How to compute the Galois Field (multiply, GF(2^n))?

Asked Jun 03 '22 at 07:43

Active Jun 03 '22 at 07:49

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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 $g(x) = \sum_{i=0}^{n-1} (b_i x^i)$ where the degree n irreducible polynomial over $GF(2)$ is $p(x) = x^n + \sum_{i=0}^{n-1} (c_i x^i)$

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

edited Jun 03 '22 at 07:49

asked Jun 03 '22 at 07:43

Chris Cheng

The latter half of this old answer of mine may help. Or this. – Jyrki Lahtonen Jun 03 '22 at 07:49
This answer I once prepared for referrals (mostly for slightly different stuff) has a few more examples. – Jyrki Lahtonen Jun 03 '22 at 07:54
And for examples and explanations about finding the inverse I refer you to this. Other examples are linked to that one. Here is a characteristic two example of the same process. – Jyrki Lahtonen Jun 03 '22 at 07:55
Thanks a lot. I’ll check and try it. – Chris Cheng Jun 03 '22 at 08:20
I still have no idea to solve my problem. – Chris Cheng Jun 05 '22 at 14:48

How to compute the Galois Field (multiply, GF(2^n))?

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