Fast and Secure Rendezvous Protocols for Mitigating Control Channel DoS Attacks

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1 Fast and Secure Rendezvous Protocos for Mitigating Contro Channe DoS Attacks Mohammad J. Abde-Rahman, Hanif Rahbari, and Marwan Krunz Det. of Eectrica and Comuter Engineering, University of Arizona, Tucson, USA Phiie Nain INRIA, Sohia Antiois, France Abstract The oeration of a wireess network reies extensivey on exchanging messages over a universay known channe, referred to as the contro channe. The network erformance can be severey degraded if a jammer aunches a denia-ofservice (DoS) attack on such a channe. In this aer, we design quorum-based frequency hoing (FH) agorithms that mitigate DoS attacks on the contro channe of an asynchronous ad hoc network. Our agorithms can estabish unicast as we as muticast communications under DoS attacks. They are fuy distributed, do not incur any additiona message exchange overhead, and can work in the absence of node synchronization. Furthermore, the muticast agorithms maintain the muticast grou consistency. The efficiency of our agorithms is shown by anaysis and simuations. I. INTRODUCTION Wireess communications are vunerabe to intentiona interference attacks, tyicay referred to as jamming. The erformance of a wireess network can be severey degraded if a jammer aunches a denia-of-service (DoS) attack on the contro channe. Conventiona anti-jamming techniques often rey on sread sectrum communications, incuding frequency hoing (FH). FH has been used in the iterature for estabishing unicast communications in dynamic sectrum access (DSA) networks, where a common contro channe does not aways exist. However, most existing FH designs are based on ad hoc aroaches that do not rovide any erformance guarantees. One way to construct FH sequences in a systematic manner is to use quorum systems 3]. Quorum-based FH designs are advantageous in ad hoc networks because of their robustness to synchronization errors 4]. However, revious quorum-based FH designs, such as 3], do not suort muticast rendezvous, where a the nodes in a muticast grou are required to meet in the same time sot. The authors in 6] roosed an FH-based jamming-resistant broadcast communication scheme. In their scheme, the broadcast oeration is imemented as a series of unicast transmissions, which can ead to muticast inconsistency. For exame, a grou of nodes may share a grou key that is used to encode/decode common secure communication messages. For security uroses, this key may have to be udated eriodicay 7]. However, the change in the grou key has to This research was suorted in art by NSF (under grants CNS-6943 and CNS-9468, IIP , IIP-2343), Raytheon, and the Connection One center. Any oinions, findings, concusions, or recommendations exressed in this aer are those of the author(s) and do not necessariy refect the views of the Nationa Science Foundation. be consistent among a nodes in the grou. Even with the jamming resiiency, such consistency cannot be guaranteed if changes in the grou key are conveyed sequentiay. Instead of designing different FH sequences that overa at common sots, the muticast rendezvous in 5] is estabished after a series of airwise rendezvous oerations that resut in tuning a nodes in the muticast grou to a common FH sequence. The effectiveness of this aroach cannot be maintained under node comromise (if one node is comromised, then the FH sequences of a nodes are exosed). The authors in ] were the first to consider muticast rendezvous in fast-varying DSA networks, using different FH sequences whie maintaining muticast consistency. In this aer, we resent three FH agorithms to maintain contro communications under a DoS attack on the contro channe. More secificay, we roose a nove nested grid quorum-based FH agorithm, caed NUDoS, for estabishing unicast communications in a hostie environment with mutie jammers. NUDoS is faster than reviousy roosed airwise rendezvous agorithms, robust to node comromise, and can function in the absence of synchronization. Next, to estabish muticast communications whie guaranteeing muticast consistency, we customize the two muticast rendezvous agorithms (AMQFH and nested-cmqfh) roosed in ]. We ca the modified agorithms KMDoS and NCMDoS, resectivey. KMDoS and NCMDoS rovide different tradeoffs between seed and robustness to node comromise. Our agorithms are distributed and do not incur any additiona message overhead. The rest of this aer is organized as foows. Section II introduces our modes, defines our metrics, and states our robem. The NUDoS agorithm is resented in Section III. Section IV briefy introduces the KMDoS and NCMDoS agorithms. We evauate our agorithms in Section V, and concude the aer in Section VI. II. MODES, METRICS, AND PROBEM STATEMENT A. System Mode We consider a wireess ad hoc network with k nodes and channes, denoted by f,f 2,...,f. Without oss of generaity, we assume that FH occurs on a er-sot basis, where the sot duration is T seconds. A acket can be exchanged between two or more nodes if they ho onto the same channe in the same time sot. We assume that one time sot is sufficient to exchange one message. If mutie grous haen

2 to meet on the same channe in the same time sot, they use a CSMA/CA-stye rocedure to resove contention. For j =,...,k, each node j has its unique FH sequence w (j). The channe used in the ith sot of FH sequence w (j) is denoted by w (j) i,w (j) i {f,...,f }. Channe f j is caed a rendezvous frequency for the FH sequences w (),..., w (k) if there exists a rendezvous sot i such that w (m) i = f j, m {,...,k}. In our setu, each FH sequence consists of severa frames. Each frame consists of a bock of time-frequency hos. B. Attack Mode We consider two tyes of attacks: an insider attack in which an attacker can comromise a egitimate node and extracts its FH sequence, and a Markovian jamming attack where a jammer foows a two-state discrete-time Markov rocess. When the jammer is in state it does not transmit; otherwise, it transmits a jamming signa. et ρ (m) be the robabiity that channe m is in state, and et T (m) be the exected time (in sots) that channe m sends in state before returning to state. Then, the transition robabiities from state to state ( (m) ) and from state to state (q (m) ) can be exressed as: (m) = ρ(m), q (m) =. () ρ (m) C. Evauation Metrics T (m) T (m) Our agorithms are evauated according to two metrics: exected evasion deay (ED) and exected Hamming distance (HD). ED is defined as the time between the successfu jamming of the contro channe and the re-estabishment of a new one. The exected ED is considered because of the existence of a randomy assigned art in our FH sequences. The exected HD for two FH sequences x = (x...x n ) and y = (y...y n ) is defined as E ( n {x i y i}) /n], where { } is the indicator function and n is the frame ength. In addition to robustness to node comromise, FH sequences with higher HD wi have a ower coision robabiity. A coision occurs when two or more neighboring grous meet on the same channe in the same time sot. D. Probem Statement The FH construction robem is stated as foows: Given f,...,f, k, and n, determine the vaues of w (j) i, i n, j k, that resut in the minimum ED, and achieve a minimum HD of d. This robem is formuated as foows: minimize {w (j) i : i n, j k} Subject to. w (i) = w (j), i,j {,...,k},i j (2) n r= s () i w (i) ] =, i {,...,k} (3) (i) {w nd, i,j {,...,k},i j (4) r w r (j) } where s (r) i f x ] {,} is the state of frequency f x {f,...,f } in the rth time sot, as seen by node i. Assume that s (r) i f x ],i {,...,k},r {,...,n},x {,...,} are given. Then, the soution to Probem gives the minimum ED, denoted by ED, and the rendezvous frequency, denoted by f u. ED and u are given by: { ( k )} s (r) i f u ] == (5) ED = min u u = argmin u { min r n min r n ( k s (r) i f u ] == )} where denotes the ogica OR oeration. Reaxing the assumtion of knowing the future states of the channes, next we roose a centraized agorithm that soves the above robem in O(kn) time, assuming that ony the channe s transition robabiities are known. The centraized agorithm, which reies on redicting the future states of the channes given the current states, can be summarized by the foowing stes: ) For each sot j =,...,n, comute j and j as foow: { k } j = max () n e+j (s(e) i f ],) (7) j = argmax { k () n e+j (s(e) i f ],) where e is the index of the sot in the current frame when channe f has been recenty sensed and () n e+j (s(e) i f ],) is the (n e + j)-ste transition robabiity of f form state s (e) i f ] to state. In genera, the v-ste transition robabiity of channe m from state s to state can be exressed as: ] s ] v q (m) + (m) q(m) (m) q (m) (m) v (s,) = (m). (m) +q (m) (9) 2) Sort sots ascendingy according to their j vaues. 3) Seect the to n nd = n( d) sots in the ist, and assign frequency f j to sot j in a FH sequences. 4) For the remaining nd sots, assign different frequencies for different FH sequences. Next, we exoit some roerties of quorum systems in designing distributed FH rendezvous agorithms. III. UNICAST COMMUNICATIONS Before describing NUDoS for unicast communications, we first give a few basic definitions. A. Preiminaries Definition. Given a set Z n = {,,...,n }, a quorum system Q under Z n is a coection of non-emty subsets of Z n, each caed a quorum, such that: G,H Q : G H. Definition 2. Given a non-negative integer i and a quorum G in a quorum system Q under Z n, we define rotate(g,i) = } (6) (8)

3 {(x+i) mod n,x G} to denote a cycic rotation of quorum G by i. Definition 3. A quorum system Q under Z n is said to satisfy the rotation k-cosure roerty for some k 2 if G,...,G k Q and i,...,i k Z n, k j= rotate(g j,i j ). Quorum systems that enjoy the above rotation k-cosure roerty can be exoited to achieve asynchronous communications. One such quorum system that satisfies the rotation 2-cosure roerty is the grid quorum system 4]. Definition 4. A grid quorum system 4] arranges the eements of the set Z n as a n n array. In this case, a quorum is formed from the eements of any coumn us any row of the grid. Figure iustrates the rotation cosure roerty for two quorums G and H in a grid quorum system Q under Z 6. One quorum s coumn must intersect with the other quorum s row, and vice versa. Hence, the two quorums have at east two intersections (abeed I in Figure ). In Figure, G = rotate(g,) and H = rotate(h,2) intersect at the two eements abeed asi. Hence, the grid quorum system satisfies the rotation 2-cosure roerty. Fig. : Rotation 2-cosure roerty of grid quorum systems. B. NUDoS Agorithm In NUDoS, every frame of every FH sequence uses n rendezvous frequencies, where n is the frame ength in sots. The foowing exame exains the oeration of the NUDoS agorithm forn = 6 (hence, each frame of every FH sequence contains n = 3 rendezvous frequencies). ) Construct a grid quorum system Q under Z 6. Q consists of 6 different quorums, each of 2 6 = 7 eements. 2) Construct an FH sequence w as foows: Seect the outer-most quorum G () from the quorum system Q (e.g., G () = {,,2,3,4,8,2}, where each entry reresents the index of a time sot in a 6-sot frame). Assign a rendezvous frequency h () {f,...,f } to the FH sots that corresond to G (). Deete quorum G () from the origina 4 4 grid and seect the next outer-most quorum G () 2 from the resuting 3 3 grid (e.g., G () 2 = {6,9,,,4}). Then, assign another rendezvous frequency h () 2 to the FH sots that corresond to G () 2. Deete quorum G () 2 from the 3 3 grid, and seect the next outer-most quorum G () 3 from the resuting 2 2 grid (e.g., G () 3 = {7,3,5}). Then, assign a third rendezvous frequency h () 3 to the FH sots that corresond to G () 3. Assign a random frequency h () x {f,...,f } \ {h (),h() 2,h() 3 } to each of the unassigned sots. Reeat the above stes for the other frames in w. 3) Reeat ste 2 for other FH sequences. Throughout this aer, h (j) i and G (j) i, i {,..., n }, denote the ith quorum-assigned frequency that is assigned to the ( n i+) ( n i+) quorum G (j) i in the jth frame. C. Features of the NUDoS Agorithm NUDoS has two main features. First, because of the nested generation of quorums, the overa ratio between two FH sequences (number of rendezvous sots in a frame divided by the frame ength) is significanty higher than the overa ratio for a non-nested grid quorum-based FH agorithm (herein denoted by UDoS). In UDoS, an FH sequence consists of ony one rendezvous frequency, assigned to a n n quorum. FH systems with a higher overa ratio work more efficienty in hostie environments, where a jammer may suddeny aear on a rendezvous channe. Besides having a higher overa ratio, NUDoS invoves mutie rendezvous frequencies er frame, which increases the ikeihood of rendezvousing. The advantage of a nested grid quorum with mutie rendezvous frequencies can be formaized by deriving the exected overa ratio for UDoS and NUDoS, denoted byv UDoS and V NUDoS, resectivey. V UDoS is comosed of the sum of two arts; the exected overa ratio between the quorumbased assigned arts of the FH sequences, denoted by V Q UDoS, and the exected overa ratio between the randomy assigned arts, denoted by VUDoS R. Simiary, V NUDoS is comosed of V Q NUDoS and VR NUDoS. For a given n, VQ UDoS and VQ NUDoS can be determined numericay. After some maniuations, VUDoS R and VR NUDoS can be exressed as foows: VUDoS(,n) R = ( n ) 2 {2 ( n ) 2 } () n VNUDoS(,n) R = {2 n } 2. () Potting V UDoS and V NUDoS vs. n, one can see that V NUDoS is arger than V UDoS, and both decrease with n. The second attractive feature of NUDoS is its robustness to node comromise. Because the quorum-based assigned art of the FH sequence is the art that is intended to suort the rendezvous caabiity, if this art is comromised, the rendezvous caabiity may be eiminated or reduced significanty. NUDoS sequences are comosed of n nested quorums that are generay different for different frames in a given FH sequence, and aso different for different FH sequences. Hence, if a node is comromised and its FH sequence is exosed, ess information wi be eaked about other FH sequences, comared with UDoS sequences. The number of different channe assignments for a given n (K n ) is given by: K n = n 2 ( n j) 2. (2) j=

4 IV. MUTICAST COMMUNICATIONS The muticast rendezvous agorithms, AMQFH and CMQFH, roosed in ] are customized for maintaining muticast communications under a DoS attack on the contro channe. The resuted agorithms are caed KMDoS and CM- DoS, resectivey. These agorithms have two main attractive features. First, they aow a node to construct its sequence by ony knowing the number of nodes in its muticast grou. Hence, they can be executed in a fuy distributed way. Second, these agorithms can sti function in the absence of node synchronization. Due to sace imitations, the detais of these agorithms are not mentioned here, but can be found in 2]. We evauate KMDoS and CMDoS based on the exected ED and HD. KMDoS and CMDoS are imemented in a distributed way as foows. First, the source node uses a series of airwise rendezvous to communicate the number of nodes in the muticast grou to the target muticast grou. Then, each receiving node constructs its own muticast FH sequence. A. Exected ED The exected ED of KMDoS and CMDoS, denoted by E k and E c, resectivey, can be exressed as foows: Resut. E k is given by: ] n i E k = iγ(γ i+ ) ( Γ(γ j )) (3) j= where Γ(γ i ) is the robabiity that sot i is a rendezvous sot and γ i is the robabiity that sot i is a quorum sot (i.e., assigned a rendezvous frequency).γ(γ i ) andγ i,i =,...,n, are given by (k is the muticast grou size minus one for KMDoS): k (k ) ( ) ] i + Γ(γ j ) = γ k+ i γj j kn k+ i= i+2 i + γ i = n Resut 2. E c is given by: ( + i n ) (4) k ( γ j ) k+ i+3 n i+. (5) kn k+ n E c = Θ i( Θ) i (6) where Θ is the robabiity that a given sot is a rendezvous sot. Θ is given by (k is the muticast grou size for CMDoS): k ( ) i k j=k i+ Θ = (e ] j )/e j e i=...e k i {e,...,e k i } {,..., k } (7) ( ) k k e +. e Potting E k and E c, one can see that for > 3, E c E k. Both, E c and E k increases with the muticast grou size. = B. Exected HD { } Resut 3. et φ def kn = n k+ +. Then, the exected HD of KMDoS, denoted by H k, and its uer bound vaue, denoted by H k,best, are given by: H k = { (ϕ )(φ+) + φ } (8) n ϕ ϕ H k,best = φ+ (9) n where H k,best corresonds to the case when different nodes seect different sequences, and nodes cannot rendezvous during the randomy assigned sots. H k reresents the case when nodes can seect different sequences or the same sequence. Resut 4. The exected HD of CMDoS, denoted by H c, and its uer bound vaue, denoted by H c,best, are given by: H c = k k ( 2k 2 ) (2) j= i j k k ( H c,best = 2 ( ) ) (2) k 2 i j j= j i where H c,best is defined simiar to H k,best. Note that as the muticast grou size increases, H c increases but H k decreases, and hence the ga between H c and H k increases with the increase in the size of the muticast grou. CMDoS is robust against node comromise but it is sow. To reduce the ED of CMDoS, we augment it with a nesting design simiar to the NUDoS agorithm, as discussed 2]. The nested version of CMDoS is caed NCMDoS. Remark. FH sequences constructed according to NUDoS, KMDoS, and NCMDoS can estabish asynchronous communications if each FH sequence continues to use the same outer-most quorum and channe in a frames of the FH sequence. This condition is sufficient but not necessary. Thus, FH sequences can sti rendezvous even if the outer-most quorum is changed in some frames, rovided that this change does not occur very frequenty. Remark 2. In Section V, channes and quorums are seected based on the forecasted avaiabiity of the channes at different quorums, as derived from the jamming mode described in Section II-B. A channe is considered avaiabe at a future sot if it is redicted to be avaiabe at that sot with robabiity greater than th. The detais of the channe and quorum seection rocedures are omitted due to sace imitation. V. PERFORMANCE EVAUATION We now resent simuation resuts for the NUDoS, KMDoS, and NCMDoS agorithms, and comare them with the centraized agorithm. The roosed agorithms are studied under different jamming robabiities (ρ (m) ), as we as different frame engths and grou sizes for unicast and muticast, resectivey. Our evauation metrics are the ED and the HD. Our agorithms are simuated under a reaistic setting of no synchronization (the misaignment between FH sequences is

5 Evasion Deay (sots) NUDoS, ρ (m) =.3 NUDoS, ρ (m) =.5 C,d =.65 C,d = n (sots) Hamming Distance (HD) n (sots) Fig. 2: ED for NUDoS ( th =.5,T (m) = 8). Fig. 3: HD for NUDoS ( th =.5,T (m) = 8) NUDoS, ρ (m) =.3 NUDoS, ρ (m) =.5 C,d =.65 C,d =.5 Evasion Deay (sots) KMDoS, ρ (m) =.3 KMDoS, ρ (m) =.5 C,d =.65 C,d = Muticast Grou Size Fig. 4: ED for KMDoS ( th =.5,T (m) = 8). randomy seected in each exeriment). The 95% confidence intervas are indicated. To achieve a minimum HD of d in the centraized agorithm, the actua HD (i.e., nd /n) might be different for different frame engths. A. Unicast Communications (NUDoS) Figure 2 deicts the ED of NUDoS, and comare it with the centraized agorithm (denoted by C). The ED for both agorithms (NUDoS and C) increases with n because of the reduction in the overa ratio. The ED aso increases with ρ (m). Whie achieving a cose HD to the centraized agorithm for sma to moderate vaues of ρ (m), the seed of NUDoS is comarabe to the centraized agorithm. Increasing d in (4) increases the ED of the centraized agorithm. The HD for NUDoS and C is otted in Figure 3. The HD of NUDoS increases with n because of the reduction in the overa ratio. It aso increases with ρ (m) because of the increase in the number of unassigned sots (in our simuations, each unassigned sot increments the HD by /n). B. Muticast Communications (KMDoS and NCMDoS) Figure 4 shows the ED of KMDoS and the centraized agorithm. The ED of KMDoS increases with the grou size for arge vaues of ρ (m). Figure 5 deicts the ED of NCMDoS vs. ρ (m) for a grou of size 3. NCMDoS is much sower than both KMDoS and the centraized agorithm. As shown in Figure 6, the HD of NCMDoS is arger than that of KMDoS, and the ga increases with the increase in the grou size. The HD increases with ρ (m) because of the increase in the number of unassigned sots. Evasion Deay (sots) NCMDoS C,d=.73 C,d= ρ (m) Fig. 5: ED for NCMDoS (grou size = 3, th =.5,T (m) = 8). Hamming Distance (HD) KMDoS, ρ (m) =.2 KMDoS, ρ (m) =.5 NCMDoS, ρ (m) =.2 NCMDoS, ρ (m) = Muticast Grou Size Fig. 6: HD for KMDoS and NCMDoS ( th =.5,T (m) = 4). VI. CONCUSIONS In this aer, we designed three FH agorithms for estabishing unicast (NUDoS) and muticast (KMDoS and NCM- DoS) communications in the resence of a contro channe DoS attack. KMDoS and NCMDoS maintain the muticast consistency, and rovide different tradeoffs between seed and robustness to node comromise. Our agorithms are distributed, do not incur additiona message exchange overhead, and work in the absence of synchronization. We simuated our agorithms under a reaistic setting of no synchronization. REFERENCES ] M. J. Abde-Rahman, H. Rahbari, and M. Krunz, Adative frequency hoing agorithms for muticast rendezvous in DSA networks, in Proc. of the IEEE DySPAN Conf., Oct. 22, ] M. J. Abde-Rahman, H. Rahbari, M. Krunz, and P. Nain, Fast and secure rendezvous rotocos for mitigating contro channe DoS attacks, University of Arizona, Tech. Re. TR-UA-ECE-22-4, Jan. 23. Onine]. Avaiabe: htt://www2.engr.arizona.edu/ mjabderahman. 3] K. Bian, J. M. Park, and R. Chen, A quorum-based framework for estabishing contro channes in dynamic sectrum access networks, in Proc. of the ACM MobiCom Conf., 29, ] J.-R. Jiang, Y.-C. Tseng, C.-S. Hsu, and T.-H. ai, Quorum-based asynchronous ower-saving rotocos for IEEE 82. ad-hoc networks, Mobie Networks and Aications, vo.,. 69 8, Feb ] Z. in, H. iu, X. Chu, and Y.-W. eung, Jum-stay based channehoing agorithm with guaranteed rendezvous for cognitive radio networks, in Proc. of the IEEE INFOCOM Conf., 2, ] S. iu,. azos, and M. Krunz, Thwarting inside jamming attacks on wireess broadcast communications, in Proc. of the ACM WiSec Conf., 2. 7] D. R. Stinson, Crytograhy: Theory and Practice. Chaman and Ha/CRC, Tayor and Francis Grou, 26.