Understanding Cryptography by Christof Paar and Jan Pelzl  Chapter 4 Solutions  Ex4.8
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 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 4.8
Find all irreducible polynomials
 of degree 3 over ,
 of degree 4 over .
The best approach for doing this is to consider all polynomials of lower degree and check whether they are factors. Please note that we only consider monic irreducible polynomials, i.e., polynomials with the highest coefficient equal to one.
Solution
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There are two irreducible polynomials in of degree 3:


There are three irreducible polynomials in of degree 4:
