We have seen that a Block cipher such as AES is insecure if an attacker can have a very large number of chosen plain-text messages (e.g.2 50 messages) for which he gets the corresponding cypher-text.

Suppose that we consider the block cipher secure if the probability of recovering the key by the attack in theorem 4.1 is less than 2 (-50) .

Determine how large Q can be so that the block cipher is still safe.