Plonk's Arithmetization

PlonK's arithmetization [GWC19] breaks the circuit into a batch of gates, namely, multiplications, additions, multiplications with constants and additions with constants. For each gate, the operation is transformed into a unified form with respective selectors, uniquely determined by the gate without assigned inputs and output. On the other hand, since breaking circuit into gates introduces the inconsistencies among wires, we additionally apply copy constraints to wires to guarantee that such inconsistencies unavailable.

We describe circuit specification in Circuit Specification. Then, we discuss how to break the circuit into gates and label wires in Breaking Circuit. Then we present unified form of gate constraints in Gate Constraints and handling copy constraints in Copy Constraints.