Assume that bit 57 of a 64 plaintext block is 1 with all other bits equal to zero. Let the key be all zeros. 2 a. How many S-boxes get different inputs compared to the case of an all-zero plaintext, in the first round of DES? b. What is the number of output bits which are different compared to the input after the first round? c. How many output bits have actually changed after the first round compared to the case of an all-zero plaintext (consider only one round). Does DES exhibit the avalanche effect (small changes in the plaintext yield significant changes in the ciphertext)?

"Do not forget to apply the initial permutation on the plaintext before passing it through the DES round".