(Not So) Secure AES

Description

We have access to a server that encrypts random messages using the AES algorithm. Since this server has been used to encrypt important messages, we want to recover its encryption key. Our expert in fault attacks has developed a system to inject faults into the internal state of AES. Unfortunately, the secure chip performing the encryption has a redundant implementation of AES and we are able to fault only a single instance at a time, as shown in the following diagram:

      Msg
       |
  +----+----+
  |         |
  v         v
+---+     +---+
|AES|     |AES|<--Fault
+---+     +---+
  |         |
  | +-----+ |
  +-| ==? |-+
    +-----+
       |
       v
      Res

In fact, the faults are detected. Nevertheless, our expert is formal: it should be possible to find the key using a SIFA attack (for Statistically Ineffective Fault Attack). He has implemented an interface that allows to target precisely which byte of the internal state of the AES to fault when the server is asked to encrypt a message according to the following indexing:

+--+--+--+--+
| 0| 4| 8|12|
+--+--+--+--+
| 1| 5| 9|13|
+--+--+--+--+
| 2| 6|10|14|
+--+--+--+--+
| 3| 7|11|15|
+--+--+--+--+

However, he informs us that it is not possible to obtain more than 200 ciphertexts. Finally, the expert warns you that such an attack may require several hours of computations.

Your goal is to decrypt the message that the server sends when we initiate a connexion.