I think that could be easily handled during the voter registration process. For example, you could do your voter registration at the DMV like we do now, but instead of just checking a box on the form, the DMV would issue you a card with your keys, as well as a QR code for easy scanning at the polling location. And I think there are other similar options that could be used to both verify the eligibility of the voter, and issue the keys they need to actually vote.  

 Would definitely be an improvement. I think there was somewhere that did it already using bitcoin.