I'm trying to understand some cryptographic properties of the s-box so I can have my own code. Example of balanced properties I read in this document that they say
A boolean function S : $ GF(2^n) $ $ \to $ $ GF(2) $ is called balanced if the output set contains equal number of ones and zeros in the corresponding truth table.
Example 2.2.3 We provide a comparison of balanced and unbalanced functions. Consider two boolean functions, XOR and AND defined as:
$ S_1 = \oplus : GF(2^n) \to GF(2) $
$ S_2 = \cdot : GF(2^n) \to GF(2) $
They define following truth table for two variables $x_1$ and $x_2$.
Table 2.12: Truth Table of XOR, AND functions
Third column has equal number of zeros and ones representing “XOR” function which is balanced while fourth column presents “AND” function which is not balanced.
With the above example, I can easily understand. But for the S-box in AES I still can't imagine how it will be represented. Could you please help me get an example of S-Box truth table in AES?