How to calculate the irreducible polynomial in galois field

Asked Jun 26 '20 at 13:26

Active Jun 27 '20 at 02:30

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I have a an expression (x^3 + x^2 + 1) / (x^6 + x^5) in GF(2^8) and its primitive polynomials (0,1,3,4,8)

How to deal with this equation and what is the logic behind this?

edited Jun 27 '20 at 02:30

RobPratt

asked Jun 26 '20 at 13:26

Kishan

1

Any finite field larger than $GF(p)$ needs a construction. I suppose the computer scientists have a standard construction for $GF(256)$, but readers of this site probably don’t know it. (I don’t) And you need to explain the notation (0,1,3,4,8). – Lubin Jun 27 '20 at 01:56
I'm fairly sure that (0,1,3,4,8) refers to the irreducible polynomial $1+x+x^3+x^4+x^8$. – Jyrki Lahtonen Jun 27 '20 at 04:08
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Too bad you don't use $1+x^2+x^3+x^4+x^8$. For then you could use a discrete logarithm table like here or here. Anyway, if this is for a piece of software I would not consider anything but a discrete log table. – Jyrki Lahtonen Jun 27 '20 at 04:13
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For a worked example your version of $GF(256)$ take a look at this. – Jyrki Lahtonen Jun 27 '20 at 04:15
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Also here. and here. – Jyrki Lahtonen Jun 27 '20 at 04:34
Thanks jyrki , that helps !! – Kishan Jun 27 '20 at 10:23

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