Question

Determine the multiplicative inverse of x 3 + x + 1 in gf(24) withm(x) = x4 + x + 1.

Answer 1

Answer:

Don't you have a calculator

Step-by-step explanation:

Answer 2

Step-by-step explanation:

The Galois Field GF(24) (also represented F24) contains 16=24 elements. The formal definition is;

F24 is the quotient ring F2[X]/(x4=x+1) of the polynomial ring F2[X] by the ideal generated by (x4=x+1) is a field of order 24.

We can list the elements of GF(24) on the polynomial representation with the defining primitive polynomial, namely

a3x3+a2x2+a1x+a0

where ai∈GF(2) for i=0,1,2,3.