Paper 2026/1133

SoK: PIOP-based SNARKs for General Computation

Abstract

Many modern SNARK constructions follow a paradigm that combines a Polynomial Interactive Oracle Proof (PIOP) with an appropriate Polynomial Commitment Scheme (PCS). In this paradigm, the PIOP reduces soundness to the verification of a collection of polynomial relations that are checked though oracle queries, while the PCS enables succinct commitments to the corresponding polynomials. Rather than transmitting the full polynomial representation, the prover commits to the polynomials and later provides evaluations at the points selected by the verifier. The verifier checks the consistency of these evaluation with the commitments and the prescribed polynomial relations. This combination of interactive polynomial queries and succinct commitments lies at the heart of the resulting argument system's efficiency, leading to compact proofs and efficient verification procedures. Focusing on this paradigm, we adopt the frontend and backend decomposition of SNARKs for general computation introduced by Thaler and develop a unified framework that refines this separation at a finer granularity. We present this framework as a single coherent structure and analyze its components in a systematic manner. Within this unified view, we incorporate lookup arguments and recursive proof composition, both of which are key to improving efficiency and applicability, as main components of the framework, showing how they interact with both the frontend and backend. This organization allows readers to reason clearly about the construction, composition and analysis of modern SNARKs.