Go to Home Depot and rent an electric floor stripping machine for taking floor tiles off of concrete floors.

In an hour you'll have all the moss/algae off so that you can shovel it into your garbage can(s).

Roberts, 1 HP, 120 Volt Floor Stripper Machine with 2 Double Edge Blades-DISCONTINUED, 10-475 at The Home Depot - Mobile

The electric floor strippers that Home Depot rents might be different, but any floor stripper designed to strip vinyl tiles off of concrete floors will make short work of moss on a drive way.

If your local Home Depot doesn't rent a machine like this, phone up any retail flooring or carpet store and ask to talk to the Installations Manager. Ask him who sells flooring installation supplies in your area. That store will almost certainly rent electric floor strippers like the one above. There will be a damage depost you'll have to pay, but the only thing that's likely to be damaged are the blades and possibly some chipping of your asphalt driveway. That doesn't really matter since your asphalt is probably at least 3 inches thick and you have to repave it every 30 or 40 years anyhow.