The transmission of significant masses of sensitive and secret images over a public network is inevitable, and demands effective tools and technology to safeguard and conceal the data. In this paper, a symmetric multiple color image encryption technique is proposed by adopting a dual permutation and dual substitution framework. Firstly, the input images are combined into a large image and then segmented into many small and equal-sized pure-image elements. Secondly, using the elementary cellular automata Rule-30, these pure-image elements are permuted to obtain mixed-image elements. Thirdly, second-level permutation is undertaken on the mixed-image elements by applying zigzag pattern scanning. Fourthly, pixel values are substituted by employing the circular shift method; subsequently, second-level pixel substitution is realized through using chaotic random sequences from a 2D logistic map. Finally, the big encrypted image is segmented into smaller encrypted images. Additionally, the keys are calculated from the input images to attain input sensitivity. The efficiency of this method is quantified, based on the unified average changing intensity (UACI), information entropy, number of pixels change rate (NPCR), key sensitivity, key space, histogram, peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) performance metrics. The outcome of the experiments and a comparative analysis with two similar methods indicate that the proposed method produced high security results.