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- import numpy as np
- from groth_poly_commit import Scalar, poly_commit, create_proof, verify_proof
- K = Scalar
- R.<x, y> = LaurentPolynomialRing(K)
- var_one = K(1)
- var_x = K(4)
- var_y = K(6)
- var_s = K(1)
- var_xy = var_x * var_y
- var_x_y = var_x + var_y
- var_1_neg_s = var_one - var_s
- var_sxy = var_s * var_xy
- var_1_neg_s_x_y = var_1_neg_s * var_x_y
- #var_s_neg_1 = -var_1_neg_s
- var_zero = K(0)
- public_value = var_s * (var_x * var_y) + (1 - var_s) * (var_x + var_y)
- # x * y = xy
- a1 = var_x
- b1 = var_y
- c1 = var_xy
- Ql1 = 0
- Qr1 = 0
- Qm1 = 1
- Qo1 = -1
- Qc1 = 0
- assert Ql1 * a1 + Qr1 * b1 + Qm1 * a1 * b1 + Qo1 * c1 + Qc1 == 0
- # x + y = (x + y)
- a2 = var_x
- b2 = var_y
- c2 = var_x_y
- Ql2 = 1
- Qr2 = 1
- Qm2 = 0
- Qo2 = -1
- Qc2 = 0
- assert Ql2 * a2 + Qr2 * b2 + Qm2 * a2 * b2 + Qo2 * c2 + Qc2 == 0
- # 1 - s = (1 - s)
- a3 = var_one
- b3 = var_s
- c3 = var_1_neg_s
- Ql3 = 1
- Qr3 = -1
- Qm3 = 0
- Qo3 = -1
- Qc3 = 0
- assert Ql3 * a3 + Qr3 * b3 + Qm3 * a3 * b3 + Qo3 * c3 + Qc3 == 0
- # s * (xy) = sxy
- a4 = var_s
- b4 = var_xy
- c4 = var_sxy
- Ql4 = 0
- Qr4 = 0
- Qm4 = 1
- Qo4 = -1
- Qc4 = 0
- assert Ql4 * a4 + Qr4 * b4 + Qm4 * a4 * b4 + Qo4 * c4 + Qc4 == 0
- # (1 - s) * (x + y) = [(1 - s)(x + y)]
- a5 = var_1_neg_s
- b5 = var_x_y
- c5 = var_1_neg_s_x_y
- Ql5 = 0
- Qr5 = 0
- Qm5 = 1
- Qo5 = -1
- Qc5 = 0
- assert Ql5 * a5 + Qr5 * b5 + Qm5 * a5 * b5 + Qo5 * c5 + Qc5 == 0
- # (sxy) + [(1 - s)(x + y)] = public_value
- a6 = var_sxy
- b6 = var_1_neg_s_x_y
- # Unused
- c6 = var_zero
- Ql6 = 1
- Qr6 = 1
- Qm6 = 0
- Qo6 = 0
- Qc6 = -public_value
- assert Ql6 * a6 + Qr6 * b6 + Qm6 * a6 * b6 + Qo6 * c6 + Qc6 == 0
- a = np.array([a1, a2, a3, a4, a5, a6])
- b = np.array([b1, b2, b3, b4, b5, b6])
- c = np.array([c1, c2, c3, c4, c5, c6])
- Ql = np.array([Ql1, Ql2, Ql3, Ql4, Ql5, Ql6])
- Qr = np.array([Qr1, Qr2, Qr3, Qr4, Qr5, Qr6])
- Qm = np.array([Qm1, Qm2, Qm3, Qm4, Qm5, Qm6])
- Qo = np.array([Qo1, Qo2, Qo3, Qo4, Qo5, Qo6])
- Qc = np.array([Qc1, Qc2, Qc3, Qc4, Qc5, Qc6])
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