Question # 08

(1 point) Note: The notation from this problem is from Understanding Cryptography by Paar and Pelzl. 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 2m1. 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) x4+x3+1 b) x4+x2+1 c) x4+x3+x1+1 d) x4+x3+x2+x1+1