With concrete, the concern is moisture. Any furring strips should be pressure treated, and I've also seen good suggestions to use the foam barrier that you would typically use under a sill plate as an extra defense, e.g. this stuff (click the photo for the product page):
![foam seal](https://i.stack.imgur.com/gpakD.jpg)
For pressure treated, make sure any nails are galvanized to avoid the chemical reaction that would eat normal nails. If you're using foam panel insulation, then seal any gaps on the sides. I'd also use a vapor barrier on top of the furring strips, behind the drywall. And finally, for the drywall, use something mold and moisture resistant to avoid future problems. Moist environments are also a good place to use the fiberglass mesh tape, instead of the paper tape, to finish the joints.
There are 2 ways to do this, the first way is in essence just cutting the wall at the top of the skirt board and capping it off and setting the handrail on top of the cap that is finishing off the cut wall, sounds a bit crude, but essentially that describes what you will have.![enter image description here](https://i.stack.imgur.com/50aDg.png)
![enter image description here](https://i.stack.imgur.com/gY9z6.jpg)
The up side to this is you will not need to do a floor repair, depending on where your wall ends where the newel will be.
The other way to do it is by removing the wall entirely, repairing the floor, removing the treads and risers, and set longer ones with return nosings on either side. and re-support the stairs with a new walls under the existing carriages.![enter image description here](https://i.stack.imgur.com/sREfx.png)
![enter image description here](https://i.stack.imgur.com/6kdwk.jpg)
This is the most work, but will give the best result in my opinion.
Jan. 2, 2014 edit
Here is the work I did in 1989 that shows what I did.![Stair1](https://i.stack.imgur.com/kiybG.jpg)
![Stair2](https://i.stack.imgur.com/sfhJj.jpg)
This one shows the best example of the effect I was trying to explain. I do not have a shot that shows how the handrail goes past the ceiling, but with a little imagination you could picture what the rail would have to do if the stairs were much wider at the bottom.![Stair4](https://i.stack.imgur.com/2sAZB.jpg)
![Stair5](https://i.stack.imgur.com/vOgza.jpg)
Edit #2
I did a little calculating to help, if it may![enter image description here](https://i.stack.imgur.com/cpBZs.png)
Best Answer
I would install thin, flexible boards against the wall and mount crossbars (ceiling joists) to them. I would not mount drywall directly to the stairs.
This strategy, along with the corner tape joints, will leave you with a very strong ceiling. It'll be isolated from the staircase, so that any vibration and movement in the stairs won't result in cracks.
One suggestion for fitting the drywall (the most challenging part of all this) is to do it one side at a time. Fit pieces that run about 2/3 the way across the span to the wall. Do this from each side, mounting loosely near the walls and lapping the center area. Then use a rotary cutter to slice up the middle through both layers. Remove the scrap and screw it all tight.