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(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 2m 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. ×4 a) x + x3 + x² + 1 4 b) x + x² + 1 c) x 1 + x ³ + x² + x¹ +1 d) x + x³ +1

(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 2m 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. ×4 a) x + x3 + x² + 1 4 b) x + x² + 1 c) x 1 + x ³ + x² + x¹ +1 d) x + x³ +1

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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(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 2m 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. ×4 a) x + x3 + x² + 1 4 b) x + x² + 1 c) x 1 + x ³ + x² + x¹ +1 d) x + x³ +1
Transcribed Image Text:(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 2m 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. ×4 a) x + x3 + x² + 1 4 b) x + x² + 1 c) x 1 + x ³ + x² + x¹ +1 d) x + x³ +1
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