Image Encryption Algorithms Based On Compressive Sensing And Fractional Mellin Transform

The theories of compressive sensing(CS) and fractional Mellin transform(FrMT) are introduced. Most of the CS-based encryption algorithms are faced with security risks and the encryption algorithms just based on FrMT suffer from encryption data expansion and jagged edges problems of ciphertexts. To solve these problems, two new image encryption algorithms are designed by combining CS with nonlinear FrMT. The performances of the algorithms are analyzed in terms of histogram, correlation of adjacent pixels, key space, key sensitivity, the abilities of resisting noise attacks and robustness. The main research results are as follows:An image encryption algorithm is proposed based on FrMT and CS. In the encryption process, the original image is transformed by FrMT, the transformed result is expressed in discrete cosine domain and re-encrypted by measuring, then the ciphertext is the measurement result. In the decryption process, the ciphertext is reconstructed by the Newton smoothed0 l norm(NSL0) algorithm, then the decrypted image can be obtained from the reconstructed result by taking inverse FrMT.An image encrypted algorithm is designed by combining 2D CS with nonlinear FrMT. In this algorithm, two partial Hadamard matrixes controlled by Logistic chaos map with different initial values are selected as the measurement matrixes. In this encryption algorithm, the original image is measured by two different measurement matrixes in two orthogonal directions. The ciphertext can be obtained from the measurement result by taking FrMT. Correspondingly, by taking inverse FrMT and reconstruction with the NSL0 algorithm, the decryption image can be recovered from the ciphertext.Simulation results indicate that the proposed encryption algorithms have large key space, strong key sensitivity and robustness. In addition, they can stand statistical attack, brute force attack and some other common attacks. It is concluded that the performance of the algorithm combining 2D CS with nonlinear FrMT is better.