Mia.......you can paint that floor - but you need a 2 component epoxy to do it.
Clean the floor well - Alcohol woorks great to strip any wax or grease.
Sand it lightly - 120 grit paper will do.
The Epoxy you need is:
Devoe Coatings 4030-6130 - Waterborne Epoxy Primer. It is a two component product. Follow the directions on the can to the letter.
Devoe Coatings 4406/4408 - Waterborne Epoxy S/G and Gloss. Also a two component product. Again - follow the directions to the letter.
These can both be applied by brush and roller - the are waterbased - so clean-up and odor aren't too bad.
I used these two on a tile floor in my own home - entry and main hall area. We were there five years and it still looked great! Keep in mind though - this is still paint - It will become very, very hard - but it still isn't as hard as ceramic tile. Dragging chairs across it can scratch it.
These products are available at ICI Paint Stores - they will cost you in the neighborhood of $75.00/gallon each.