On the security and robustness of encryption via compressed sensing

The compressed sensing (CS) paradigm unifies sensing and compression of sparse signals in a simple linear measurement step. Reconstruction of the signal from the CS measurements relies on the knowledge of the measurement matrix used for sensing. Generation of the pseudo-random sensing matrix utilizing a cryptographic key, offers a natural method for encrypting the signal during CS. This CS based encryption has the inherent advantage that encryption occurs implicitly in the sensing process - without requiring additional computation. Additionally, the robustness of recovery from compressed sensing, allows a new form of ldquorobust encryptionrdquo for multimedia data, wherein the signal is recoverable with high fidelity despite the introduction of additive noise in the encrypted data. In this paper, we examine the security and robustness of this CS based encryption method. The security implications are investigated by considering brute force and structured attacks. Robustness is characterized empirically. Our analysis and results indicate that the computational complexity of these attacks renders them infeasible in practice. In addition, the CS based encryption is found to have fair robustness against additive noise, making it a promising ldquorobust encryptionrdquo technique for multimedia.