Australia has a system where you are anonymous and can prove that you only voted once:

You have to be registered and must vote within your electorate, so your name appears on a certified list for that electorate and each voting location has that list. When you vote, they strike your name from the list.

After the election, the lists from these locations are compared. Anyone who votes twice has their name struck twice, and are investigated for electoral fraud.

Whether people know if you voted or not is immaterial, as voting is mandatory in Australia.

Works pretty well for a paper system.