We all know the classic definitions of perfect secrecy, being $$\Pr[M=m|C=c]=\Pr[M=m]$$ and $$H(M|C)=H(M)$$
But now what I've asked myself:
If we were to remove the polynomial restriction on the attacker, which game-based security definition would be equivalent to perfect secrecy and how would one show this?
Of course I've thought about this myself and it's obvious that known- and chosen-plaintext security is a given as we still can't learn anything new about the plaintext if a scheme is perfectly secret.
Even with chosen-ciphertext attacks I don't see how one could deduce more information on a perfectly secret scheme, given that the challenge ciphertexts would still be independently encrypted.
What I kinda can't grasp though is the reverse direction and of course the formal proof of equivalence.