2. (10 points) The S-boxes have an internal structure in AES. There is a Galois field inversion and then a matrix multiplication. In contrast, the S-boxes in DES were not structured. There are three...

2. (10 points) The S-boxes have an internal structure in AES. There is a Galois field inversion and then a matrix multiplication. In contrast, the S-boxes in DES were not structured. There are three implications that this internal algebraic structure of the S-boxes in AES; three reasons this is important. Please identify two of these.(a) (5 points) Reason 1:(b) (5 points) Reason 2:(c) (5 points) Reason 3 (extra credit option):3. (10 points) The key schedule in AES ensures confusion, which is the distribution of the key is distributed across the entire ciphertext. In class the key schedule had two additional functions related to resilience against cryptanalysis. Please identify them.(a) (5 points) Function 1:(b) (5 points) Function 2:4. (10 points) In class we illustrated how the key schedule results in every bit of the key being distributed across the ciphertest.If we start with the key addition step that results in W0 = (0x2B7E1516),W1 = (0x28AED2A6), W2 = (0xABF71588), W3 = (0x09CF4F3C),Calculate the next four keys W4 - W7 so that you have all the keys for the first round. Please describe your process.(a) (2.5 points) W4:(b) (2.5 points) W5:(c) (2.5 points) W6:(d) (2.5 points) W7:5. (30 points) Using the keys calculated in the previous problem, compute the first round of AES assuming that all inputs of the plaintext are zero. Show the results at each stage and describe your process. Recall that this is the first stage, so there is an additional first step. The Monday video describing the use of x times will make these calculations easier to complete.(a) (5 points) Initial operation:(b) (5 points) Stage 1:(c) (5 points) Stage 2:(d) (10 points) Stage 3:(e) (5 points) Stage 4:6. (20 points) Decryption in AES requires taking the inverse of each encryption step in order. List the stages from the first problem IN THE ORDER of decryption and state the inverse operation.(a) (5 points) Stage 1:(b) (5 points) Stage 2:(c) (5 points) Stage 3:(d) (5 points) Stage 4: