Rijndael uses a second interpretation for the components in a byte x = (x0, x1, …, x6, x7) ∈ namely, as the coefficients of a polynomial of degree 7
The addition of bytes x + y is according to the usual rules for the addition of polynomials, Rijndael refers to addition as EXOR rather than XOR.
Associating a byte with a polynomial provides a way to define the multiplication; if
where m(ζ) is a primitive (see Table 8.3) but not irreducible polynomial
For fixed x = (x1, x1, …, x6, x7) ∈ the transformation