2-plonk-lagrange-basis

[hattiepwvi]

请问：代码中的 galois.Poly([1, 12], field = GF13) 里面的 1 是什么

z_H = galois.Poly([1, 12], field = GF13) * galois.Poly([1, 8], field = GF13) * galois.Poly([1, 1], field = GF13) * galois.Poly([1, 5], field = GF13)

import numpy as np
import galois

GF13 = galois.GF(13)

# Given two 1-D arrays x and y
# Returns the Lagrange interpolating polynomial through the points (x, y).
def lagrange_poly_in_finite_field(x, y):
    return galois.lagrange_poly(GF13(x), GF13(y))

q_M = [1, 0, 1, 0]
L_0 = [1, 0, 0, 0]

x_points = [1, 5, 12, 8]

# Do the interpolation, return polynomial
q_M_x = lagrange_poly_in_finite_field(x_points, q_M)
L_0_x = lagrange_poly_in_finite_field(x_points, L_0)

print("Output:")
print("Lagrange interpolating polynomial q_M_x: ", q_M_x)
print("Lagrange interpolating polynomial L_0_x: ", L_0_x)

# Vanishing polynomial: (X - 1)(X - 5)(X - 12)(X - 8)
z_H = galois.Poly([1, 12], field = GF13) * galois.Poly([1, 8], field = GF13) * galois.Poly([1, 1], field = GF13) * galois.Poly([1, 5], field = GF13)

# Quotient polynomial
q = L_0_x * (q_M_x - GF13(1)) // z_H

print("Quotient polynomial q: ", q)
print("Vanishing polynomial z_H: ", z_H)

assert L_0_x * (q_M_x - GF13(1)) == q * z_H, "Division has a remainder(should not have)"

# Use 4 as an example. This number should be be a random number
zeta = 4

y_1_x = L_0_x * (q_M_x - GF13(1))
y_1 = y_1_x(4)
print("y_1: ", y_1)

y_2_x = q * z_H
y_2 = y_2_x(4)
print("y_2: ", y_2)

assert y_1 == y_2, "Check failed"

[hattiepwvi]

来源： 理解 PLONK（二）：多项式编码
https://github.com/sec-bit/learning-zkp/blob/master/plonk-intro-cn/python_notebook/2-plonk-lagrange-basis.ipynb