Connectivity of Multi-channel Wireless Networks Under Jamming Attacks Chengzhi Li and Huaiyu Dai Department of Electrical and Computer Engineering North Carolina State University, Raleigh, NC email: {cli3, hdai}@ncsu.edu Abstract—Jamming attacks can cause serious destruction to communication systems without much cost, especially when secret keys shared by the system are exposed. Uncoordinated Frequency Hopping (UFH) is an effective countermeasure to jamming attacks without dependence on pre-shared secret keys. In this paper we study the connectivity of a multi-channel network under jamming attacks, where each communication link can switch from regular transmission to UFH transmission when jamming attacks are detected. Under the framework of percolation theory, we show that as the jammer density increases, two phase transitions occur: from strong connection where there exists an infinite component composed of regular links, to weak connection where there exists an infinite component composed of both regular and UFH links, then to disconnection. I. I NTRODUCTION A. Motivation As an intentional powerful attack, jamming aims at drowning out the legitimate transmission by either overpowering wire- less receivers at the physical layer or disrupting the protocols at the MAC layer. Due to the shared nature of radio propaga- tion, wireless communication is highly vulnerable to jamming attacks. Legitimate wireless signals may be severely interfered or even fully blocked by jammers, rendering corresponding systems and infrastructures under jeopardy. A popular scheme against jamming threat at the physical layer is the spread-spectrum (SS) techniques, including direct- sequence spread spectrum (DSSS) and frequency hopping (FH). However, the success of these classic countermeasures relies on the feasibility and efficiency of pre-sharing se- cret keys, such as spreading code sequences and frequency hopping patterns, within the legitimate system. Before the establishment or after the compromise of secrete keys, these approaches are inefficacious. The dependency on secret keys is removed in the recently proposed uncoordinated spread spectrum (USS) scheme [1], including uncoordinated DSSS (UDSSS), uncoordinated FH (UFH) and hybrid UFH-UDSSS. USS randomizes the key selection so that neither attackers nor malicious insider nodes are able to jam the communication except for the brute-force approach. In this work, we adopt UFH as a jamming countermeasure, both for concreteness of discussion and for its connection to multi-channel networks. When a network is under jamming attacks one of our primary concerns is the network connectivity. This problem This work was supported in part by the National Science Foundation under Grants ECCS-1002258, CNS-1016260 and ECCS-1307949. would be trivial if a single jammer was powerful enough to jam the whole space the network nodes occupy, which fortunately is not the general case in practice. Jammers are usually limited in power both due to hardware constraint and for the sake of reducing the risk of being detected. Therefore each jammer is typically associated with a jamming region bounded in size. In this study, we consider a multi-hop multi- channel network, where the legitimate nodes staying in the jamming regions can switch to the UFH scheme to improve jamming resistance when jamming attacks are detected 1 .It is assumed that a single jammer cannot block all available channels in its region; however for the nodes under the attack of multiple jammers, UFH may still fail. As a consequence, the connectivity issue in the scenarios we consider is different and more complex than that of a stand-alone network, and worth further investigation. In this work, we investigate the connectivity of a multi- hop multi-channel network subject to insider jamming attacks, under the framework of percolation theory. We show that the network experiences two phase transitions as the jammer density increases: from strong connection where there exists an infinite component composed of regular links, to weak connection where there exists an infinite component composed of both regular and UFH links, then to disconnection. Addi- tionally there are two cutting jammer densities such that if the jammer density is beyond one of these densities, the network is either disconnected, or no longer strongly connected, for any network density. B. Related Works As we mentioned above conventional jamming defense such as SS requires pre-determined keys to built up jamming re- sistance, which suffers from poor scalability and severe threat once the keys are exposed. An effective strategy to defend against this vulnerability is to introduce randomness on the key selection. Besides USS [1], [2], randomized differential DSSS (RD-DSSS) [3] also adopts this strategy, where each bit is encoded using the correlation of unpredictable spreading codes. Randomness enhances the jamming immunity, yet typically degrades the communication efficiency due to lack of coordination between the transmitters and receivers. One technique to improve the efficiency of USS is to combine it 1 Jammer detection is beyond the scope of this study.