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I’m a rookie for finite fields.

I know that the solution of computing multiplication in GF(2^n), needs to use the degree n irreducible polynomial over GF(2). But I have no idea of the details.

Here is an example,

example

(x-1)^(-1) g(x) in GF(2^n) for g(x) = ∑_(i=0)^(n-1) (b_i^x^i) where the degree n irreducible polynomial over GF(2) is p(x) = x^n + ∑_(i=0)^(n-1) (c_i x^i )

I also understand that the GF(2) multiplication is equalized to the logical AND operation. Could someone explain more details of this example?

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