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Cellular automata are dynamical systems, discrete in terms of both space and time. Many cellular automata are capable of generating chaos and are well suited for applications like digital image encryption and scrambling. Various cellular automata-based digital image scrambling techniques have been proposed in literature. An adversary may have access to a set of images from which the particular image is scrambled. The problem with these techniques in this particular case is that an adversary may be able to find out the true content of the scrambled image just by comparing its histogram with the histograms of a suspected set of images. In this paper, a secure digital image encryption technique based on outer totalistic cellular automata is proposed that modifies the histogram of the scrambled image so that it is difficult to guess the true content carried in the digital image.

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Purpose The purpose of this paper is to investigate two-dimensional outer totalistic cellular automata (2D-OTCA) rules other than the Game of Life rule for image scrambling. This paper presents a digital image scrambling (DIS) technique based on 2D-OTCA for improving the scrambling degree. The comparison of scrambling performance and computational effort of proposed technique with existing CA-based image scrambling techniques is also presented. Design/methodology/approach In this paper, a DIS technique based on 2D-OTCA with von Neumann neighborhood (NvN) is proposed. Effect of three important cellular automata (CA) parameters on gray difference degree (GDD) is analyzed: first the OTCA rules, afterwards two different boundary conditions and finally the number of CA generations (k) are tested. The authors selected a random sample of gray-scale images from the Berkeley Segmentation Data set and Benchmark, BSDS300 (www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/) for the experiments. Initially, the CA is setup with a random initial configuration and the GDD is computed by testing all OTCA rules, one by one, for CA generations ranging from 1 to 10. A subset of these tested rules produces high GDD values and shows positive correlation with the k values. Subsequently, this sample of rules is used with different boundary conditions and applied to the sample image data set to analyze the effect of these boundary conditions on GDD. Finally, in order to compare the scrambling performance of the proposed technique with the existing CA-based image scrambling techniques, the authors use same initial CA configuration, number of CA generations, k=10, periodic boundary conditions and the same test images. Findings The experimental results are evaluated and analyzed using GDD parameter and then compared with existing techniques. The technique results in better GDD values with 2D-OTCA rule 171 when compared with existing techniques. The CPU running time of the proposed algorithm is also considerably small as compared to existing techniques. Originality/value In this paper, the authors focused on using von Neumann neighborhood (NvN) to evolve the CA for image scrambling. The use of NvN reduced the computational effort on one hand, and reduced the CA rule space to 1,024 as compared to about 2.62 lakh rule space available with Moore neighborhood (NM) on the other. The results of this paper are based on original analysis of the proposed work.

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