Question

I am trying to verify the statement above. So far I only know that a One-Time-Pad is the only

Answer 1

Imagine that you have a ciphertext:

• Perfect secrecy means, that without knowing the key, any plaintext has to be a possible preimage. Because otherwise the ciphertext would give you information about the plaintext.
• Encryption is an injective function, because otherwise it could not be reversed. That means, for a given key and ciphertext you have at most one possible preimage.
• Then it is just an argument about the sizes of the sets of plaintexts and keys: If the keyspace is less than the keyspace, then there is no key for some pair (p,c), and it can't be perfectly secure any more.