Rijndael S-box

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(2⁸) = GF(2)/(x⁸ + x⁴ + x³ + 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:

<math>begin

1&0&0&0&1&1&1&1 \1&1&0&0&0&1&1&1 \1&1&1&0&0&0&1&1 \1&1&1&1&0&0&0&1 \1&1&1&1&1&0&0&0 \0&1&1&1&1&1&0&0 \0&0&1&1&1&1&1&0 \0&0&0&1&1&1&1&1endbeginx_0\x_1\x_2\x_3\x_4\x_5\x_6\x_7end+begin1\1\0\0\0\1\1\0end</math>

where is the multiplicative inverse as a vector.

The matrix multiplication can be calculated by the following algorithm:

1. Store the multiplicative inverse of the input number in two 8-bit unsigned temporary variables: s and x.
2. 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.
3. Exclusive or the value of x with the value of s, storing the value in x
4. For three more iterations, repeat steps two and three;......
...

Read More