# Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 4 Solutions - Ex4.6

- 2 mins- Return to index
- Exercise 4.1
- Exercise 4.2
- Exercise 4.3
- Exercise 4.4
- Exercise 4.5
- Exercise 4.6
- Exercise 4.7
- Exercise 4.8
- Exercise 4.9
- Exercise 4.10
- Exercise 4.11
- Exercise 4.12
- Exercise 4.13
- Exercise 4.14
- Exercise 4.15
- Exercise 4.16

## Exercise 4.6

Compute in :

where the irreducible polynomial is the one used by AES, .

Note that Table 4.2 contains a list of all multiplicative inverses for this field.

### Solution

*I haven’t yet verified this solution independently. If you spot any mistakes, please leave a comment in the Disqus box at the bottom of the page.*

The multiplicative inverse could be found via the Euclidian Algorithm, though in this instance I have simply looked it up in the table mentioned above:

Next we perform a naive multiplication of with the inverse we just looked up:

All that’s left to do now is to reduce it via the reduction polynomial

The result of this calculation is therefore . This answer can be verified as correct (assuming my code is correct) by placing the following python code in the __main__ section of the script written for Ex4.3: