I think I'd check out the product literature or possibly the manufactures website and see what they recommend. There are all kinds of concrete fasteners available depending on what type of framing the shed has - not sure if its wood or steel or plastic.

Katie, Suncast's website has assembly instructions for what I believe to be the one you're describing. For securing it to the ground, it mentions four round recessed areas on the base that can be drilled out and 12" nails/landscape spikes driven through them into the ground.

For your application with the slab, I would recommend 3"-4" masonry screws(Assuming a 4" thick slab, slightly longer depending on how thick the base is) with galvanized washers to prevent them from tearing through the base. You would need four of them and an appropriately sized masonry bit, probably 1/8" or 3/16". The screws and bit can probably be had for under $10. You can ask someone at HD what size bit would be appropriate for what masonry screws they have.

As an alternative, you might try a construction adhesive such as Liquid Nails or a polyurethane adhesive. These can be bought in tubes for caulk guns for around $5 or so. I probably wouldn't use a continuous bead around the bottom, just several dabs of it where the base will contact the concrete. You could then use a scraper to separate the base from the pad if you want to either move it or purchase something bigger. Either would probably be good enough to keep your shed stable and in place. I personally favor poly adhesives.

Here's a link to what I believe to be the unit you describe. Under the picture is a link for "Assembly instructions". Never hurts to be prepared. :-) Good luck!

Here is a link that might be useful: Suncast Vertical Shed