Consider a new block cipher, DES$2,$ that consists of only two rounds of the DES block cipher. DES$2$ has the same block and key size as DES. For this question, you should consider the DES F function as a black box that takes two inputs, a $32-$bit data segment, and a $48-$bit round key, and produces a $32-$bit output. Using the chosen$-$plaintext attack $($CPA$)$ without any restrictions on the number of oracle calls. a$)$ Give an algorithm to recover the $48-$bit round keys for round $1()$ and round $2().$ Your algorithm should have fewer operations than the exhaustive key search for DES$2.$ b$)$ Can your algorithm be converted into a distinguishing attack against DES$2,$ i$.$e$.,$ an attack that distinguishes DES$2$ from a random permutation?