With the advent of digital communication, securing digital images during transmission and storage has become a critical concern. The traditional s-box substitution methods often fail to effectively conceal the information within highly auto-correlated regions of an image. This paper addresses the security issues presented by three prevalent S-box substitution methods, i.e., single S-box, multiple S-boxes, and multiple rounds with multiple S-boxes, especially when handling images with highly auto-correlated pixels. To resolve the addressed security issues, this paper proposes a new scheme SRSS-the Single Round Single S-Box encryption scheme. SRSS uses a single S-box for substitution in just one round to break the pixel correlations and encrypt the plaintext image effectively. Additionally, this paper introduces a new Chaos-based Random Operation Selection System-CROSS, which nullifies the requirement for multiple S-boxes, thus reducing the encryption scheme's complexity. By randomly selecting the operation to be performed on each pixel, driven by a chaotic sequence, the proposed scheme effectively scrambles even high auto-correlation areas. When compared to the substitution methods mentioned above, the proposed encryption scheme exhibited exceptionally well in just a single round with a single S-box. The close-to-ideal statistical security analysis results, i.e., an entropy of 7.89 and a correlation coefficient of 0.007, validate the effectiveness of the proposed scheme. This research offers an innovative path forward for securing images in applications requiring low computational complexity and fast encryption and decryption speeds.