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Just enumerate all powers of your primitive element. There are only 15 of them. That will give you a lookup table that allows you to translate from field element to its expression as a power of the primitive element.


According to the original NESSIE submission of Whirlpool: "The finite field ${\rm GF}(2^8)$ will be represented as ${\rm GF}(2)[x]/p(x)$, where $p(x) =$ $x^8 +$ $x^4 +$ $x^3 +$ $x^2 +$ $1$ is the first primitive polynomial of degree $8$ listed in [19]. The polynomial $p(x)$ was chosen so that $g(x) = x$ is a generator of ${\rm GF}(2^8) \setminus \{0\}$." ...

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