GCM optimisation using $M_0$ and $R$ tables - Calculation of $R$
$P$, defined on p. 8, is a representation of a primitive element in $\operatorname{GF}(2^{128})$; specifically, if we represent the field by $\operatorname{GF}(2)[t]/(f)$ where $f = t^{128} + t^7 + t^2 + t + 1$, $P$ represents the polynomial $t$, i.e. $0 + t + 0 t^2 + 0 t^3 + \cdots + 0 t^{127}$.

If $x$ is a byte, represented as some polynomial in $\operatorname{GF}(2)[t]$, then there are only 256 possible values of $x$.  The table $x\cdot P^{128}$ maps each possible byte to the corresponding polynomial $x\cdot t^{128}$ reduced modulo $f$.