Do I Need Greenboard on the Walls Surrounding a PreFab Steam Shower?

I'm putting in a prefab steam shower in my bathroom, replacing a standard bathtub/shower.  My question is do I need to put greenboard on the walls surrounding the steam shower--two outside and one inside wall.  Currently the three walls have regular sheetrock with insulation on the two outside walls, and the steam shower will sit about 2 inches from the walls.  The steam shower will be sealed so any moisture will be contained.  It does not have an independent exhaust to the outside, so am installing a much larger bathroom exhaust fan, for when the door is opened after use.  A toilet is also in the bathroom, with a door leading to the sink and vanity in another space.  On first look, my gut says the sheetrock should be OK as I don't expect much moisture to be retained in the bathroom, but I'm not sure.  Any help would be appreciated. 

I think all you need is drywall and a very good primer as you should do anyway. I like Zinser and Kilz gold.... They are oil based but you can paint over them with latex in 60 minutes.

I would go all the way to cement board, myself.  You probably don't want to ever have to mess with this again, and cement board will stand up the best to a moist environment.