# Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 2 Solutions - Ex2.7

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- 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 2.7

Compute the first two output bytes of the LFSR of degree 8 and the feedback polynomial from Table 2.3 where the initialization vector has the value FF in hexadecimal notation.

*Note*: The polynomial referred to is \(x^8 + x^4 + x^3 + x + 1\).

### Solution

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

This LFSR derived from this polynomial can be visualised as such:

The sequence generated by \(FF_{16}\), which is \(11111111_2\), is as follows:

The resulting first two output bytes are \(1001000011111111_2 = {90FF}_{16}\).