Secure Communications With Asymptotically Gaussian Compressed Encryption

In this letter, we study the security of a cryptosystem over wireless channels that employs the asymptotically Gaussian compressed encryption. We investigate the indistinguishability and the energy sensitivity of the cryptosystem, where the total variation (TV) distance is examined as a statistical measure for the indistinguishability. To characterize the TV distance, we compute the Hellinger distance between probability distributions of ciphertexts, each of which can be modeled as a circularly symmetric complex Gaussian random vector with a constraint on plaintexts. Using the distance metrics, we show that the cryptosystem can be a promising option for secure wireless communications by guaranteeing the indistinguishability against an eavesdropper, as long as each plain text has constant energy.