If you want a system based on Scantron-style paper ballots that allows cast ballots to be published, allows anyone to verify that the count was correct, and allows voters to verify that their vote was counted correctly without being able to prove they voted for a particular candidate, see this [1]. It's been around for several years, and has been used successfully in a few elections.

[1] https://en.wikipedia.org/wiki/Scantegrity