$1.[5$ points$]$ What are the three key lengths for AES. Draw the four layers of AES encryption round $8.$

$2.[6$ points$]$ Compute the output of the AES S$-$box for the input bytes a$)29$ b$)$ F$3$ and c$)01,$where each byte is given in hexadecimal notation.

$3.[10$ points$]$ We consider AES with $128-$bit block length and $128-$bit key length. What is the output of the first round of AES if the plaintext consists of $128$ ones and the first subkey also consists of $128$ ones?