Are there encryption schemes that can be performed using an adding machine? There's been a lot of talk about encryption that can be done by hand, but what if the user is allowed an adding machine?

Let's say addition, subtraction, multiplication, and division are easy. Memory (i.e. the user writing things down) is possible but undesirable. Are there any good encryption algorithms that can be performed like this?
That means you have a turing machine, using a small memory is ok, but wasting memory is not desirable (as usual).  

You can do all known encryption algorithms with that.