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 1 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, ie., PC-1, CoDo LS, CiDi PC-2 subkey ki 5. For a bit string A, let A' denote the complementary string obtained by changing all the 1s to 0s and all the 0s to ls (equivalently, A' = A 1 111 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-1(k))', LS,(C) (LS,(C)) 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(Ri (E(Ri) e) using these results, show that if R-, Li generate Ri, then R, L., k,' genate Ri. f) then you show the statement is true and complete the proof Submission: Put all answers to the five questions in one pdf file and upload it from your Blackboard account, or bring your (handwritten) hardcopy to the class on the due day. Your file should be named as LastNameFirstInitial _hw2.pdf. For example, if your name is John Smith, the file name should be SmithJ_hw2.pdf