The difficulty here is about proving that you have a well-formed ciphertext. If we try to turn it into a circuit using many of the current ZKs Snarks, you end up with things with millions and millions of dates. So the performance is really bad. You need either a lattice-based proof system, which will allow you to more efficiently prove things about lattices,. Or you need to find some sort of clever hack of how might you connect a lattice encryption scheme with some non-lattice-basedProof system.

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