Determine the multiplicative inverse of \left(x^{3}+x+1\right) in GF\le

miyoko23q3

miyoko23q3

Answered question

2021-11-11

Determine the multiplicative inverse of (x3+x+1) in GF(24) with m(x)=x4+x+1.

Answer & Explanation

Wasither1957

Wasither1957

Beginner2021-11-12Added 17 answers

(x3+x+1) in GF(x3+x+1) with m(x)=x4+x+1.
x4+x+1=x(x3+x+1)+(x2+1)
x3+x+1=x(x2+1)+1
1=x3+x+1+x(x2+1)
x2+1=x4+x+1+x(x3+x+1)
1=x2+x+1+x(x3+x+1+x(x4+x+1))
1=(x2+1)(x3+x+1)+x(x4+x+1)
The final result is (x3+x+1)1=x2+1

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