Here is the Scheme:
Here is the HIDE game:
Here is my idea but I am not quite sure. I would appreciate some input.
We want to bring advantage = 0 for all adversaries. We can show that advantage = 0 if we can prove that all of the C values are uniformly random and independent of the Message we give. If we prove that then we can argue that the adversary won't be able to tell which game its in.
So L is a n-bit string chose uniformly at random. C is also random as well since it uses L? I am not sure about this but it seems like the algorithm is basically doing a One-time Pad. We know that OTP is perfectly secure.
Is this correct? What else can I argue to prove advantage=0 for any adversary? Thanks in advance!