76 lines
3.5 KiB
Python
76 lines
3.5 KiB
Python
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from typing import List, Sequence
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from eth2spec.deneb.mainnet import KZGProof as Proof, BLSFieldElement
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from eth2spec.utils import bls
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from da.kzg_rs.common import G1, BLS_MODULUS, PRIMITIVE_ROOT
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from da.kzg_rs.fft import fft, fft_g1, ifft_g1
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from da.kzg_rs.poly import Polynomial
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from da.kzg_rs.roots import compute_roots_of_unity
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from da.kzg_rs.utils import is_power_of_two
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def __toeplitz1(global_parameters: List[G1], polynomial_degree: int) -> List[G1]:
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"""
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This part can be precomputed for different global_parameters lengths depending on polynomial degree of powers of two.
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:param global_parameters:
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:param roots_of_unity:
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:param polynomial_degree:
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:return:
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"""
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assert len(global_parameters) == polynomial_degree
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# algorithm only works on powers of 2 for dft computations
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assert is_power_of_two(len(global_parameters))
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roots_of_unity = compute_roots_of_unity(PRIMITIVE_ROOT, polynomial_degree*2, BLS_MODULUS)
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vector_x_extended = global_parameters + [bls.Z1() for _ in range(polynomial_degree)]
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vector_x_extended_fft = fft_g1(vector_x_extended, roots_of_unity, BLS_MODULUS)
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return vector_x_extended_fft
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def __toeplitz2(coefficients: List[BLSFieldElement], extended_vector: Sequence[G1]) -> List[G1]:
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assert is_power_of_two(len(coefficients))
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roots_of_unity = compute_roots_of_unity(PRIMITIVE_ROOT, len(coefficients), BLS_MODULUS)
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toeplitz_coefficients_fft = fft(coefficients, roots_of_unity, BLS_MODULUS)
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return [bls.multiply(v, c) for v, c in zip(extended_vector, toeplitz_coefficients_fft)]
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def __toeplitz3(h_extended_fft: Sequence[G1], polynomial_degree: int) -> List[G1]:
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roots_of_unity = compute_roots_of_unity(PRIMITIVE_ROOT, len(h_extended_fft), BLS_MODULUS)
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return ifft_g1(h_extended_fft, roots_of_unity, BLS_MODULUS)[:polynomial_degree]
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def fk20_generate_proofs(
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polynomial: Polynomial, global_parameters: List[G1]
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) -> List[Proof]:
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"""
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Generate all proofs for the polynomial points in batch.
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This method uses the fk20 algorthm from https://eprint.iacr.org/2023/033.pdf
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Disclaimer: It only works for polynomial degree of powers of two.
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:param polynomial: polynomial to generate proof for
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:param global_parameters: setup generated parameters
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:return: list of proof for each point in the polynomial
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"""
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polynomial_degree = len(polynomial)
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assert len(global_parameters) >= polynomial_degree
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assert is_power_of_two(len(polynomial))
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# 1 - Build toeplitz matrix for h values
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# 1.1 y = dft([s^d-1, s^d-2, ..., s, 1, *[0 for _ in len(polynomial)]])
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# 1.2 z = dft([*[0 for _ in len(polynomial)], f1, f2, ..., fd])
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# 1.3 u = y * v * roots_of_unity(len(polynomial)*2)
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roots_of_unity = compute_roots_of_unity(PRIMITIVE_ROOT, polynomial_degree, BLS_MODULUS)
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global_parameters = list(reversed(global_parameters[:polynomial_degree]))
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extended_vector = __toeplitz1(global_parameters, polynomial_degree)
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# 2 - Build circulant matrix with the polynomial coefficients (reversed N..n, and padded)
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toeplitz_coefficients = [
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*(BLSFieldElement(0) for _ in range(polynomial_degree)),
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*polynomial.coefficients
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]
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h_extended_vector = __toeplitz2(toeplitz_coefficients, extended_vector)
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# 3 - Perform fft and nub the tail half as it is padding
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h_vector = __toeplitz3(h_extended_vector, polynomial_degree)
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# 4 - proof are the dft of the h vector
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proofs = fft_g1(h_vector, roots_of_unity, BLS_MODULUS)
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proofs = [Proof(bls.G1_to_bytes48(proof)) for proof in proofs]
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return proofs
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