This set of homework is for the contents covered in Chapter 3 Data Encryption Standard. 1. Answer the following concept questions about DES 1) What are the block size and key length? 2) How many rounds does DES iterate? How many S-boxes does DES use? 3) How many round-keys (sub-keys) does DES have? What is the length of a round-key? 4) What are the input and output sizes of a S-box? 5) What are the inputs and output of round function f, and their sizes? 2. One important property which makes DES secure is that the S-Boxes are nonlinear. Here we want you to verify this property by computing the output of S for the following two pairs of inputs. The S-box S is given as follows: S-box S2 S201 2345 6 789 10 11 12 13 14 15 0 15 01 08 14 06 11 03 04 09 07 02 13 12 00 05 10 1 03 13 04 07 15 02 08 14 12 00 01 10 06 09 11 05 2 00 14 07 11 10 04 13 01 05 08 12 06 09 03 02 15 3 13 08 10 01 03 15 04 02 11 06 07 12 00 05 14 09 Show that S2(X1l S2(X2) 2(xx2), where "e" denotes bitwise XOR for: 1) x! = 000000, x2 = 000001 2) x1-0100, x2-100111 3. Please verify that IP) and IP) are truly inverse operations. We consider a vector x -(xi, x2, x64) of 64 bit. Show that IP i(IP(x)) 9, 10 x for the first 10 bits of x, .e. for x, i 1,2,3,4, 5, 6, 7, 8, 4 What is the output L Ri of the first round of the DES algorithm when the plaintext is a block of 1010.... 1010" (alternate one-zeros) and the key is "" (all ones)? Please make sure that your plaintext goes through IP, Round-1, Lo Ro Feistel Network L,I, including E-box (expansion) round function f, S-boxes, P-box; and your key goes through key schedule procedures, i.e., PC-1, CoDoLSCD PC-2 -> subkey ki 5. For a bit string A, let A' denote the complementary string obtained by changing all the Is to 0s and all the 0s to Is (equivalently, A-A11). Show that if the DES key K encrypts x to y then K, encrypts x, to y', i.e., ify 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 worlk through the encryption algorithm. You can use the following steps: show that for any bit strings A, B of equal size. A, a) b) B, A B and A' B (A B) show that PC-I (k') = (PC-l (k))', LS,(C"u)-(LS,(C,J) c) using the above two results, show that if k, are subkeys generated from k, then k,' are the subkeys generat d) show that IP(x') (IP(x))' and E(Ri (E(R e) using these results, show that if Ri-i, Li-l, ki generate R., then R,H, L'm, k,' genate Ri f) then you show the statement is true and complete the proof. ed from k', where i-1,2,.., 16. i-1