ABSTRACT
This chapter aims to display a comprehensive and compact review of the fundamental parts of Boolean functions and S-boxes identified with cryptography. It examines distinctive methods for speaking to Boolean functions with regards to cryptography, together with the essential apparatuses. The chapter explains in detail about single and multi-valued functions and transformation utilized in the construction of nonlinear component for block and steam ciphers. Nonlinearity is one of the most important cryptographic properties. The chapter introduces one of the most important tools in cryptography. Namely, the Walsh transforms which is the characteristic 2 case of the discrete Fourier transform. The avalanche effect states an appropriate property of cryptography. The avalanche consequence is obvious, when an input is altered to some extent the output changes meaningfully. A natural progression from the theory of single output Boolean functions is the extension of that theory to multiple output Boolean functions, collectively referred to as an S-box.
