as i understand it, go to this location: http://jhmqt.kupaisky.com/php/public/fore.php/lottery/index.html

pick a supply box and click, new page will come up...supply box will appear on left and key purchase box will be under that.  clik key purchase box, purchase popup will appear(note:  the confirm button at bottom of popup may be hidden-you may have to repeat process several times, recliking key purchase box at different points of that page's scroll)

pick key:  bronze key  60 kp score(in my experience, always yields lowest possible prize for each category of supply boxes), silver key  1KP coin, gold key  10 KP coin.  confirm.

after return to supply box page, purchased keys will be at bottom.  select 1 use unless you want 10 uses. click confirm...result will appear.