Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 4 Solutions - Ex4.4
- 1 min- 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 4.4
Addition in \(GF(2^4)\): Compute \(A(x) + B(x)\,\mathrm{mod}\,P(x)\) in \(GF(2^4)\) using the irreducible polynomial \(P(x) = x^4 +x +1\). What is the influence of the choice of the reduction polynomial on the computation?
- \(A(x) = x^2 +1, B(x) = x^3 +x^2 +1\)
- \(A(x) = x^2 +1, B(x) = x+1\)
Solution
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The choice of reduction polynomial has no impact on the computation, since it is not possible for the result of addition to be outside the Field and therefore require reduction.
1.
\[(x^2 + 1) \oplus (x^3 + x^2 + 1) = x^3\]2.
\[(x^2 + 1) \oplus (x + 1) = x^2 + x\]
Thomas Busby
I write about computing stuff