Four dimensional chaotic ciphers for secure image transmission

This paper proposes a chaotic encryption scheme for image data transmission and multimedia communication. To this end, we first extend the definition of the well-known Arnold 2-D chaotic map to the four-dimensional context. We demonstrate that the chaotic behaviour of the Arnold function is enhanced through our extension to four dimensions. Second, we develop a cryptosystem based on the use of chaotic maps and wavelet decomposition. In fact, by involving the wavelet decomposition filters in the encryption process in addition to the pixel positions and the image gray levels, the 4-D chaotic map is defined in a way that it extends the 3-D chaotic map presented in the literature. This allows to adapt the efficiency of the encryption algorithm to the security needs and the available bandwidth through progressive encryption. According to the length of the symmetric key, different resolutions of the image can be obtained at the decryption level.