looks like turf algae to me. It's calcareous and hard to get rid of. In fact, I think it has the potential of overrunning your tank.
It will outcompete coral growth,
It will trap detritus and thus increase nutrient load for the tank, spurring it's own growth and causing noxious algal blooms of other types of algae.
Snails won't touch it, neither will most types of tangs. It's too hard for them. It becomes very tightly rooted into the rock structure, so that if you find something that will eat it, it will probably only cut the tops off, and the turf will grow back.
Animals that MAY have a chance at eating this, are the sea urchins. There may also be a type of nudibranch that will eat it. But I doubt they will survive long enough to eradicate the entire rock
Treatment options.
Take the rock out avoiding the spread.
"Cook" the affected pieces of Rock in a dark container for several weeks, but I bet this stuff still comes back.
Good luck. It's a wonderful shade of green. It really is beautiful, but I wouldn't have it in my tank.