Pinocchio-Based Adaptive zk-SNARKs and Secure/Correct Adaptive Function Evaluation

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 proposal 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 particular, it cannot be combined with Trinocchio, a system in which Pinocchio is outsourced to three workers that do not learn the inputs thanks to multi-party computation (MPC). In this paper, we show how to make Pinocchio adaptive in a zero-knowledge way; apply this to make Trinocchio work on computation-independent commitments; present tooling to easily program flexible verifiable computations (with or without MPC); and use it to build a prototype in a medical research case study.