Abstract—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 measurement matrix of compressive sensing is analysed from the detection theory perspective. Here, the detection probability of intended and unintended receivers are compared by applying the Neyman-Pearson test. We prove that the detection probability of eavesdropper will be reduced significantly because he does not know the transform domain subspace. Furthermore, in some situations, unintended receiver’s probability of detection may be decreased to 0.5 which makes the eavesdropped data to be useless, i.e. the perfect secrecy will be achieved theoretically. On the other hand, from information theoretic point of view, since the signal to noise ratio are different for main and wiretapper channels, we showed that it is possible to design a measurement matrix for secure transmission even wiretapper knows the measurement matrix.
 

Index Terms—Compressive Sensing, Detection, Perfect Secrecy, secret communication, probability of detection, measurement rate, secrecy rate region

Cite: Mahmoud Ramezani-Mayiami, Hamid G. Bafghi, and Babak Seyfe, "Compressed Sensing Encryption: Compressive Sensing Meets Detection Theory," Journal of Communications, vol. 13, no. 2, pp. 82-87, 2018. Doi: 10.12720/jcm.13.2.82-87.