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Question on Galois Fields

Hi C'Punks.

Here's a rather mathematical question.

Can anyone explain or give an example of how to use arithmetic in GF(q^n)?

Often in cryptography we work in GF(p). I knew the existence of other fields,
like elliptic curves and so, but I found a short comment in Applied
Cryptography page 210 that I couldn't understand.

Thanks in advance for your help.

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