In this paper, a novel image encryption scheme is proposed based on permutation–diffusion architecture using cellular automata. In the permutation phase, Wolfram class III radius 2 cellular automata rules are utilized for shuffling the pixels of the plain image and in the diffusion phase; the rules based on unity attractors of elementary cellular automata are employed to encrypt the pixels of the shuffled plain image. Addition to the encryption scheme, a new non-parametric statistical method for measuring the pixel randomness in the shuffled and encrypted images is also proposed in this paper. The strength of the proposed image encryption scheme is first assessed by standard methods for security analysis, and the pixel randomness is then determined by the newly proposed non-parametric method. The results of the assessment exhibit the high security of the diffusion process and its computational efficiency. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.