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Computer Security and Cryptography by Alan G. Konheim

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9.15 THE RIJNDAEL OPERATIONS

Rijndael uses a second interpretation for the components in a byte x = (x0, x1, …, x6, x7) image namely, as the coefficients of a polynomial of degree 7

image

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

image

then

image

TABLE 9.23 Number of Rijndael Rounds Nr

image

where

image

and

image

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

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

image

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