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). [This is Question 3.3 of the textbook. Hint: this can be proved using the “high-level” description of DES encryption Feistel structure algorithm.