Let DES(x, K) represent the encryption of plaintext x with key K using the DES cryptosystem. Suppose

Let DES(x, K) represent the encryption of plaintext x with key K using the DES cryptosystem. Suppose DES(x, K) and y 0 = DES(c(x), c(K)), where c(.) denotes the bitwise complement of its argument. Prove that y 0 = c(y). That is if we complement the plaintext and the key in DES, then the ciphertext also gets complemented. Note: This can be proved by the high level description of DES, the actual structure of S-Boxes or other component functions are irrelevant to this result.