# Securing Ad Hoc Wireless Networks Against Data Injection Attacks Using Firewalls

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3 TABLE I TRANSLATION TO THE k COVERAGE PROBLEM S i a set of throttled attack links S i S 1 {A 2 (2),..., A 2 (6), A 3 (6)} 6 S 2 {A 1 (2),..., A 1 (5), A 2 (3),..., A 2 (6), A 3 (5), A 3 (6)} 10 S 3 {A 1 (3),..., A 1 (5), A 2 (4),..., A 2 (6), A 3 (4),..., A 3 (6)} 9 S 4 {A 1 (4), A 1 (5), A 2 (5), A 2 (6)} 4 S 5 {A 1 (5), A 2 (6), A 4 (4)} 3 S 6 { } (victim node) 0 S 7 { } (victim node) 0 S 8 {A 4 (3), A 4 (4)} 2 S 9 {A 3 (2),..., A 3 (6), A 4 (2),..., A 4 (4), A 5 (2), A 5 (3)} 10 S 10 {A 3 (3),..., A 3 (6)} 4 S 11 { } (victim node) 0 S 12 {A 5 (3)} 1 General k-coverage Approximate Algorithm: GenKCover Input: F = {S 1, S 2,..., S n } where S i is a subset of elements in a universal set U, k < n is an integer, an associated weight function w(u) for each element u U, and a set weight function W (T ) (= u T w(u)) for T U. F = F ; C = φ; I = φ for (iter=0; iter< k; iter++) { select S i among F to maximize W (S i C) C = C S i ; I = I i F = F {S i } } Output: C is a near-optimal solution and I is an associated index set. Fig. 2. GenKCover the attack nodes continue to generate malicious packets. As a result, A i (1) for all attack flow id i in Fig. 1, is not in U. Now the problem of finding the k nodes at which firewall functions should be placed such that the weighted sum of the protected links is maximized is equivalent to the k-coverage problem of finding which k subsets of F can maximize the weight of the union of selected subsets. A. Approximate Algorithm, GreedyUnion The k-coverage problem has been shown to be NP-hard in [1]. A simple way to find an optimal solution is to use a brute-force search of all the cases of C(n, k) for subset selection. However, since the brute-force search algorithm runs in an exponential order of time, it is infeasible for large n. Therefore, we need to develop a heuristic firewall placement algorithm that runs in polynomial time while minimizing the impact of the attacks flows or maximizing the weighted sum of protected links. Fig. 2 shows a general approximate algorithm [1], GenKCover, for the k-coverage problem, which will be our base algorithm to solve the optimal firewall placement problem. When an approximate algorithm guarantees to find a solution that is at least ρ times the optimal solution, it is called a ρ-approximation algorithm. The GenKCover turns out to be a (1 1/e)-approximation algorithm [1]. It GreedyU nion Input: F = {S 1, S 2,..., S n } where S i is a subset of all attack links denoted by A i (j), w(u) for each attack link u, W (T ) (= u T w(u)), and a threshold σ. for (iter=1; iter< maxk; iter++) { C = GenKCover(iter) // iter for k in GenKCover if W (C)/W (U) > σ, then stop; else continue; } Output: C is a near-optimal solution and I is an associated index set. Performance Ratio (%) Fig Fig. 3. GreedyUnion Attack Ratio Performance of GreedyUnion, compared to optimal algorithm runs in polynomial time of O(mnk) where m is the size of S i, n is the size of F. When k << n, it asymptotically runs in O(mn). Now we refine the original k-coverage problem so that at least σ% of the links that are under attack can be protected. Instance: F = {S 1, S 2,..., S n } where S i is a subset of all attack links, an associated weight function w(u) for each attack link u denoted by A i (j) for all i, j, a set weight function W (T ), and a threshold σ. Problem: Given a threshold σ, which nodes are the optimal locations for firewall placement? Fig. 3 describes the GreedyU nion algorithm that solves our refined problem. The GreedyUnion is still a (1 1/e)- approximation algorithm because each call to GenKCover guarantees (1 1/e)-approximation. It runs in polynomial time in O(mnk 2 ), where k satisfies σ. As before, when k << n, it asymptotically runs in O(mn). The weight function w(u) of a link u can be considered as the achieved benefit when the link is protected using firewalls. We can use this weight function to incorporate different characteristics of ad hoc network link including loss, bandwidth, and delay etc. B. Incorporation Of Loss Rates In this work, we use the metric ETT [3] as a weight function of a link, that is, w(u) = ET T (u) where ET T (u) is ETT value of the link u. Since ETT corresponds to the average medium occupancy time while delivering a data packet on a wireless link, it could be considered a measure of the wasted medium occupancy time, when the link transmits a malicious data packet. With ETT as the weight function, the goal of our near-optimal heuristic algorithm is to place firewalls such that the total sum of ETT values on saved links is maximized. Refer to our technical report [19] for alternative weight functions.

5 base station inform of attack with marked data packets α (p, h) p = 0.01 p = 0.02 p = 0.03 p = 0.04 p = 0.05 Fig. 7. path length h Data Data, (M i, timestamp) s i d attack node intermediate node i M i = HMAC (K ib, Data timestamp node i) attaching (M i, timestamp) with marking probability p victim node Random marking algorithm with probability p for path length h (Section III-A), and then securely setting up firewall functionality using the shared keys with the selected nodes. A. Provable Attack Detection A fundamental question in our architecture is how a victim ad hoc node can prove to the base station that it is being attacked by certain attacker nodes. The base station must make sure that malicious packets have really been delivered to a victim node from a certain source node. We develop a provable attack detection mechanism using a random marking scheme as depicted in Fig. 7. The key idea of our scheme is to attach a timestamp to a data packet. A message authentication code (MAC) of the data packet, the timestamp, and the node id is computed and also attached to the packet. Nodes do not attach MACs to all packets. Instead, they do so with a probability p. This probabilistic marking scheme allows us to tradeoff the overhead of marking scheme and the number of packets marked. Incorporating timestamps is crucial not only in preventing replay attacks, but also in proving in what period of time those attack packets are sent to the victim nodes. More formally, let mark i (t) denote a 3- tuple of (t, i, M i (t)) where t is a timestamp, i is an ad hoc node id, and M i (t) is the MAC associated with the mark, mark i (t). M i (t) is computed as follows: M i (t) = MAC(K ib, Data timestamp t node id i) where is the concatenation operator. More specifically, we use an HMAC (keyed-hash MAC) [23] function to protect the integrity of the mark 3. When the node decides to mark a packet (with probability p), it appends, unlike existing probabilistic packet marking schemes [24] [27], its own mark to the data packet which might already have marks from previous nodes. The marking node does not overwrite an existing mark. This helps in reducing the overall number of marked packets required to prove attacks. In the case of ad hoc networks, we do not have to restrict ourselves to fitting the marks in the IP header. As opposed to the universally deployed Internet, additional functionality can be relatively easily added in ad hoc networks. 3 The size of a mark would be 24, 28, or 40 bytes in total: 4 bytes for timestamp, 4 bytes for node id [3], and 16, 20, or 32 bytes for HMAC-MD5, HMAC-SHA1, or HMAC-SHA256 [23]. Fig. 8. Marking Probability p Fig Path Length h Expected fraction of data packets being marked Path Length h Marking probability p v.s. path length h when α=0.05 Already, in the DSR protocol, a data packet includes the entire ad hoc path. We also show later in this section that the overhead of appending marks is very low. A victim node stores only those data packets that are marked. However, it counts all the unwanted packets, including those that do not have any marks, towards its threshold-based attack detection. When it detects an attack flow, the victim node forwards the stored marked data packets to the base station as a provable evidence together with a request to block the attacker node. On receiving this request, and the attack evidence, the base station verifies whether the timestamps are within a legitimate time-bound, and also checks the integrity of each mark by using the secret keys, K ib, that it shares with each ad hoc node in the attack path. B. Selection Of Marking Probability We describe a simple methodology for an ad hoc node to select the probability p with which it randomly mark packets before forwarding them. An important goal of our random marking scheme is to minimize the marking overhead while being robust enough to prove an attack detection. Let the random marking probability be p for every node on an ad hoc path and the path length be h. Let α(p, h) be the expected fraction of data packets being marked. α(p, h) can be expressed as follows. α(p, h) = 1 (1 p) h 1 (1) This is because α(p, h) is 1 - the probability that a data packet does not have a single mark from any of the intermediate nodes excluding the attack node and the victim node. Fig. 8 shows the value of α as h increases for various marking probabilities from 0.01 to In other words, p represents the minimal random marking probability at each node when a victim node requires α fraction of data packets marked to be able to detect an attack, and prove the attack to the base station. p = 1 e ln(1 α) (h 1) (2) Therefore, once we fix α to a desired value, the marking probability p of each node can be determined by Eq. (2). The

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