4.10. In the following, we check the diffusion properties of AES after a single round. Let W = (w0,w1,w2,w3)=(0x01000000, 0x00000000, 0x00000000, 0x00000000) be the input in 32-bit chunks to a 128-bit AES. 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 this book to figure out how the input is processed in the first round (e.g., SBoxes). For the solution, you might also want to write a short computer program or use an existing one. 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? Remark that we only consider a single round after every further round, more output bits will be affected (avalanche effect).