PLONK Simplified: A Pedagogical Zero-Knowledge Proof Framework with KZG Commitments

Abstract

Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) allow for elegant, privacy-preserving validation of computations. PLONK, a subclass of the zk-SNARKs, is certainly useful, but its complex interactions with permutation arguments, lookup tables, and blinding, among other considerations, make the protocol difficult to follow, let alone understand. This paper describes a framework centered around the core components of zk-SNARKs. In particular, we detail the construction of arithmetic gate constraints, representation of witness polynomials, and the Kate-Zaverucha-Goldberg (KZG) commitment scheme. By removing permutation proofs, lookup, and blinding, we aim to simplify the pedagogy of zk-SNARKs and preserve their essential properties of soundness and completeness. We describe a Python module from the ground up that demonstrates the generation and validation of proofs in a PLONK-modified zk-SNARK. We validate the framework and its foundations with a benchmark of a module generating and validating proofs in a PLONK-modified zk-SNARK. We validate the module against a circuit of 1,000 gates and demonstrate that the system correctly rejects all invalid witnesses. We illustrate the expected asymptotic behavior, with a pro tor of tight the module is quasi-linear, and verification, tight. We justify the foundations of the module and describe tight with zero private inputs. We have also bridged the gap between abstract zk-SNARK theoretical arguments and their practical implementation and research. We have provided a simple, empirically grounded mechanism that describes the key components of PLONK. We have done this in such a way that researchers, developers, and teachers can build on this base module and create production-ready systems without the abstraction.