# Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 2 Solutions - Ex2.5

- 2 mins- Return to index
- Exercise 2.1
- Exercise 2.2
- Exercise 2.3
- Exercise 2.4
- Exercise 2.5
- Exercise 2.6
- Exercise 2.7
- Exercise 2.8
- Exercise 2.9
- Exercise 2.10
- Exercise 2.11
- Exercise 2.12

## Exercise 2.5

We will now analyze a pseudorandom number sequence generated by a LFSR characterized by .

- What is the sequence generated from the initialization vector ?
- What is the sequence generated from the initialization vector ?
- How are the two sequences related?

### Solution

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

This LFSR can be visualised as such:

1. The sequence generated by is as follows:

*Note*: the final row is the same as the first, meaning it will loop infinitely.

2. The sequence generated by is as follows:

*Note*: the final row is the same as the first, meaning it will loop infinitely.

3. Since is part of the sequence for , its loop is exactly the same, but rotated back by three positions. Both of them give the same loop of states (which contains of all non-zero 3-bit binary numbers), but starting from whatever was chosen to initialise it.