$(6$ Points$)$ Diffusion is also a desirable property for the key $($i$.$e$.$ a one$-$bit change in the

key should result in a dramatically different ciphertext if the plaintext is unchanged$).$

$($a$)$ Assume an encryption with a given key. Now assume that the key bit at position

$1,$ prior to PC$1$ is being flipped. Which S$-$boxes in which rounds are affected by

the bit flip during DES encryption?

$($b$)$ Which S$-$boxes in which DES rounds are affected by this bit flip during DES

decryption?