−k+12)
(1− 2k P)(P−2k+
12)
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 23
Analysis (Cont’d)
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 24
Improvements for the Probabilistic Key Pre-Distribution • q-composite key pre-distribution
– Two nodes have to have at least q shared keys to derive a valid pairwise key
– Better resilience when the number of compromised nodes is small
• Multi-path enforcement – Derive each path key through multiple node-
disjoint paths, each of which derives one sub-key – Path key is the XOR of all sub keys – Better resilience to compromised nodes in key
paths
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 25
Random Pairwise Keys Scheme
• Approach – Calculate the smallest probability p of two nodes
being connected so that the entire network is connected with a high probability.
– Consider a network of n nodes – Each node needs to store np pairwise keys
• Limitation – The network size is limited by n=m/p, where m is
the available memory on each node for keys
Computer Science
Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 26
Polynomial Pool Based Key Pre-Distribution
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 27
Outline
• Background – Polynomial based key predistribution
• A framework for key predistribution in sensor networks – Polynomial pool based key predistribution
• Two efficient key predistribution schemes – Random subset assignment – Grid based key predistribution
• Efficient implementation in sensor networks • Conclusion and future work
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 28
Polynomial Based Key Predistribution
• By Blundo et al. [CRYPTO ’92] – Developed for group key predistribution – We consider the special case of pairwise key predistribution
• Predistribution: – The setup server randomly generates
where f (x,y) = f (y, x) – Each sensor i is given a polynomial share f(i, y)
• Key establishment: – Node i computes f (i, y = j) = f (i, j) – Node j computes f (j, y =i) = f (j, i) = f (i, j)
€
f (x,y) = aij xiy j
i, j= 0
t
∑ ,
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 29
Polynomial Based Key Predistribution (Cont’d) • Security properties (by Blundo et al.)
– Unconditionally secure for up to t compromised nodes • Performance
– Storage overhead at sensors: (t +1)log q bits – Computational overhead at sensors: t modular
multiplications and t modular additions – No communication overhead
• Limitation – Insecure when more than t sensors are compromised – An invitation for node compromise attacks
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 30
Polynomial Pool Based Key Predistribution
• A general framework for key predistribution based on bivariate polynomials – Let us use multiple polynomials
• A pool of randomly generated bivariate polynomials
• Two special cases – One polynomial in the polynomial pool
• Polynomial based key predistribution – All polynomials are 0-degree ones
• Key pool by Eschenauer and Gligor
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 31
f1(x,y), f2(x,y), …, fn(x,y)
Random polynomial pool F
A subset: {fj(i, y), …, fk(i, y)}
i
Polynomial Pool Based Key Predistribution (Cont’d) • Phase 1: Setup
– Randomly generates a set F of bivariate t-degree polynomials
– Subset assignment: Assign a subset of polynomials in F to each sensor
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 32
Polynomial Pool Based Key Predistribution (Cont’d) • Phase 2: Direct Key Establishment
– Polynomial share discovery: Communicating sensors discover if they share a common polynomial
• Pairwise keys can be derived if they share a common polynomial.
– Two approaches: • Predistribution:
– Given predistributed information, a sensor can decide if it can establish a direct pairwise key with another sensor.
• Real-time discovery: – Sensors discover on the fly if they can establish a
direct pairwise key.
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 33
Polynomial Pool Based Key Predistribution (Cont’d) • Phase 3: Path Key Establishment
– Establish pairwise keys through other sensors if two sensors cannot establish a common key directly
– Path discovery • Node i finds a sequence of nodes between itself and node j such that
two adjacent nodes can establish a key directly • Key path: the above sequence of nodes between i and j
– Two approaches • Predistribution
– Node i can find a key path to node j based on predistributed information
• Real-time discovery – Node i discover a key path to node j on the fly
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 34
Random Subset Assignment Scheme
• An instantiation of the polynomial pool-based key predistribution.
• Subset assignment: random
f1(x,y), f2(x,y), …, fn(x,y)
Random polynomial pool F
A random subset: {fj(i, y), …, fk(i, y)}
i
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 35
Broadcast IDs in clear text. Broadcast a list of challenges.
i
α, Ekv(α), v = 1, …, m.
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 36
Random Subset Assignment (Cont’d)
• Path discovery – i and j use k as a KDC – Alternatively, i contacts nodes with which it shares a key;
any node that also shares a key with j replies. – Each key path has 2 hops
i j
k
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 37
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60 70 80 90
s
p
s'=2 s'=3 s'=4 s'=5
Probability of Sharing Direct Keys between Sensors
• s: polynomial pool size • s’: number of polynomial shares for each sensor • p: probability of sharing a polynomial between two sensors
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 38
Probability of Sharing Keys between Sensors
0
0.2
0.4
0.6
0.8
1
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
p
Ps
d=20 d=40 d=60 d=80 d=100
• d: number of neighbors • p: probability that two sensors share a polynomial • ps: probability of sharing a common key Note: each key path is at most two hops
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 39
• Comparison with basic probability and q-composite schemes – Probability to establish direct keys p = 0.33 – Each sensor has storage equivalent to 200 keys
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 40
Dealing with Compromised Sensors (Cont’d)
0
0.2
0.4
0.6
0.8
1
1.2
0 500 1000 1500 2000 2500 3000 3500 4000
Maximum supported network size
Prob
abili
ty o
f sha
ring
a co
mm
on
key
RS(s'=2,t=99) RS(s'=6,t=32) RS(s'=10,t=19) Random pairwise keys
• Comparison with random pairwise keys scheme – Assume perfect security against node compromises
• Each polynomial is used at most t times in our scheme – Each sensor has storage equivalent to 200 keys
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 41
Grid Based Key Predistribution • Create a m×m grid • Each row or column is
assigned a polynomial • Assign each sensor to an
interaction • Assign each sensor the
polynomials for the row and the column of its intersection – Sensor ID: coordinate
• There are multiple ways for any two sensors to establish a pairwise key
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 42
Grid Based Key Predistribution (Cont’d)
• Order of node assignment
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 43
Grid Based Key Predistribution (Cont’d)
• Polynomial share discovery – No communication overhead
Same row
Same column
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 44
Grid Key Predistribution (Cont’d)
• Path discovery – Real-time discovery – Paths with one
intermediate node – Paths with two
intermediate nodes – They know who to
contact!
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 45
Properties
1. Any two sensors can establish a pairwise key when there is no compromised node;
2. Even if some sensors are compromised, there is still a high probability to establish a pairwise key between non-compromised sensors;
3. A sensor can directly determine whether it can establish a pairwise key with another node.
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 46
• Comparison with basic probabilistic scheme, q-composite scheme, and random subset assignment scheme – Assume each sensor has storage equivalent to 200 keys
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 47
Dealing with Compromised Sensors (Cont’d)
0
0.2
0.4
0.6
0.8
1
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fraction of compromised nodes
Pro
babi
lity
to e
stab
lish
pair
wis
e ke
ys
d=1 d=3 d=5d=7 d=9
• Probability to establish pairwise keys when there are compromised sensors – d: number of non-compromised sensors to contact – Assume each sensor has storage equivalent to 200 keys
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 48
Implementation • Observations
– Sensor IDs are chosen from a field much smaller than cryptographic keys
• Field for cryptographic keys: Fq • Field for sensor IDs: Fq’
– Special fields: q’=216+1, q’ = 28+1 • No division operation is needed for modular multiplications
l bits each
f1(i,y) f2(i,y) fr(i,y)
Sensor ID j
Key: n bits
Polynomials over Fq’ Same storage as 1 polynomial over Fq
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Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 49
Implementation (Cont’d)
• Lemma 1. In this implementation, the entropy of the key for a coalition of no more than t other sensors is
where and . • Examples
– 64 bit keys – When q’=216+1, the above entropy is 63.9997 bits – When q’ = 28+1, the above entropy is 63.983 bits
€
r ⋅ [log2 q'−(2 −2l+1
q')]
€
l = log2 q'⎣ ⎦
€
r =nl⎡ ⎢ ⎢ ⎤ ⎥ ⎥
Computer Science Dr. Peng Ning CSC/ECE 774 -- Adv. Net. Security 50
TinyKeyMan
• Polynomial pool based key pre-distribution on TinyOS – http://discovery.csc.ncsu.edu/software/TinyKeyMan/