AES is designed to work on bytes. However, each byte is interperted as a representation of the polynomial:
2d = 00101101 = | x^{5} + x^{3} + x^{2} + 1 |
a3 = 10100011 = | x^{7} + x^{5} + x + 1 |
2d * a3 = | (x^{12} + x^{10} + x^{9} + x^{7}) + (x^{10} + x^{8} + x^{7} + x^{5}) + (x^{6} + x^{4} + x^{3} + x) + (x^{5} + x^{3} + x^{2} + 1) |
= | x^{12} + x^{9} + x^{8} + x^{6} + x^{4} + x^{2} + x + 1 |
- modulus * x^{4} = | x^{9} + x^{7} + x^{6} + x^{5} + x^{2} + x + 1 |
- modulus * x = | x^{7} + x^{6} + x^{4} + 1 |
2d * a3 = | 11010001 = d1 |