Determine the multiplicative inverse of x^3 + x^2 + 1 in GF(2^4), using the prime (irreducible) polynomial m(x) = x^4 + x + 1 as the modulo polynomial. (Hint: Adapt the Extended Euclid's GCD algorithm, Modular Arithmetic, to polynomials.)
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This means we need to find a polynomial such that when it is multiplied with x^3 + x^2 + 1, the result is 1 modulo the irreducible polynomial x^4 + x + 1. Show more…
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