<p>Substitution boxes (S-boxes) are a vital part of modern ciphers. They provide the crucial nonlinearity that keeps encrypted data secure. While many methods exist to create S-boxes, they can often be complex. This paper introduces a new and straightforward method to build powerful S-boxes using fractional transformations over a prime field. Our approach combines a Linear Fractional Transformation (LFT) with carefully selected power functions. This creates a new, highly effective permutation function. To further strengthen the result, we apply a random permutation. Our method is simple, yet it allows for precise control over the S-box’s properties, leading to exceptionally high nonlinearity. We put our generated S-box through a series of standard tests. The results show excellent cryptographic qualities: low differential uniformity, robust nonlinearity, and ideal scores in SAC and BIC analyses. When compared with many contemporary S-boxes, ours performs exceptionally well. To show its practical strength, we also designed an image encryption algorithm using our S-box. The algorithm securely encrypts images by substituting and shuffling pixels. Security tests confirm its effectiveness, showing strong performance in NPCR, UACI, and entropy analysis. This work provides a clear and effective method for generating high-performance S-boxes for real-world cryptographic applications.</p>