Indistinguishability of Compressed Encryption With Circulant Matrices for Wireless Security

The principle of compressed sensing (CS) can be applied to a cryptosystem in which the sensing matrix is employed for the secret key. In this letter, we study the security of a CS-based cryptosystem that encrypts a plaintext with a secret circulant matrix and transmits the ciphertext over a wireless channel. The relative entropy is considered as a security measure for the indistinguishability of the CS-based cryptosystem. By developing an upper bound on the entropy, the security analysis reveals that the presence of wireless channels and additive noise contributes to reducing the relative entropy of the cryptosystem. Consequently, the CS-based cryptosystem with circulant matrices can guarantee wireless security in terms of the indistinguishability, as long as the channel gains and the plaintext-to-noise power ratio of an adversary are kept to be low for a long keystream and a short ciphertext.