I just made the strawbox of potatoes that is recommended by Bill Mollison in his permaculture techniques pamphlet. It is listed somewhere within the first four pages of the pamphlet and he says that it can also be built on concrete.
I used a regular store-bought straw rather than organic herbicide free straw -- I may regret that. But otherwise I think it is a pretty cool project. Here in the hot sunny south I would recommend places this box where it gets morning sun, maybe a little at noon, but afternoon shade - especially on concrete.
Here is a link to the post, picture of the straw box and the pamphlets
strawbox of potatoes