Computer Security and Cryptography

9.15 THE RIJNDAEL OPERATIONS

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

then

TABLE 9.23 Number of Rijndael Rounds Nr

where

and

where m(ζ) is a primitive (see Table 8.3) but not irreducible polynomial

For fixed x = (x₁, x₁, …, x₆, x₇) ∈ the transformation