PLONKish Arithemetization

We recommend readers who are not familiar with PlonK's arithmetization to read the article PlonK's Arithmetization. In this chapter, we further discuss a more customized version of PlonK's arithmetization, namely, PLONKish arithmetization. Customization aims to handle more general gates with more complicated structures rather than employing only multiplication, addition, multiplication with constants and addition with constants gates.

PLONKish arithmetization can be pictured as a table of the following types of columns:

  • Constant columns for putting constants,
  • Instant columns for putting public inputs,
  • Advice columns for putting private inputs, literally known as witnesses,
  • Selector columns for putting selectors.

For simplicity, in this section, we present a transformation from a program, represented by an arithmetic circuit, to the form of PLONKish arithmetization. This transformation can be showed by an example that proves the knowledge of a \(2\)-variable polynomial specified in A Simple Arithmetic Circuit. Then, we explain the method for transforming this polynomial to the form of PLONKish arithmetization in Transforming to PLONKish Arithmetization and programming in A Simple Halo 2 Program.