Rijndael S-Box

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This article describes the S-box used by the Rijndael (aka AES) cryptographic algorithm.

## Forward S-box

The S-box is generated by determining the multiplicative inverse for a given number in GF(2<sup>8</sup>) = GF(2)/(*x*<sup>8</sup> + *x*<sup>4</sup> + *x*<sup>3</sup> + *x* + 1), Rijndael's finite field (zero,which has no inverse, is set to zero). The multiplicative inverse is then transformed using the following affine transformation:

where is the multiplicative inverse as a vector.

The matrix multiplication can be calculated by the following algorithm:

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where is the multiplicative inverse as a vector.

The matrix multiplication can be calculated by the following algorithm:

- Store the multiplicative inverse of the input number in two 8-bit unsigned temporary variables:
*s*and*x*. - Rotate the value
*s*one bit to the left; if the value of*s*had a high bit (eighth bit from the right) of one, make the low bit of*s*one; otherwise the low bit of*s*is zero. - Exclusive or the value of
*x*with the value of*s*, storing the value in*x* - For three more iterations, repeat steps two and three;...... ...

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