The analysis of Boolean functions is a core part of the design of secure cryptographic primitives, especially to make them more resistant to linear and differential cryptanalysis. This work explores further analytical methods in enhancing nonlinearity, correlation immunity and algebraic complexity of Boolean functions. The paper focuses on using the representations of algebraic normal forms, Walsh Hadamard spectral analysis and optimization techniques to create strong functions which can be applied to modern ciphering systems. An evaluation framework is created based on systematic evaluation to determine resistance to statistical and structural attacks. The experimental findings show that optimized Boolean functions attain a greater nonlinearity and lower correlation biases and thus improve cryptographic security. Comparative analysis shows the superiority of the constructions in comparison with the conventional ones on the level of resilience, efficiency and the ability to implement it. The discoveries are used to design safe substitution boxes and stream cipher elements of modern cryptographic designs.