This question asks about perfect ciphers.
Assume that m1 and m2 are messages selected from M, the set of all possible messages.
You should not assume that all messages are equally likely.
c is a ciphertext selected randomly from the set of all possible ciphertexts.
k1 and k2 are keys selected randomly from K, the set of keys.
The question asks to check all statements that are true.
If a cipher has fewer keys then possible messages, it is not a perfect cipher.
AES is a perfect cipher.
If the probability of m1 encrypted using the key k1 equals c is
greater than the probability of m2 encrypted using the key k1 equals c,
then E--the encryption function--must not be a perfect cipher.
The last statement--if E is ap perfect cipher, then the probability of m1
encrypted using k1 equals c is equal to the probability of m1
encrypted using key k2 is equal to c.
