Compressed Sensing Encryption: Compressive Sensing Meets Detection Theory

Mahmoud Ramezani-Mayiami, WISENET Lab, University of Agder, Grimstad, Norway, Hamid G. Bafghi, Babak Seyfe
2018 Journal of Communications  
Since compressive sensing utilizes a random matrix to map the sparse signal space to a lower dimensional transform domain, it may be possible to apply this matrix at the same time for encrypting the signal opportunistically. In this paper, a compressed sensing based encryption method is considered and the secrecy of the measurement matrix of compressive sensing analyzed from the detection theory perspective. Here the detection probabilities of the intended and unintended receivers are compared
more » ... y applying the Neyman-Pearson test. We prove that the detection probability of the eavesdropper will be reduced significantly because he does not know the transform domain sub-space. Furthermore, in some situations, the unintended receiver's probability of detection may be decreased to 0.5, which makes the eavesdropped data useless, i.e., perfect secrecy will be achieved theoretically. On the other hand, from an information theoretic point of view, since the signal to noise ratio are different for the main and wiretapper channels, we showed that it is possible to design a measurement matrix for secure transmission even when the wiretapper knows the measurement matrix.  Index Terms-Compressive sensing, detection, perfect secrecy, secret communication, probability of detection, measurement rate, secrecy rate region.
doi:10.12720/jcm.13.2.82-87 fatcat:gss22rpu5fbqzosuqs6ixaqh5q