Proof and Argument Based Verifiable Computing

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In this chapter the state of the art with respect to proof based verifiable computing schemes is presented. In this setting a prover wants to convince a verifier of the correctness of a computed result. The first proof based solutions that achieve this were interactive proof systems. Depending on the computation power of the prover we distinguish here between proof based and argument based approaches. While all proof based schemes are interactive protocols, the argument based solutions were further improved, such that also non-interactive solutions are available. In this chapter, we first provide an introduction presenting the setting and the notions, i.e. quadratic span program (QSP), quadratic arithmetic program (QAP), and succinct non-interactive arguments of knowledge (SNARKs). Then, we present the interactive proof based solutions, i.e. “Verifiable Computation with Massively Parallel Interactive Proofs” by Thaler et al. and “Allspice” by Vu et al., and the argument based approaches, i.e. “Pepper” by Setty et al., “Ginger” by Setty et al., “Zaatar” by Setty et al., “Pantry” by Braun et al., and “River” by Xu et al. Afterwards, we present the definitions and solutions for the non-interactive argument based verifiable computing schemes, i.e. “Pinocchio” by Parno et al., “Geppetto” by Costello et al., “SNARKs for C” by Ben-Sasson et al., “Succinct Non-interactive Zero Knowledge for a von Neumann Architecture” by Ben-Sasson et al., “Buffet” by Wahby et al., “ADSNARK” by Backes et al., and “Block Programs: Improving Efficiency of Verifiable Computation for Circuits with Repeated Substructures” by Xu et al.