I design Smart-Card based payment systems. Like many applied cryptographers, I believe cryptography and computers are antagonist to voting security if we want to keep vote secret.
The most important goals of a voting system are that
1) voters will trust the result
2) massive fraud by few individuals is impossible
3) voting under duress or bribery can not get massive.
Requirement 3 is why vote is cast in the secret of a booth, and shall remain secret. Experience has proved secrecy is important, and straight antagonist with vote-by-mail, and by extension vote-at-home or vote-on-one's-mobile.
And once we accept most voters should vote secretly (with duly justified exception for vote by proxy and remote locations), we just do not know a cryptography-based system that meets either 1 or 2.
The reasonable layperson does not understand how cryptography and computers really work, thus is more likely to trust their cote is counted when they have put a paper in an envelope, have seen it fall in a transparent box, and have confidence that it is watched by observers until and when the envelopes are opened and hand-counted locally (and counts at each voting places made public, which makes alteration of these counts detectable by observers). Sure, this is subject to local manipulation. But that can't lead to massive undetected fraud on a large scale.
And the reasonable layperson is right! Cryptography does not guard against the risk that the voter's intention is disclosed and/or changed between the button pressed and the computerized treatment made of that, by way of a hardware or software modification made by the makers or guardians of a voting device. The more knowledgeable, the more reluctant security experts are to tell no such disclosure or alteration is possible.
No countermeasure exists against "we spy on the voting machine to know how you voted, so you'd better vote as we instruct"; and that can actually be true for virtually all voting machine design (by Van Eck phreaking, and so many other ways). And voters can't check the vote they cast on a machine are counted in the right direction (for any verification mean could be used to prove how the vote was cast, making bribery/threatening effective), unless the check they make is from an unalterable audit trail (like paper) that ultimately is what defines the vote cast.