This paper proposes a multiple-image encryption (MIE) approach that uses a novel exponent–sine–cosine (ESC) chaotic map along with the dynamic permutation and DNA-based diffusion. In the first phase of the proposed approach, the three components of a color image (‘R’, ‘G’, ‘B’) for all given images are split, cross-shuffled, and combined randomly to create three big images. These resultant three images are permuted using dynamic permutation during the second phase. In the third phase, the permutated image is diffused using the DNA-based diffusion process. Both permutation and diffusion phases use the novel proposed ESC chaotic map. The proposed ESC chaotic map has been analyzed using Shannon entropy, Lyapunov exponent, and bifurcation diagram. The results show that the ESC map is chaotic in the range of 1.5–10. In addition, the proposed MIE algorithm has been evaluated using various standard metrics such as number of pixel change rate (NPCR), unified average change intensity (UACI), entropy, brute force attack, key sensitivity, and bit corrected ratio (BCR). The results show that the value of the NPCR, UACI, and entropy lies close to 99.59, 32.9, and 7.9995, respectively. Therefore, it is validated that the proposed algorithm provides a good encryption mechanism.