New answers tagged s-boxes
You performed the matrix component of the affine tranformation correctly, what you did wrong was the addition of the vector prior to field inversion. The value 10100010 (0xA2) is the correct result of the inverse affine matrix. The final vector of the inverse affine transform however is 00000101 (0x05). The resultant 0xA7 is then inverted, which is 0x48, ...
You forgot to compute the inverse of 02 first; the inverse of 02 is 8d (as $02 \cdot 8d = 01 $in the AES $GF(2^8)$ representation; you then apply the affine transform to the value 8d
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