Torsors over the punctured affine line

We provide a classification of $G$-torsors over the punctured affine line ${\rm Spec}(k[t^{\pm 1}])$ where $G$ is a reductive algebraic group defined over a field $k$ of good characteristic. Our classification is in terms of the Galois cohomology of the complete field $k((t))$ with values in $G$.