Q1) Let DES(x, K) represent the encryption of plaintext x with key K using the DES cryptosystem. Suppose y = DES(x, K) and y' = DES(c(x), c(K)), where c(·) denotes the bitwise complement of its argument [i.e. changing all the 1's to 0's and all the 0's to 1's. For example, if t = 10000110, then c(t) = 01111001; equivalently, c(t) = t ⊕ 11111111]. Prove that y' = c(y) (i.e., if we complement the plaintext and the key, then the ciphertext is also complemented).