Relationship between hyperalgebra (algebra of distributions) of an affine group scheme to its cohomology

Question

Let $G$ be an affine group scheme, and $\mathrm{Dist}(G)$ its hyperalgebra.

I am wondering what is the relationship between $\mathrm{Dist}$(G) and $G$ interms of Cohomology?

Is there a cohomology theory for $\mathrm{Dist}(G)$, if so what information does it give?