In this chapter, we will present the construction of [GWC19], i.e., permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge.
PlonK is a succinct non-interactive zero-knowledge argument (SNARK) system that proves the correct execution of a program, i.e., in this case, an arithmetic circuit with only addition \((+)\) and multiplication \((\cdot)\) operations.
As an overview of the construction, we separate it into \(2\) parts. First, we transform the arithmetic circuit into a set of constraints, called arithmetization and represented under some form of polynomials. Then, by applying some proof technique, it compiles the arithmetization into the proof.