Cryptographic security of symmetric primitives relies on the discrete mathematical properties of Boolean functions and S-boxes. While machine learning (ML) has shown effectiveness in cryptanalysis, many approaches lack theoretical grounding. This paper proposes an ML-based cryptanalysis framework rooted in Boolean function theory, integrating Walsh–Hadamard analysis, nonlinearity computation, and algebraic characterization. Boolean functions and S-boxes are modeled for precise evaluation of cryptographic strength. The study establishes theoretical links between nonlinearity and ML learnability, validated using neural classifiers. The framework is further extended to side-channel analysis under the Hamming weight model, enabling reliable key recovery. Results show that higher nonlinearity reduces ML learnability, though S-boxes may still exhibit vulnerabilities. Overall, ML-based cryptanalysis is shown to exploit inherent Boolean structural weaknesses, emphasizing the importance of discrete mathematical analysis in security evaluation.