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Initial docs added to recover_shifted_data() and recover_original_data()

This commit is contained in:
George Kadianakis 2024-01-31 13:45:04 +02:00
parent be5e5c5a75
commit 4d01d50437
1 changed files with 18 additions and 6 deletions
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24
specs/_features/eip7594/polynomial-commitments-sampling.md
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@ -520,6 +520,12 @@ def recover_shifted_data(cell_ids: Sequence[CellID],
Sequence[BLSFieldElement],
Sequence[BLSFieldElement],
BLSFieldElement]:
"""
Given Z(x), return polynomial Q_1(x)=(E*Z)(k*x) and Q_2(x)=Z(k*x) and k^{-1}
"""
shift_factor = BLSFieldElement(PRIMITIVE_ROOT_OF_UNITY)
shift_inv = div(BLSFieldElement(1), shift_factor)
extended_evaluation_rbo = [0] * (FIELD_ELEMENTS_PER_BLOB * 2)
for cell_id, cell in zip(cell_ids, cells):
start = cell_id * FIELD_ELEMENTS_PER_CELL
@ -527,15 +533,15 @@ def recover_shifted_data(cell_ids: Sequence[CellID],
extended_evaluation_rbo[start:end] = cell
extended_evaluation = bit_reversal_permutation(extended_evaluation_rbo)
# Compute (E*Z)(x)
extended_evaluation_times_zero = [BLSFieldElement(int(a) * int(b) % BLS_MODULUS)
for a, b in zip(zero_poly_eval, extended_evaluation)]
extended_evaluations_fft = fft_field(extended_evaluation_times_zero, roots_of_unity_extended, inv=True)
shift_factor = BLSFieldElement(PRIMITIVE_ROOT_OF_UNITY)
shift_inv = div(BLSFieldElement(1), shift_factor)
# Compute (E*Z)(k*x)
shifted_extended_evaluation = shift_polynomialcoeff(extended_evaluations_fft, shift_factor)
# Compute Z(k*x)
shifted_zero_poly = shift_polynomialcoeff(zero_poly_coeff, shift_factor)
eval_shifted_extended_evaluation = fft_field(shifted_extended_evaluation, roots_of_unity_extended)
@ -551,6 +557,10 @@ def recover_original_data(eval_shifted_extended_evaluation: Sequence[BLSFieldEle
eval_shifted_zero_poly: Sequence[BLSFieldElement],
shift_inv: BLSFieldElement,
roots_of_unity_extended: Sequence[BLSFieldElement]) -> Sequence[BLSFieldElement]:
"""
Given Q_1, Q_2 and k^{-1}, compute P(x)
"""
# Compute Q_3 = Q_1(x)/Q_2(x) = P(k*x)
eval_shifted_reconstructed_poly = [
div(a, b)
for a, b in zip(eval_shifted_extended_evaluation, eval_shifted_zero_poly)
@ -558,6 +568,7 @@ def recover_original_data(eval_shifted_extended_evaluation: Sequence[BLSFieldEle
shifted_reconstructed_poly = fft_field(eval_shifted_reconstructed_poly, roots_of_unity_extended, inv=True)
# Unshift P(k*x) by k^{-1} to get P(x)
reconstructed_poly = shift_polynomialcoeff(shifted_reconstructed_poly, shift_inv)
reconstructed_data = bit_reversal_permutation(fft_field(reconstructed_poly, roots_of_unity_extended))
@ -571,10 +582,11 @@ def recover_original_data(eval_shifted_extended_evaluation: Sequence[BLSFieldEle
def recover_polynomial(cell_ids: Sequence[CellID],
cells_bytes: Sequence[Vector[Bytes32, FIELD_ELEMENTS_PER_CELL]]) -> Polynomial:
"""
Recovers a polynomial from 2 * FIELD_ELEMENTS_PER_CELL evaluations, half of which can be missing.
Recover original polynomial from 2 * FIELD_ELEMENTS_PER_CELL evaluations, half of which can be missing. This
algorithm uses FFTs to recover cells faster than using Lagrange implementation, as can be seen here:
https://ethresear.ch/t/reed-solomon-erasure-code-recovery-in-n-log-2-n-time-with-ffts/3039
This algorithm uses FFTs to recover cells faster than using Lagrange implementation. However,
a faster version thanks to Qi Zhou can be found here:
A faster version thanks to Qi Zhou can be found here:
https://github.com/ethereum/research/blob/51b530a53bd4147d123ab3e390a9d08605c2cdb8/polynomial_reconstruction/polynomial_reconstruction_danksharding.py
Public method.