S-Boxes–parameters, characteristics and classifications

S-Boxes are the key building blocks in the design of the block ciphers. They are basically used to hide the relationship between the plaintext and the ciphertext. In this paper we study the parameters of Boolean functions and S-boxes, which are important in the design of good cryptosystems. We give a brief overview of the selection criteria on S-boxes to be resistant to different type of cryptanalytic attacks. For this goal optimality of S-box is defined. We present different variants for classification of S-boxes and give some examples. Also we list the results of our computer calculations for the parameters of Boolean functions and S-boxes that are essential in the cryptographic research. Finally, we give general framework of the direction in which our study is focused.