In the field of cryptography, Boolean functions and their generalizations, known as vectorial Boolean functions or S-boxes, play a crucial role in symmetric key cryptography. The use of carefully selected S-boxes is essential for ensuring the security of ciphers, as without them, the ciphers would be susceptible to attacks. Symmetric key cryptography can be classified into stream ciphers and block ciphers, both of which use Boolean functions (including vectorial Boolean functions) for different purposes but with the common goal of improving cipher resilience against various cryptanalyses. Since other ciphers have additional requirements for Boolean functions or S-boxes, designing a cipher is a complex process that requires adherence to multiple principles to create a strong cipher. During the design phase, one must consider the properties of cryptographic primitives and the complete cipher and test them against many possible attacks to ensure their strength. While computers are heavily used in the design process for testing specific aspects of the cipher, modern ciphers are exclusively designed by human experts. However, poor implementation choices can lead to side-channel leakage, making even mathematically secure ciphers vulnerable to attackers. This thesis aims to achieve several objectives. Firstly, we demonstrate that it is possible to construct Boolean functions that satisfy the cryptographic criterion of non-linearity using a non-binary base. Secondly, we aim to build S-boxes with output dimensions smaller than input dimensions, meeting cryptographic criteria such as non-linearity and differential uniformity. The first two goals are considered challenging optimization problems, which we solve using evolutionary computing. Thirdly, we show how to automatically construct a symmetric block algorithm without requiring the intervention of human experts. Finally, we explore how to make side-channel attacks more successful by utilizing machine learning and neuroevolutionary computing.