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Is "Pinocchio zk-SNARK" a specific type of "zk-SNARK"? And if yes, what is difference?

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Yes, Pinocchio is a practical zk-SNARK that allows a prover to perform cryptographically verifiable computations with verification effort potentially less than performing the computation itself. A recent propo- sal showed how to make Pinocchio adaptive (or “hash-and-prove”), i.e., to enable proofs with respect to computation-independent commitments. This enables computations to be chosen after the commitments have been produced, and for data to be shared between different computations in a flexible way. Unfortunately, this proposal is not zero-knowledge. In par- ticular, it cannot be combined with Trinocchio, a system in which Pinoc- chio is outsourced to three workers that do not learn the inputs thanks to multi-party computation (MPC).

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