1. Using the multiplicative inversion table shown below (which is used as part of AES S-box), (a) find the inverse of hex entry 'F3' from the table (as you know, 'F' is for the vertical axis x and '3' is for the horizontal axis y). (b) For verification, perform a GF(28) multiplication of input and output polynomials using the irreducible polynomial of the AES (P(x) = x18+x^4+x^3+x+1) and show the result is 1. Note that you have to represent each byte first as polynomials in GF(28). The MSB of each byte represents the x? coefficient. Multiplicative inverse table in GF (2) for bytes xy used within the AES S-Box Y 0 1 2 3 4 5 6 7 8 9 A B C D E F 0100 01 8D P6 CB 52 7B D1 E8 4F 29 CO BO EL ES C7 174 B4 AA 4B 99 2B 60 5F 58 3F FD CC FF 40 EE B2 23A 6E 5A Pi 55 4D A8 C9 Ci OA 98 15 30 44 A2 C2 32C 45 92 6C F3 39 66 42 F2 35 20 6F 77 BB 59 19 41D FE 37 67 2D 31 F5 69 27 64 AB 13 54 25 E9 09 5 ED 5C 05 CA 4C 24 87 BF 18 3E 22 FO 51 EC 61 17 6 16 5E AF D3 49 A6 36 43 14 47 91 DF 33 93 21 3B 779 B7 97 85 10 B5 BA 3C B6 70 DO 06 A1 FA 81 82 X 883 7E7F 80 96 73 BE 56 9B 9E 95 D9 F7 02 B9 A4 9 DE 6A 32 6D D8 8A 84 72 2A 14 9F 88 F9 DC 89 9A A FB 7C 2E C3 8F B8 65 48 26 C8 12 4A CE E7 D2 62 BOC EO 1F EF 11 75 78 71 A5 SE 76 3D BD BC 86 57 COB 28 2F A3 DA D4 E4 OF A9 27 53 04 1B FC AC E6 D|7A 07 AE 63 C5 DB E2 EA 94 8B C4 D5 9D FB 90 6B E BI OD D6 EB C6 OE CF AD 08 4E D7 E3 5D 50 IE B3 F|5B 23 38 34 68 46 03 8C DD 9C 7D AO CD 1A 41 1c 1. Using the multiplicative inversion table shown below (which is used as part of AES S-box), (a) find the inverse of hex entry 'F3' from the table (as you know, 'F' is for the vertical axis x and '3' is for the horizontal axis y). (b) For verification, perform a GF(28) multiplication of input and output polynomials using the irreducible polynomial of the AES (P(x) = x18+x^4+x^3+x+1) and show the result is 1. Note that you have to represent each byte first as polynomials in GF(28). The MSB of each byte represents the x? coefficient. Multiplicative inverse table in GF (2) for bytes xy used within the AES S-Box Y 0 1 2 3 4 5 6 7 8 9 A B C D E F 0100 01 8D P6 CB 52 7B D1 E8 4F 29 CO BO EL ES C7 174 B4 AA 4B 99 2B 60 5F 58 3F FD CC FF 40 EE B2 23A 6E 5A Pi 55 4D A8 C9 Ci OA 98 15 30 44 A2 C2 32C 45 92 6C F3 39 66 42 F2 35 20 6F 77 BB 59 19 41D FE 37 67 2D 31 F5 69 27 64 AB 13 54 25 E9 09 5 ED 5C 05 CA 4C 24 87 BF 18 3E 22 FO 51 EC 61 17 6 16 5E AF D3 49 A6 36 43 14 47 91 DF 33 93 21 3B 779 B7 97 85 10 B5 BA 3C B6 70 DO 06 A1 FA 81 82 X 883 7E7F 80 96 73 BE 56 9B 9E 95 D9 F7 02 B9 A4 9 DE 6A 32 6D D8 8A 84 72 2A 14 9F 88 F9 DC 89 9A A FB 7C 2E C3 8F B8 65 48 26 C8 12 4A CE E7 D2 62 BOC EO 1F EF 11 75 78 71 A5 SE 76 3D BD BC 86 57 COB 28 2F A3 DA D4 E4 OF A9 27 53 04 1B FC AC E6 D|7A 07 AE 63 C5 DB E2 EA 94 8B C4 D5 9D FB 90 6B E BI OD D6 EB C6 OE CF AD 08 4E D7 E3 5D 50 IE B3 F|5B 23 38 34 68 46 03 8C DD 9C 7D AO CD 1A 41 1c