Public Key Image Encryption Based on Compressed Sensing

Abstract

The compression feature of compressed sensing (CS) enables that the ciphertext lengths of multimedia encryption schemes have reduced dramatically, and the simple linear measurements make the encryption process extremely efficient. Therefore, CS based image encryption schemes have attached wide attentions in recent years. However, almost all CS based image encryption schemes follow the framework of symmetric encryption. In this paper, we propose the first CS based public key image encryption scheme PKIE-CS with accurate decryption. As is known to all, two important conditions for successful signal reconstruction in CS are signal sparsity and measurement matrix satisfying some properties (e.g., restricted isometry property). In our scheme, the relationship between the public key and the secret key can be expressed by $\mathbf {B}_{\mathbf {P}}[\mathbf {T};\mathbf {I}]=\mathbf {A}^{T}\mathbf {P}$ , where $\mathbf {B}_{\mathbf {P}}$ and $\mathbf {A}$ are public parameters, $\mathbf {T}$ is the secret key, and $\mathbf {B}_{\mathbf {P}}$ can not be used as the measurement matrix in CS. Thus, anyone can not extract the secret key $\mathbf {T}$ from public key. We first give the specific descriptions of PKIE-CS and then give some theoretical analysis for providing strong security evidence. Last, the experimental results and the comparison with similar works demonstrate the feasibility and the superiority of the proposed scheme.