I'm trying to find the logic for introducing the S-box, but having trouble understanding why. In a simple cipher, e.g.
c = pt xor key
I understand that I can easially find the key when choosing the plaintext myself
key = pt xor C
But I don't see why an S-box can help in this at all, given that the S-box is public.
C = S[pt xor key]
Because then I could just do
key = S^-1[pt xor C]
I understand by adding multiple rounds and keys, this gets harder, but what is the S-box giving, when we can just reverse it?