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> There is no known scheme that has similar properties but non-trusted setup. There's not a proof that it's impossible either, so something might get invented. But at the moment, no.

Already invented. It's called MimbleWimble.

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... that's a system with entirely different properties.

And? It provides privacy.

With a very different set of tradeoffs. MW does not provide anonymity. It provides, at best, pseudo-anonymity with coinjoin mixing by default, with N=2 in the implementations being considered. Careful repeated application with the right counter-parties can compound that into larger anonymity sets. That's a step forward from bitcoin, for sure. And if you're very careful, it could achieve whatever privacy requirement you might have.

The Zcash-like approach on the other hand is to provide a transaction mode where your anonymity set is everyone who has ever transacted with the system before. That's N=everybody; the source of funds is entirely obscured.

The two achieve totally different goals, with a different set of tradeoffs. Apples to oranges.

I’m a massive MW proponent but the privacy claims are very weak compared to ZCash and Monero. What MW does well is scalability.

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