CSC 774 Advanced Network Security
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1 CSC 774 Advanced Network Security Topic 7. Wireless Sensor Network Security Dr. Peng Ning CSC 774 Adv. Net. Security 1 Wireless Sensor Networks 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 Communication and processing module sensor Node to sink Group communication Location? a. Key management b. Broadcast authentication c. Security of fundamental services d. Detection of attacks, etc. CSC 774 Adv. Net. Security Dr. Peng Ning 2 1
2 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 CSC 774 Adv. Net. Security Dr. Peng Ning 3 Security in Sensor Networks Sensor network security Key management Point-to-point authentication Encryption Broadcast authentication Secure localization Secure clock synchronization CSC 774 Adv. Net. Security Dr. Peng Ning 4 2
3 Challenges in Sensor Network Security Resource constraints Limited storage, computation, and communication Expensive mechanisms such as public key cryptography is not practical Depletable resources (e.g. battery power) Resource consumption attacks Threat of node compromises Sensor nodes are usually deployed in an unattended fashion Subject to node captures CSC 774 Adv. Net. Security Dr. Peng Ning 5 Challenges (Cont d) Local computation/communication v.s. global threat Sensor network applications often depend on local computation and communication due to resource constraints A determined attacker may Attack any node in a network, and Use information gathered from compromised nodes to attack non-compromised ones CSC 774 Adv. Net. Security Dr. Peng Ning 6 3
4 Research Problems Cryptographic services Broadcast authentication Key management Security mechanisms for fundamental services Clock synchronization Secure location discovery Secure aggregation and in-network processing Cluster formation/cluster head election CSC 774 Adv. Net. Security Dr. Peng Ning 7 Research Problems (Cont d) Securing sensor network applications Intruder detection Tracking of moving targets Intrusion detection A desirable component Require different solutions than traditional techniques Others CSC 774 Adv. Net. Security Dr. Peng Ning 8 4
5 CSC 774 Network Security Topic 9.1 Key Pre-distribution in Wireless Sensor Networks Dr. Peng Ning CSC 774 Adv. Net. Security 9 Establishing Pairwise Keys in Sensor Networks Traditional techniques are not practical in sensor networks Public cryptography: not practical Key distribution centers (KDC): not practical CSC 774 Adv. Net. Security Dr. Peng Ning 10 5
6 Probabilistic Key Pre-Distribution Dr. Peng Ning CSC 774 Adv. Net. Security 11 Probabilistic Key Pre-Distribution Basic idea Assign a random subset of keys of a key pool to each node Two nodes can establish secure communication if they have at least one common key i A set of random keys j CSC 774 Adv. Net. Security Dr. Peng Ning 12 6
7 Probabilistic Key Pre-Distribution (Cont d) Key distribution (three phases) Key pre-distribution Shared-key discovery Path-key establishment CSC 774 Adv. Net. Security Dr. Peng Ning 13 Probabilistic Key Pre-Distribution (Cont d) Key pre-distribution Generate a large pool of P keys and their ids For each sensor, random draw k keys out of P without replacement This forms the key ring of the sensor Load the key ring into the memory of the sensor Save the key ids of each key ring and the sensor id on a trusted controller For each node, load the i-th controller node with the key shared with that node. CSC 774 Adv. Net. Security Dr. Peng Ning 14 7
8 Probabilistic Key Pre-Distribution (Cont d) Key pre-distribution (Cont d) Parameters k and P are critical Only a small number of keys need to be placed on each node s key ring Any two nodes share at least a key with a chosen probability CSC 774 Adv. Net. Security Dr. Peng Ning 15 Probabilistic Key Pre-Distribution (Cont d) Shared-key discovery Each node discovers its neighbors in wireless communication range with which it shares keys Method 1: Each node broadcasts the list of key ids on its key ring Give an adversary additional knowledge of key distribution No direct ways to comprise keys CSC 774 Adv. Net. Security Dr. Peng Ning 16 8
9 Probabilistic Key Pre-Distribution (Cont d) Shared-key discovery (Cont d) Method 2 (private shared-key discovery) For each key on a key ring, each node broadcasts a list α, E Ki (α), i= 1,, k, where α is a challenge If a node receives this list, it tries to decrypt each ciphertext with every key it has The node establishes a shared key if it can successfully decrypt a cipher-text CSC 774 Adv. Net. Security Dr. Peng Ning 17 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 CSC 774 Adv. Net. Security Dr. Peng Ning 18 9
10 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 K e, 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 key from its key ring CSC 774 Adv. Net. Security Dr. Peng Ning 19 Probabilistic Key Pre-Distribution (Cont d) Re-keying Restart shared-key discovery and path-key discovery CSC 774 Adv. Net. Security Dr. Peng Ning 20 10
11 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? CSC 774 Adv. Net. Security Dr. Peng Ning 21 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 P c for graph connectivity and number of nodes, n, the threshold function p is defined by: where P c = limpr[g(n, p) is connect] = e $e $ c n "# p = ln(n) n + c and c is any real constant. n CSC 774 Adv. Net. Security Dr. Peng Ning 22 11
12 Analysis (Cont d) CSC 774 Adv. Net. Security Dr. Peng Ning 23 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] ((P " k)!)2 p'=1" (P " 2k)!P! Simplify with Stirling s approximation n!" 2# n n e $n (1" k + 1 p )2(P"k 2 ) p'=1" (1" 2k ) (P"2k ) p CSC 774 Adv. Net. Security Dr. Peng Ning 24 12
13 Analysis (Cont d) CSC 774 Adv. Net. Security Dr. Peng Ning 25 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 nodedisjoint 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 CSC 774 Adv. Net. Security Dr. Peng Ning 26 13
14 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 CSC 774 Adv. Net. Security Dr. Peng Ning 27 Polynomial Pool Based Key Pre-Distribution Dr. Peng Ning CSC 774 Adv. Net. Security 28 14
15 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 CSC 774 Adv. Net. Security Dr. Peng Ning 29 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: t The setup server randomly generates f (x, y) = " a ij x i y j, i, j= 0 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) CSC 774 Adv. Net. Security Dr. Peng Ning 30 15
16 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 CSC 774 Adv. Net. Security Dr. Peng Ning 31 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 CSC 774 Adv. Net. Security Dr. Peng Ning 32 16
17 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 A subset: {f j (i, y),, f k (i, y)} f 1 (x,y), f 2 (x,y),, f n (x,y) i Random polynomial pool F CSC 774 Adv. Net. Security Dr. Peng Ning 33 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. CSC 774 Adv. Net. Security Dr. Peng Ning 34 17
18 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 CSC 774 Adv. Net. Security Dr. Peng Ning 35 Random Subset Assignment Scheme An instantiation of the polynomial pool-based key predistribution. Subset assignment: random A random subset: {f j (i, y),, f k (i, y)} f 1 (x,y), f 2 (x,y),, f n (x,y) i Random polynomial pool F CSC 774 Adv. Net. Security Dr. Peng Ning 36 18
19 Random Subset Assignment (Cont d) Polynomial share discovery Real-time discovery Broadcast IDs in clear text. Broadcast a list of challenges. i f j,, f k i α, E kv (α), v = 1,, m. CSC 774 Adv. Net. Security Dr. Peng Ning 37 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 CSC 774 Adv. Net. Security Dr. Peng Ning 38 19
20 Probability of Sharing Direct Keys between Sensors s'=2 s'=3 s'=4 s'= p s s: polynomial pool size s : number of polynomial shares for each sensor p: probability of sharing a polynomial between two sensors CSC 774 Adv. Net. Security Dr. Peng Ning 39 Probability of Sharing Keys between Sensors d=20 d=40 d=60 d=80 d= Ps d: number of neighbors p: probability that two sensors share a polynomial p s : probability of sharing a common key Note: each key path is at most two hops p CSC 774 Adv. Net. Security Dr. Peng Ning 40 20
21 Dealing with Compromised Sensors Comparison with basic probability and q-composite schemes Probability to establish direct keys p = 0.33 Each sensor has storage equivalent to 200 keys Fraction of compromised links between noncompromised sensors RS(s'=2,s=11,t=99) RS(s'=3,s=25,t=66) RS(s'=4,s=43,t=49) q-composite(q=1) q composite(q=2) q composite(q=3) Basic probabilistic Number of compromised nodes CSC 774 Adv. Net. Security Dr. Peng Ning 41 Dealing with Compromised Sensors (Cont d) 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 RS(s'=2,t=99) RS(s'=6,t=32) RS(s'=10,t=19) Random pairwise keys Probability of sharing a common key Maximum supported network size CSC 774 Adv. Net. Security Dr. Peng Ning 42 21
22 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 CSC 774 Adv. Net. Security Dr. Peng Ning 43 Grid Based Key Predistribution (Cont d) Order of node assignment CSC 774 Adv. Net. Security Dr. Peng Ning 44 22
23 Grid Based Key Predistribution (Cont d) Polynomial share discovery No communication overhead Same column Same row CSC 774 Adv. Net. Security Dr. Peng Ning 45 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! CSC 774 Adv. Net. Security Dr. Peng Ning 46 23
24 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. CSC 774 Adv. Net. Security Dr. Peng Ning 47 Dealing with Compromised Sensors Comparison with basic probabilistic scheme, q-composite scheme, and random subset assignment scheme Assume each sensor has storage equivalent to 200 keys Fraction of compromised links between non-compromised sensors Basic probabilistic(p=0.014) q-composite(q=1,p=0.014) RS(s'=2,s=287,t=99,p=0.014) Grid-based(N=20000,p=0.014) Number of compromised nodes Basic probabilistic(p=0.33) q-composite(q=1,p=0.33) RS(s'=2,s=11,t=99,p=0.33) CSC 774 Adv. Net. Security Dr. Peng Ning 48 24
25 Dealing with Compromised Sensors (Cont d) 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 d=1 d=3 d=5 d=7 d=9 Probability to establish pairwise keys Fraction of compromised nodes CSC 774 Adv. Net. Security Dr. Peng Ning 49 Implementation Observations Sensor IDs are chosen from a field much smaller than cryptographic keys Field for cryptographic keys: F q Field for sensor IDs: F q Special fields: q = , q = No division operation is needed for modular multiplications Key: n bits l bits each f 1 (i,y) f 2 (i,y) f r (i,y) Polynomials over F q Same storage as 1 Sensor ID j polynomial over F q CSC 774 Adv. Net. Security Dr. Peng Ning 50 25
26 Implementation (Cont d) Lemma 1. In this implementation, the entropy of the key for a coalition of no more than t other sensors is 2l +1 r " [log 2 q'#(2 # )] q' " where l = " log 2 q' # and r = n $ #. l % Examples 64 bit keys When q = , the above entropy is bits When q = , the above entropy is bits CSC 774 Adv. Net. Security Dr. Peng Ning 51 TinyKeyMan Polynomial pool based key pre-distribution on TinyOS CSC 774 Adv. Net. Security Dr. Peng Ning 52 26
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