How do I secure the bottom of the stringer to the paving slab?
Depending how long the stairs are and how the stairs are supported at the top and in the middle, the bottom of the stringer doesn't have to be supported. It will just sit down on the pavement by itself.
Usually when I want to nail the bottom of the stringer secure, I either notch out the stringer bottoms to fit over a 2x4 nailed to a landing or nail the 2x4 between the two stringers. The 2x4 is then nailed or screwed into the landing or wood or concrete pad, before the bottom tread is installed.
If you want to do this, nail a couple of concrete nails into the paving through the 2x4. I'm assuming that the paving you are refering to is asphalt paving.