One of the bigger hurdles in implementing RSA is having an algorithm which can multiply the large numbers in real time. If you try a niave multiplication algorithm, you might find you'll never get an answer. A lot of hardware now comes with special instructions which implement efficient algorithms for doing this.

Sure, you can't use built in multiplication, but it isn't a very big hurdle. Just use repeated squares, it's fairly trivial to implement. I've worked on software that did this on very low power mobile payment devices.