Also consider that there are faster drop-in replacement like the atmega328 (cost < $3)
The atmega328 isn't actually faster, it just has more memory. Also, it might be worth looking at one of the cheaper low-end ARM microcontrollers with integrated USB; they have a lot more processing power and aren't much more expensive.
Also, one very important warning: do
not screw up and use a weak random number source. Your users will never forgive you.