'Zero-Knowledge Proof Algorithm, PLONK—Protocol: Sin7Y Tech Review (17)' by Sin7Y_Labs sin7y blockchain
L=L2, R=R2, O=O2F=L * R - O=0If the polynomial function F has zeros at X=1,2,3, then the constraint relationship of the gates is valid.
w represents the input and output in the circuit, with a total of 3n. n is the number of multiplication gates in the circuit, and each gate has a left input, right input, and output, so there are 3n w in total. The order of the polynomial σ is 3n. Since the highest order of CRS related to the polynomial commitment is n+2, it is necessary to split σ into three polynomials S and record each polynomial’s permutation relationship .
Distinguish between ω and w. ω is the generator of the group H and the value of the independent polynomial variable. w is the left input, right input, and output of the circuit, and is the value of the polynomial L, R, O corresponding to group H. The order of t is up to 3n. Still, the CRS used to compute the commitment only reaches the level of n, so it is necessary to split the polynomial t and then calculate the commitment value separately.
From the input perspective, they are public inputs and proof outputs by the prover P, which are relatively straightforward.
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