It is theoretically possible to devise a mathematically secure electronic voting system using cryptography, but only if everyone can follow instructions perfectly and people can understand how it works and why their vote is secure. In other words, not in any way that would work in real life.

The principal benefit of pen-and-paper voting is that it is really easy to convince people that taking a ballot paper into a booth, marking it, and then depositing the ballot into a locked glass box which is later counted in front of a room of independent observers is a secure way to run elections. It is impossible to convince the average voter that cryptographically secure voting schemes are actually immune from tampering.

Edit: I never understood why we have "election days". Why not have an "election week"?