Construction of S-box

Question

Explain how the S-box is constructed?

Answer 1

The S-box is constructed in the following manner:

Initialize S-box with the byte values in ascending sequence row by row. The first row consist of {00}, {01}, {02}, ……….., {0F}; the second row consist of {10},{11}, and so on. Therefore, value of the byte at row x, column y is {x y}. Map each byte within the S-box to its multiplicative inverse within the finite field GF (28); the value {00} is mapped to itself. Consider that each byte within the S-box comprises of the 8 bits labelled by (b7, b6, b5, b4, b3, b2, b1, b0). Apply following transformation to every bit of each byte within the S-box.