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I was able to find the irreducible polynomial used in AES128-GCM: $x^8+x^4+x^3+x+1$.

But I cant' find the one for AES256, I'm searching in OpenSSL implementation of AES256 but with no luck so far.

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The AES block cipher supports various key sizes of 128, 192, and 256 bits, and a single block size of 128 bits. The degree-8 polynomial $x^8+x^4+x^3+x+1$ is the one used in AES-{128,192,256} for MixColumn and SubBytes.

There is no $\operatorname{GF}(2^{256})$ in GCM because GCM only supports block size of 128 bits. The degree-128 polynomial $x^{128}+x^7+x^2+x+1$ is the one used in GCM.

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