4. What is the output LRi of the first round of the DES algorithm when the plaintext is a block of 1010 1010" (alternate one-zeros) and the key is "l 1 1 1 1 1 1 1" (all ones)? Please make sure that your plaintext goes through IP. Round-1, Lo Ro Feistel Network LR, including E-box (expansion) round function f, S-boxes, P-box; and your key goes through key schedule procedures i.e., PC-1, CoDo LSI >CiDi > PC-2 > subkey ki 5. For a bit string A, let A' denote the complementary string obtained by changing all the 1s to Os and all the 0s to Is (equivalently, A' = A 1 1 1 1 1 ). Show that if the DES key K encrypts x to y, then K, encrypts x' to y', i.e., if y-DESK(x), then y'-DESK(x'). Hint: This has nothing to do with with the structure of the S-boxes. All you need to do is to work through the encryption algorithm. You can use the following steps a) show that for any bit strings A, B of equal size, A, B'-A + B and A' B-A B)," b) show that PC-l (k') = (PC-I (k))', LS,(C,i-i)-(LS(Cin), c using the above two results, show that if k are subkeys generated from k, then k' are the subkeys generated from k', where i-1,2,., 16. d) show that IP(x) (IP(x))' and E(R) (E(Ri) e) using these results, show that if Ri-i, Li-i, ki generate Ri, then Ri,i-1, ki, genate Ri. f then you show the statement is true and complete the proof. 4. What is the output LRi of the first round of the DES algorithm when the plaintext is a block of 1010 1010" (alternate one-zeros) and the key is "l 1 1 1 1 1 1 1" (all ones)? Please make sure that your plaintext goes through IP. Round-1, Lo Ro Feistel Network LR, including E-box (expansion) round function f, S-boxes, P-box; and your key goes through key schedule procedures i.e., PC-1, CoDo LSI >CiDi > PC-2 > subkey ki 5. For a bit string A, let A' denote the complementary string obtained by changing all the 1s to Os and all the 0s to Is (equivalently, A' = A 1 1 1 1 1 ). Show that if the DES key K encrypts x to y, then K, encrypts x' to y', i.e., if y-DESK(x), then y'-DESK(x'). Hint: This has nothing to do with with the structure of the S-boxes. All you need to do is to work through the encryption algorithm. You can use the following steps a) show that for any bit strings A, B of equal size, A, B'-A + B and A' B-A B)," b) show that PC-l (k') = (PC-I (k))', LS,(C,i-i)-(LS(Cin), c using the above two results, show that if k are subkeys generated from k, then k' are the subkeys generated from k', where i-1,2,., 16. d) show that IP(x) (IP(x))' and E(R) (E(Ri) e) using these results, show that if Ri-i, Li-i, ki generate Ri, then Ri,i-1, ki, genate Ri. f then you show the statement is true and complete the proof