Chapter 2: Problem 8 Previous Problem Problem List Note: The notation from this problem is from Understanding Cryptography by Paar and Pelzi. A LFSR with m internal state bits is said to be of maximal...

Extracted text: Chapter 2: Problem 8 Previous Problem Problem List Note: The notation from this problem is from Understanding Cryptography by Paar and Pelzi. A LFSR with m internal state bits is said to be of maximal length if any seed state (except 0) produces an output stream which is periodic with the maximal period 2" - 1. Recall that a primitive polynomial corresponds to a maximum length LFSR. Primitive polynomials are a special case of irreducible polynomials (roughly, polynomials that do not factor). In the context of LFSRS, a polynomial is irreducible if every seed state (except zero) gives an LFSR with the same period (though the period length may not be maximal). We will call a polynomial with neither of these properties composite. Classify the following polynomials as either primitive, Irreducible, or composite by writing either P. I or C in the corresponding answer blank below. a) x* +x' +x + x! +1 b) x* +x' +1 c) xt x +: d) x* +x +1