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Consider the polynomial f(x) = x ^4 + x ^3 + x ^2 + x +...

Consider the polynomial f(x) = x ^4 + x ^3 + x ^2 + x + 1 with roots in GF(256). Let b be a root of f(x), i.e., f(b) = 0.

The other roots are b^ 2 , b^4 , b^8 .

e) Write b 4 as a combination of smaller powers of b.

Prove that b 5 = 1. f) Given that b 5 = 1 and the factorization of 255, determine r such that b = α r

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