# Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 4 Solutions - Ex4.15

- 2 mins

## Exercise 4.15

Derive the bit representation for the following round constants within the key schedule:

• RC[8]
• RC[9]
• RC[10]

### Solution

This solution is verified as correct by the official Solutions for Odd-Numbered Questions manual.

Starting from $RC[1] = 01$, $RC[i] = 02 \times RC[i - 1]\,\mathrm{mod}\,P(x)$ where $P(x)$ is the AES polynomial.

As such, the first 10 RC values are as follows:

After 8 is where the reduction polynomial comes into play to bring the result back into the field.

I wrote a python script which can calculate any number of RC constants (This uses the Mod2Polynomial class I created for another exercise):