a) Show that 4B is the multiplicative inverse of 13 in GF(2) = Z[x] x +...

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a) Show that 4B is the multiplicative inverse of 13 in GF(2³) = Z₂[x] x³ + x² + x³ + x + 1 (Here the bytes are shown in hexadecimal). (Hint: 4B13 = 1 mod x³ + x² + x³ + x + 1 must apply) b) When does the multiplicative inverse of a(x) modulo m(x) exist? What is the name of the algorithm that it can be calculated? a) Show that 4B is the multiplicative inverse of 13 in GF(2³) = Z₂[x] x³ + x² + x³ + x + 1 (Here the bytes are shown in hexadecimal). (Hint: 4B13 = 1 mod x³ + x² + x³ + x + 1 must apply) b) When does the multiplicative inverse of a(x) modulo m(x) exist? What is the name of the algorithm that it can be calculated?