Jamming attacks have been shown to disrupt secret key generation (SKG) in systems that exploit the reciprocity of the wireless medium to generate symmetric keys at two remote locations through public discussion. In this study, the use of frequency hopping/spreading in Rayleigh block fading additive white Gaussian noise (BF-AWGN) channels is investigated as a means to counteract such attacks. The competitive interaction between a pair of legitimate users and a jammer is formulated as a zero-sum game and the corresponding Nash equilibria (NE) are characterized analytically and in closed form. It is found that the jammer's optimal strategy is to spread its power across the entire spectrum. On the contrary, the pair of legitimate users should use frequency spreading only in favorable transmission conditions, and frequency hopping otherwise (e.g., low signal to jamming power ratio). Numerical results show that frequency hopping/spreading in BF-AWGN channels is an effective technique for combating jamming attacks in SKG systems; a modest increase of the system bandwidth can substantially increase the SKG rates.
Jamming attacks have been shown to disrupt secret key generation (SKG) in systems that exploit the reciprocity of the wireless medium to generate symmetric keys at two remote locations through public discussion. In this study, the use of frequency hopping/spreading in Rayleigh block fading additive white Gaussian noise (BF-AWGN) channels is investigated as a means to counteract such attacks. The competitive interaction between a pair of legitimate users and a jammer is formulated as a zero-sum game and the corresponding Nash equilibria (NE) are characterized analytically and in closed form. It is found that the jammer's optimal strategy is to spread its power across the entire spectrum. On the contrary, the pair of legitimate users should use frequency spreading only in favorable transmission conditions, and frequency hopping otherwise (e.g., low signal to jamming power ratio). Numerical results show that frequency hopping/spreading in BF-AWGN channels is an effective technique for combating jamming attacks in SKG systems; a modest increase of the system bandwidth can substantially increase the SKG rates.
Jamming attacks represent a critical vulnerability for wireless secret key generation (SKG) systems. In this paper, two counter-jamming approaches are investigated for SKG systems: first, the employment of energy harvesting (EH) at the legitimate nodes to turn part of the jamming power into useful communication power, and, second, the use of channel hopping or power spreading in block fading channels to reduce the impact of jamming. In both cases, the adversarial interaction between the pair of legitimate nodes and the jammer is formulated as a two-player zero-sum game and the Nash and Stackelberg equilibria are characterized analytically and in closed form. In particular, in the case of EH receivers, the existence of a critical transmission power for the legitimate nodes allows the full characterization of the game's equilibria and also enables the complete neutralization of the jammer. In the case of channel hopping versus power spreading techniques, it is shown that the jammer's optimal strategy is always power spreading while the legitimate nodes should only use power spreading in the high signal-to-interference ratio (SIR) regime. In the low SIR regime, when avoiding the jammer's interference becomes critical, channel hopping is optimal for the legitimate nodes. Numerical results demonstrate the efficiency of both counter-jamming measures.
Secret key generation (SKG) from shared randomness at two remote locations has been shown to be vulnerable to denial of service attacks in the form of jamming. Typically, such attacks are alleviated with frequency hopping/spreading techniques that rely on expansion of the system bandwidth. In the present study, energy harvesting (EH) is exploited as a novel counter-jamming approach that alleviates the need for extra bandwidth resources. Assuming the legitimate users have EH capabilities, the idea is that part of the jamming signal can potentially be harvested and converted into useful communication power. In this framework, the competitive interaction between a pair of legitimate users and a jammer is formulated as a zero-sum game. A critical transmission power for the legitimate users is identified which allows to completely characterize the unique NE of the game in closed form. Remarkably, this threshold also provides the option to effectively neutralize the jammer, i.e., prevent the jammer from carrying out the attack altogether. Through numerical evaluations, EH is shown to be a counter-jamming approach that can offer substantial gains in terms of relative SKG rates.
Secret key generation (SKG) schemes have been shown to be vulnerable to denial of service (DoS) attacks in the form of jamming. In this paper, a comprehensive study on the impact of correlated and uncorrelated jamming in wireless SKG systems is presented. First, optimal signalling schemes for the legitimate users and jamming approaches for an active adversary launching a DoS attack on the SKG system are derived. It is shown that the legitimate users should employ constant signalling. On the other hand, the jammer should inject either correlated jamming when imperfect channel state information (CSI) regarding the main channel is at their disposal, or, uncorrelated jamming when the main channel CSI is completely unknown. In both cases, optimal power allocation policies are studied under short-term power constrains for M block fading additive white Gaussian noise (BF-AWGN) channels. Numerical evaluations demonstrate that equidistribution of the jamming power is near-optimal in the case of uncorrelated jamming.
The topic of physical layer key agreement in Gaussian block fading channels in the presence of active adversaries is investigated in the present contribution. Frequency hopping versus frequency spreading are studied as potential defence strategies against denial of service (DoS) attacks in the form of jamming. We begin by investigating the optimal power allocation policy for the jammer - in the case of frequency spreading - when side information is available. Through numerical evaluations it is shown that effect of the availability of side information on the jammer's impact is minimal. Next, the competitive interaction between the legitimate nodes and the jammer is formulated as a one-shot zero-sum game; it is found that under short term power constraints, the legitimate nodes should not always employ frequency hopping while the jammer should always use frequency spreading. This result contradicts the common practice of using frequency hopping to defend against jamming attacks in standard wireless systems.
Secret key generation (SKG) schemes have been shown to be vulnerable to denial of service (DoS) attacks in the form of jamming. In this paper, a comprehensive study on the impact of correlated and uncorrelated jamming in wireless SKG systems is presented. First, optimal signalling schemes for the legitimate users and jamming approaches for an active adversary launching a DoS attack on the SKG system are derived. It is shown that the legitimate users should employ constant signalling. On the other hand, the jammer should inject either correlated jamming when imperfect channel state information (CSI) regarding the main channel is at their disposal, or, uncorrelated jamming when the main channel CSI is completely unknown. In both cases, optimal power allocation policies are studied under short-term power constrains for M block fading additive white Gaussian noise (BF-AWGN) channels. Numerical evaluations demonstrate that equidistribution of the jamming power is near-optimal in the case of uncorrelated jamming.
This work proposes a jamming-resistant frequency hopping (FH) system that utilizes local channel observations for secret key generation (SKG). FH is a spread spectrum technique used in both military and consumer wireless applications to avoid jamming attacks, but requires pre-shared secret keys among communicating terminals, say Alice and Bob, to ensure that the same FH sequence is used at both sides. In our scheme, Alice and Bob utilize local observations of the channel between them as the source of common randomness to generate the shared secret key. By gathering multiple time slots into a frame, the sequence of channels observed in each frame can be used to determine the FH sequence in the next frame. In this case, the key generation rate must be high enough to identify the FH sequence in the next frame and, thus, to sustain the operation over time. However, by further considering the data transmission, an interesting tradeoff exists between the power allocated for SKG and channel estimation in the training phase and that for communication in the data transmission phase. Given the number of FH channels and the number of channels that the adversary can jam at once, we derive the minimum pilot signal power required for sustainability and also determine the optimal power allocation between pilot and data signals that maximizes the ergodic rate between the two users. Simulations are provided to demonstrate the effectiveness of the proposed scheme.