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Notes -
I do think there would be some technical challenges to be solved, but I think we have a lot of really useful pieces that could help solve those problems. I'm not going to pretend that I have a fleshed-out whitepaper with full technical specification or anything, but I can give you some of my general thoughts.
A lot of work has gone into anonymization protocols. They're probably not perfect yet. There are all sorts of timing issues or side channel issues and even just the fundamental problem that metadata is hard. But I think progress is being made. To the extent that one is bullish on the idea that real anonymization is plausible in the not-too-distant future for some form of cryptocurrency, I think they can be bullish on something here, too. Moreover, it's not just cryptocurrency where work is being done on anonymization. TOR was a big leap forward on that front, even if there are still some challenges there, too. Again, to the extent one is bearish/bullish on any hope there, I'd expect them to be likewise bearish/bullish here.
Consider some TOR-like properties. A message can be routed through multiple intermediaries, such that those intermediaries mathematically cannot know the content of the message in question. Those intermediaries aren't even really trusted. They can refuse to pass your message along, but you can realize that it hasn't been passed along by the non-response or inappropriate response you receive. I don't think it's too big of a step to imagine that one can leverage intermediaries, even perhaps untrusted ones, in a way such that those intermediaries are mathematically unable to determine the content of your message (who you're voting for or how much you're spending). Those intermediaries can choose things like random delay times, which can help thwart timing attacks. I agree that timing attacks may pose unique challenges, and again, I haven't solved all of them right off the top of my head, but I think the idea would be to try to show some property that so long as some low percentage of those untrusted intermediaries are observing random delays, we could get in front of those problems.
Tornado Cash gave us a significant step toward anonymity in the transactions, as well. The very basic idea is that you dump a bunch of things into a pot, mix them up, divide them out, and make it significantly more difficult to correlate inputs/outputs. Details here are more complicated; I'd say that it's probably still not perfect, but to the extent that there are lessons to be learned, I think we can learn them and continue to iterate. Again, general bearish/bullish sentiments.
Of course, I'd like to also call back to the 'receipt-freeness' business that the digital election nerds really like. The idea is that they want a way that the the final election tally can be 'published', but in a way that is still specially encrypted. Thus, while people can perform the proper cryptographic operations on the output to determine what the result was, no one can determine from the encrypted, published final tally what any of the individual votes are. Even the people who voted do not have sufficient information to prove how they voted, but they do retain sufficient information to prove that their vote was counted correctly in the final tally. Side note here would be that if you have a system where someone can freely rescind their vote later, even if you had someone watching your computer when you initially voted, and even if they kept that piece of information which could be used to prove that the initial vote was correctly counted, they would not have sufficient information to prove that it was not later rescinded. (There are still tricky choices here, perhaps, and I do think more work would need to be done to decide on every detail.) In any event, this would be another check to make sure that intermediaries couldn't just refuse to include your vote.
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