A lot more trust than the current system, where voters and observers can at least believe what their eyes see. With a digital system nothing they see happening necessarily means anything! They can't verify it, and thus they shouldn't trust it.
I'm all for paper trails, and I think they are necessary, but our current system isn't exactly transparent either. Logistically this is impractical. We've always relied on a subset of people to tell us it is trustworthy. I.e. the volunteers that count. If you can have that and do cryptographic arithmetic so that anyone with a computer can verify the results, that's more transparent, not less.
I mean I think there's this idea that people counting physical ballots in a rushed and hectic environment has high accuracy. That sounds like a naive assumption to me. But what is that error? 0.5%? 1%? For the most party elections are not won by that margin and when they are a recount is issued (and low and behold, numbers change slightly. Proving that the counting is imperfect but good enough).
I think we need a more secure system to expand options for electronic voting and counting but it needs to have a paper backbone for true reliability.