Bricks, Masonry, Asphalt and Concrete - Stair Railing Problem?

Hi,
I recently bought a 3 family home in Mass.
I noticed the front steps are brick,but the bottom step is a large thick stone or granite?
The metal railings on each side are attached to the house at the top,and were cemented into the granite slab at the bottom step.
On side the bottom has come loose (rusted out) where it was cemented into the granite...
Otherwise they were in good shape.
I need to re-secure the rusted portion,and somehow re-attach it to the granite or stone bottom step.I was thinking about a heavy "L" bracket attached with an anchor into the stone?But how can I drill into stone or granite?Will a masonry drill work?The railing is 1" sq tubing type steel.Do you have any othe ideas?Thanks:cool:

best way is to remove railings, fix the bottoms weld or sleave the pipe, drill out the hole with a masonry bit 1 1/2" , a hammer drill would help, install repaired railing and cement in place.