Spatial image encryption algorithm based on chaotic map and pixel frequency

Images, as a multimedia resource, for example, medical, education, sensing, and military images, have been playing an important role in digital information communications. To prevent unauthorized access and protect the security of an image, a direct approach is to encrypt the image [1, 2] to hide its information. Chaotic maps (systems) have some excellent inherent properties [3,4], such as nonlinearity, sensitivity to initial conditions, and ergodicity. Therefore, they have received increasing attention and have been widely used in image encryption schemes. Tong et al. [5] proposed a hyper-chaotic system-based image encryption scheme together with data compression. A discrete cosine transformation dictionary was used to sparsely represent the plain-image, followed by a diffusion operation, to implement the encryption. In this scheme, however, the plain-image cannot be fully recovered due to the compression of data. To balance security and efficiency in designing a chaos-based image encryption algorithm, the image encryption scheme presented in [6] simulates a one-time pad design. In this scheme, with a key of 256 fixed bits and 128 random bits, a chaotic map was iterated to generate four chaotic sequences. Then, pixels with scrambling and value transformation were used to encrypt the plainimage. However, the keystreams were produced independent of the plain-image. Aiming to enhance security, many algorithms have also been proposed with the help of chaotic maps or systems, for example, DNA and SHA3. Unfortunately, many algorithms, such as [3], have been found to be insecure. Main reasons include: (1) only one round of permutation, (2) only one round of diffusion, (3) keystream generated independent of the plain-image, and (4) small key space. Higher-dimensional chaotic maps or systems, and quantum maps for generating random sequences have been proposed to resolve the small key space problem by using more initial conditions as inputs. Using two or more rounds of encryption, and making the keystreams dependent on the plain-images, seem to show higher security. Yet, most of these algorithms suffer from unsatisfactory sensitivity to the plain-image [7] due to the invariance of the pixel summation. Moreover, some need extra information transmissions [8]. In this article, considering the aforementioned technical issues, the use of random confusion for the plain-image is suggested, with the help of pixel frequency, followed by double diffusion operations to change the pixel distribution. The keystreams used in both stages of confusion and diffusion are produced in dependence on the plain-image. The pixel frequency is introduced to produce a random sequence in the confusion stage and select a chaotic sequence in the diffusion stage, with respect to different plain-images. As a result, the knownplaintext and chosen-plaintext attacks are infea-