Question 2 [5 points]. In the context of extension field GF(25 ), answer the following questions: (a) Represent A(x) = 22 in the above field. (Note: It will be a polynomial) (b) Represent B(x) = 24 in the same field. (c) Determine A(x)+B(x) (as a polynomial) and express as an integer.

Question 3 [5 Points] Using Table 4.2, of GF(28 ), determine the multiplicative inverses of 3F16 and D816. Also, determine the AES S-box substitutions for these two 8-bits (use Table 4.3). Note: this is just a table look. No math is needed.

Question 4 [5 Points]. Given the following 128-bits (expressed as Hexa characters) as input to the AES ShiftRows sublayer (just for one round), determine the 128-bit output (as 32 Hexa characters): (A0B1C2D3E4F5061728394A5B6C7D8E9F).

Table 43 AES S-Box: Substitution values in hexadecimal notation for input byte (xy) 0 1 2 3 4 5 6 7 8 9 A B C D E 063 70 77 7B F 6B 6 CS 3001 67 2B FE D7 AB 76 1 CA 82 C9 7D FA 59 47 FO AD D4 A2 AF 9C A4 72 CO 2 B7 FD 93 26 36 3F F7 CC 34 AS ES F1 71 DS 31 15 3 04 07 23 C3 18 96 OS 9A 07 12 80 E2 EB 27 B2 75 409 83 2C 1A 1B 6E SA AO 52 3B D6 B3 29 E3 2F 84 553 DI 00 ED 20 FC BI SB 6A CB BE 39 4A 4C 58 CF 6 DO EF AA FB 43 4D 33 85 45 F9 02 7F 50 3C9FA8 751 A3 40 8F 92 9D 38 FS BC B6 DA 21 10 FF F3 D2 X 8 CD OC 13 EC SF 97 44 17 C4 A7 7E 3D 64 SD 1973 960 81 4F DC 22 2A 90 88 46 EE BS 14 DE SE OB DB AEO 32 3A OA 49 06 24 SC C2 D3 AC 62 91 95 E4 79 BE7 C8 37 6D 8D DS 4E A9 6C 56 F4 EA 65 7A AE 08 CBA 78 25 2E IC A6 B4 C6 ES DD 74 IF 4B BD 8B 8A Dl 70 3E BS 66 48 03 F6 OE 61 35 57 B9 86 CI ID 9E EEI F8 98 1169 D9 8E 94 9B IE87 E9 CE 55 28 DF FSC AL 89 OD BF E6 42 68 41 99 2D OF BO 54 BB 16 e: crypto-textbook.com Table 43 AES S-Box: Substitution values in hexadecimal notation for input byte (xy) 0 1 2 3 4 5 6 7 8 9 A B C D E 063 70 77 7B F 6B 6 CS 3001 67 2B FE D7 AB 76 1 CA 82 C9 7D FA 59 47 FO AD D4 A2 AF 9C A4 72 CO 2 B7 FD 93 26 36 3F F7 CC 34 AS ES F1 71 DS 31 15 3 04 07 23 C3 18 96 OS 9A 07 12 80 E2 EB 27 B2 75 409 83 2C 1A 1B 6E SA AO 52 3B D6 B3 29 E3 2F 84 553 DI 00 ED 20 FC BI SB 6A CB BE 39 4A 4C 58 CF 6 DO EF AA FB 43 4D 33 85 45 F9 02 7F 50 3C9FA8 751 A3 40 8F 92 9D 38 FS BC B6 DA 21 10 FF F3 D2 X 8 CD OC 13 EC SF 97 44 17 C4 A7 7E 3D 64 SD 1973 960 81 4F DC 22 2A 90 88 46 EE BS 14 DE SE OB DB AEO 32 3A OA 49 06 24 SC C2 D3 AC 62 91 95 E4 79 BE7 C8 37 6D 8D DS 4E A9 6C 56 F4 EA 65 7A AE 08 CBA 78 25 2E IC A6 B4 C6 ES DD 74 IF 4B BD 8B 8A Dl 70 3E BS 66 48 03 F6 OE 61 35 57 B9 86 CI ID 9E EEI F8 98 1169 D9 8E 94 9B IE87 E9 CE 55 28 DF FSC AL 89 OD BF E6 42 68 41 99 2D OF BO 54 BB 16 e: crypto-textbook.com