1-Plonkish Arithmetization

pure text:

Arithmetization refers to transforming computations into mathematical objects and then performing zero-knowledge proofs. Plonkish arithmetization is a specific arithmetization method in the Plonk proof system. Prior to the introduction of Plonkish, the mainstream circuit representation was R1CS, widely used in systems such as Pinocchio, Groth16, and Bulletproofs. In 2019, the Plonk scheme proposed a seemingly retrograde circuit encoding method. However, due to its extreme application of polynomial encoding, Plonk is no longer limited to “addition gates” and “multiplication gates” in arithmetic circuits, but can support more flexible “custom gates” and “lookup gates”.

电路中有4个变量，其中三个变量为输入变量

text with inline formula like $abc..$

电路中有4个变量，其中三个变量为输入变量 $(x_1,x_2,x_3)$ ，一个输出变量 $out$，其中还有一个输入为常数，其值为 $2$。

Error formula:

$$\begin{array}{ccccc}1& x_1& x_2& x_3& out\\ 0& 1& 1& 0& 0\end{array}$$