Secret key generation in Rayleigh block fading AWGN channels under jamming attacks

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.