Another thing that makes it work is having total, mathematical confidence in the correctness of the circuit. That's where formal verification and other auditing plays a role.
More details about perfect shielded pools soon.
Shielded protocols give you privacy in exchange for placing supply integrity in the faith of cryptographic assumptions. This is true for all of these protocols, every one of them, without exception.
There is no cheap trick that lets you get around this, like another technique that verifies what's "really happening" inside the pool. You will always find yourself just repeating what the SNARKs are already doing, using (possibly different) cryptographic assumptions.
The only thing we can do is rely on safe assumptions, and make our code flawless. Prior to a few years ago neither of these were practical, but we're beyond this. We can formally verify our shielded protocols and their implementations so that their correctness mathematically reduces to these cryptographic assumptions.
We may soon even do this with the current version of Orchard itself (there are at least three different teams competing to implement a fully verified proof of Orchard's circuit right now, for example). These proofs don't have to be checked by humans in their entirety, just the small theorems that describe the security notions and specifications.
Perfect shielded pools.
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