Establishing secure measurement matrix for compressed sensing using wireless physical layer security

The simple structure of compressed sensing allows its use not only for low-complexity compression but also for low-complexity encryption. Augmenting compressed sensing to secure information is based on using the sensing matrix as a symmetric encryption key. This imposes the requirement that the key is either preinstalled before deployment or is agreed over some secure communication channel. Both options are problematic when considering a wireless network comprised of nodes with limited resources that could be compromised. This paper proposes an encryption framework where the sensing matrix is established using wireless physical layer security and linear feedback shift register with corresponding m-sequences. Using a Rician fading channel, it is shown that the proposed framework generates valid compressed sensing matrices while preventing access from an eavesdropper in close proximity to one of the legitimate participants.