Abstract: The research aimed to investigate and reveal the construction mechanism of a component-based nonlinear S-box (substitution box). The S-box operates within a Boolean space, performing substitution through nonlinear mapping between input and output vectors to enhance confusion in the encryption process. The proposed nonlinear S-box (vectorial Boolean function) can be straight, compressible, and expandable when utilized in modern block ciphers. To engage the attention of scientific readers, this article explains how to construct a component-based nonlinear S-box using the n-variable affine, linear, and nonlinear Boolean functions. In essence, this procedure alludes to an action of the S-box, which is a mathematical function. The primary motivation for conducting this research was to review several existing S-box construction techniques and apply innovative ideas mathematically to construct a new S-box. The study employed both computational and exploratory research methods. The data collection methods included conducting a literature review, using critical thinking strategies, and facilitating focus group discussions to capture the mathematical notion underlying the nonlinear S-box construction technique.