I need to do a little research on this one. Just off the top of my head, I think that any alkyd floor enamel would provide a vapor barrier. The question is, will that solve your problem. The answer to that I'm sure will prove to be a debate, but I think that it won't. Is this a finished basement or is it bare cement/cinder-block? Some people have confused Effluorescence (did I spell that right?) with mold. There are procedures to deal with that, but I'm not real knowledgable in that area.
Mold and mildew both penetrate the surface somewhat. What you see on the surface is like the tip of the iceberg. You need to kill what is there with Clorine Bleach and rince well. If you don't kill what's there, it will contine to grow regardless of what you do. There are mildewicides that can added to paints, but they generally are for exterior use. You would need to contact the manufacturer to see if it is suitable for interior use. There are mildew proof paints but they aren't suitable for use on a floor.
If you indeed are facing mold or mildew, I'd start with the bleach, and then paint with floor enamel, applying two coats, the first laced with mildewicide.