You need check the diffusion properties of AES after a single round.

1)Let W = (w0, w1, w2, w3) = (0x01000000, 0x00000000, 0x00000000, 0x00000000) be the input in 32-bit chunks to a 128-bit AES.

2) The subkeys for the computation of the result of the first round of AES are W0, . . . ,W7 with 32 bits each are given by
W0 = (0x2B7E1516),
W1 = (0x28AED2A6),
W2 = (0xABF71588),
W3 = (0x09CF4F3C),
W4 = (0xA0FAFE17),
W5 = (0x88542CB1),
W6 = (0x23A33939),
W7 = (0x2A6C7605).

Use the main textbook to figure out how the input is processed in the first round (e.g., S-Boxes). For the solution, you might also want to write a short computer program or
use an existing one (You need to clearly reference if you use a ready code, otherwise a penalty deduction from the grade will be applied).

In any case, indicate all intermediate steps for the computation of [ShiftRows, SubBytes and MixColumns]

1. Compute the output of the first round of AES to the input W and the subkeys W0, . . . ,W7 .
2. Compute the output of the first round of AES for the case that all input bits are zero.
3. How many output bits have changed?