Just one quick note about the misuses of the Gaussian blur induced by bad implementation of it (most notably in Nuke, maybe in other VFX software).
The Gaussian filter is supposed to be an IIR (infinite impulse response filter), so that the process you are describing (premult-blur-unpremult) gives very inaccurate results when premulting with a matte that has zero values (due to the division of very small values, very close to machine precision) if the Gaussian filter is really implemented as an IIR, which it is in Natron (try premult-blur-unpremult with a hand-drawn matte).
Nuke implements the Gaussian filter as a FIR (finite impulse response) by cropping its impulse response (at 2.5*sigma if I remember well), so that people use it as an FIR and leave the default "gaussian" setting everywhere (note the capitalization, which perhaps indicates that it's not the one by Mr Gauss himself, but a mere knock-off). I suppose other comp software did/do the same, so that there is clearly a misunderstanding in the community about what is a Gaussian filter, and what it should be used for.
A good fast FIR filter to do exactly that task (premult-blur-unpremult) is the quadratic filter. I use it in PIKColor, and you should use it in any process that does that premult-blur-unpremult thing. Even faster alternatives, but less isotropic, are the box and triangle filters.