You don't need crypto. You just need a machine that prints out a human readable receipt that the voter can see but not alter, which then drops into a secure holding area on the machine.

At the end of the day, you randomly select say 1% of all the machines and hand count all the ballots inside, making sure the counts and votes match. If they do, then you can be reasonably sure it wasn't tampered with, and if they don't match, then you can hand count all the paper ballots using the old system to verify the computer.