Chaotic image encryption system using phase-magnitude transformation and pixel substitution

Abstract

We proposed an algorithm to encrypt an image in hybrid domain, frequency and time domains. The proposed method is a private key encryption system with two main units, chaotic phase-magnitude transformation unit and chaotic pixel substitution unit. Chaotic phase-magnitude transformation unit works in frequency domain and a 2-D DFT is performed on the plain image to change the domain. A chaotic function, the tent map, is used to generate the pseudo random image, which are combined with the plain image in frequency domain. Chaotic pixel substitution unit works in time domain Bernoulli map is applied to produce another pseudo random image that is mixing with the encrypted image nonlinearly. The performance of the proposed chaotic image encryption system is analysed using a computer simulation. The distribution of histogram of encrypted image is uniform. Chi-square value for encrypted image of our proposed method is considerably low. The MSE of the proposed encrypted image is big enough. The correlation coefficients of the proposed encrypted image in all three directions are sufficiently small. The total key length is large enough to resist the proposed system against any brute-force attack. The proposed scheme is robust against chosen plaintext attacks too. The proposed chaotic image encryption system, which is used frequency and time domain together, is more secure than most of single domain image encryption systems.