Assignment 3
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($2^8$) multiplication of input and output polynomials using
the irreducible polynomial of the AES ($P(x) = x^8+x^4+x^3+x+1$) and show the result is 1.
Note that you have to represent each byte first as polynomials in GF($2^8$). The MSB of each
byte represents the $x^7$ coefficient.
Multiplicative inverse table in GF($2^8$) 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
0 00 01 8D F6 CB 52 7B D1 E8 4F 29 C0 B0 E1 E5 C7
1 74 B4 AA 4B 99 2B 60 5F 58 3F FD CC FF 40 EE B2
2 3A 6E 5A F1 55 4D A8 C9 C1 0A 98 15 30 44 A2 C2
3 2C 45 92 6C F3 39 66 42 F2 35 20 6F 77 BB 59 19
4 1D FB 37 67 2D 31 P5 69 A7 64 AB 13 54 25 E9 09
5 ED 5C 05 CA 4C 24 87 BF 18 3E 22 F0 51 EC 61 17
6 16 5E AF D3 49 A6 43 F4 47 91 DF 33 93 21 3B
7 79 B7 97 85 10 B5 BA 3C B6 70 D0 06 A1 FA 81 82
X 8 83 7E 7F 80 96 73 BE 56 9B 6A 0B 53 4E 86 C6 8A
9 DE 6A 32 6D D8 84 8A 72 2A 14 9F B8 F9 DC 89 9A
A FB 7C 2E C3 8F B8 65 48 26 C8 12 4A CE E7 D2 62
B 0C B0 1F EF 11 75 78 71 A5 8E 76 3D BD BC 86 57
C 0B 28 2F A3 D4 D4 E4 0F A9 27 53 04 1B FC AC E6
D 7A 07 AE 63 C5 DB E2 EA 94 8B C4 D5 9D F8 90 6B
E B1 0D D6 EB C6 0E CF AD 08 4E D7 E3 5D 50 1E B3
F 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10 11