Consider A\left(x\right)=x^{3}+x^{2}+1 and B\left(x\right)=x^{2}+x+1

yogi55hr

yogi55hr

Answered question

2021-11-08

Consider A(x)=x3+x2+1 and B(x)=x2+x+1 in GF(17). Also, the irreducible polynomial is given as p(x)=x3+1
1. Find A2(x)B(x). (13 pts)
Hint: Use p(x) if the initial result does not fall in GF(17).
2. Find A2(x)B2(x). (12 pts)
Hint: Use p(x) if the initial result does not fall in GF(17).

Answer & Explanation

Lounctirough

Lounctirough

Beginner2021-11-09Added 14 answers

1) Find A2(x)B(x)
A2(x)=(x3+x2+1)2
=(x3+x2+1)(x3+x2+1)
=x6+x5+x3+x5+x4+x2+x3+x2+1
=x6+2x5+x4+2x3+2x2+1
A2(x)=x6+2x5+x4+2x3+2x2+1
A2(x)B(x)
=x6+2x5+2x3+x4+2x3+2x2+¬1x2x¬1
=x6+2x5+2x3+x4+x2x
A2(x)B(x)=x6+2x5+2x3+x4+x2x
2) Find A2(x)B2(x)
A2(x)=x6+2x5+x4+2x3+2x2+1
B2(x)=(x2+x+1)(x2+x+1)
=x4+x3+x2+x3+x2+x+x2+x+1
=x4+2

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