Tuesday, November 13, 2018

galois theory - Irreducible Polynomial for $GF(2^{256})$

I'm looking for a pattern to generate Galois Field multiplication for $2^{256}$ binary value. So far I have come up with a patter as follows;



$$
1 \rightarrow 1 \\

x \rightarrow x \\
x^2\rightarrow x^2\\
...\\
x^{256} \rightarrow x + 1
$$



Is it $x + 1$ for $x^{256}$?
If so, for $x^{257} \rightarrow (x^2 + x)$?



Thanks in advance!

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