setup.py

from utils import *
import py_ecc.bn128 as b
from curve import ec_lincomb, G1Point, G2Point
from compiler.program import CommonPreprocessedInput
from verifier import VerificationKey
from dataclasses import dataclass
from poly import Polynomial, Basis

# Recover the trusted setup from a file in the format used in
# https://github.com/iden3/snarkjs#7-prepare-phase-2
SETUP_FILE_G1_STARTPOS = 80
SETUP_FILE_POWERS_POS = 60


@dataclass
class Setup(object):
    #   ([1]₁, [x]₁, ..., [x^{d-1}]₁)
    # = ( G,    xG,  ...,  x^{d-1}G ), where G is a generator of G_1
    # =
    # f(x) = 5 + 20x + 10x^2
    # hash(5, 20, 10)
    # [f(x)] =
    # a0G + a1[xG] + a2[x^2*G]
    powers_of_x: list[G1Point]
    # [x]₂ = xH, where H is a generator of G_2
    X2: G2Point

    @classmethod
    def from_file(cls, filename):
        contents = open(filename, "rb").read()
        # Byte 60 gives you the base-2 log of how many powers there are
        powers = 2 ** contents[SETUP_FILE_POWERS_POS]
        # Extract G1 points, which start at byte 80
        values = [
            int.from_bytes(contents[i : i + 32], "little")
            for i in range(
                SETUP_FILE_G1_STARTPOS, SETUP_FILE_G1_STARTPOS + 32 * powers * 2, 32
            )
        ]
        assert max(values) < b.field_modulus
        # The points are encoded in a weird encoding, where all x and y points
        # are multiplied by a factor (for montgomery optimization?). We can
        # extract the factor because we know the first point is the generator.
        factor = b.FQ(values[0]) / b.G1[0]
        values = [b.FQ(x) / factor for x in values]
        powers_of_x = [(values[i * 2], values[i * 2 + 1]) for i in range(powers)]
        print("Extracted G1 side, X^1 point: {}".format(powers_of_x[1]))
        # Search for start of G2 points. We again know that the first point is
        # the generator.
        pos = SETUP_FILE_G1_STARTPOS + 32 * powers * 2
        target = (factor * b.G2[0].coeffs[0]).n
        while pos < len(contents):
            v = int.from_bytes(contents[pos : pos + 32], "little")
            if v == target:
                break
            pos += 1
        print("Detected start of G2 side at byte {}".format(pos))
        X2_encoding = contents[pos + 32 * 4 : pos + 32 * 8]
        X2_values = [
            b.FQ(int.from_bytes(X2_encoding[i : i + 32], "little")) / factor
            for i in range(0, 128, 32)
        ]
        X2 = (b.FQ2(X2_values[:2]), b.FQ2(X2_values[2:]))
        assert b.is_on_curve(X2, b.b2)
        print("Extracted G2 side, X^1 point: {}".format(X2))
        # assert b.pairing(b.G2, powers_of_x[1]) == b.pairing(X2, b.G1)
        # print("X^1 points checked consistent")
        return cls(powers_of_x, X2)

    # Encodes the KZG commitment that evaluates to the given values in the group
    # 接受多项式的LAGRANGE形式并转换成系数形式，在形成commitment
    def commit(self, values: Polynomial) -> G1Point:
        assert values.basis == Basis.LAGRANGE

        # Run inverse FFT to convert values from Lagrange basis to monomial basis
        # Optional: Check values size does not exceed maximum power setup can handle
        # Compute linear combination of setup with values
        coeffs = values.ifft().values
        if len(coeffs) > len(self.powers_of_x):
            raise Exception("Not enough powers in setup")
        points = [(s, x) for s, x in zip(self.powers_of_x, coeffs)]  #points的格式为 (s^k*G, coeff), G 为曲线上的点，coeff 为系数
        return ec_lincomb(points)


    # Generate the verification key for this program with the given setup
    def verification_key(self, pk: CommonPreprocessedInput) -> VerificationKey:
        # Create the appropriate VerificationKey object
        return VerificationKey(
            pk.group_order,
            self.commit(pk.QM),
            self.commit(pk.QL),
            self.commit(pk.QR),
            self.commit(pk.QO),
            self.commit(pk.QC),
            self.commit(pk.S1),
            self.commit(pk.S2),
            self.commit(pk.S3),
            self.X2,
            Scalar.root_of_unity(pk.group_order),
        )