# Tag Info

## New answers tagged finite-field

2

You need to recall how the extension is built. $\mathbb{F}_{p^{12}}$ is built on top of $\mathbb{F}_{p^2}$ using the reduction polynomial $f(x) = x^6 - \xi$, where $\xi \in \mathbb{F}_{p^2}$ is a non-square and non-cube (using the notation from the paper). In other words, this is the set of polynomials with coefficients in $\mathbb{F}_{p^2}$, modulo $f(x)$. ...

3

Yes, you are correct. The modulo operation (in general, not only over polynomials) is defined such that this is always true: $A \equiv A + B\ \ (\bmod\ B)$ Thus, if $A = X^3$ and $B = X^3+X^2+1$, that implies that $X^3$ is equivalent to the sum of $X^3$ and $X^3+x^2+1$, which is $X^2+1$, which is represented by $101$.

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