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Add helper method: construct_vanishing_polynomial()

This commit is contained in:
George Kadianakis 2024-01-31 13:45:49 +02:00
parent ae3ef6f330
commit 8b3ac46a2d
1 changed files with 41 additions and 25 deletions
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66
specs/_features/eip7594/polynomial-commitments-sampling.md
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@ -471,6 +471,45 @@ def verify_cell_proof_batch(row_commitments_bytes: Sequence[Bytes48],
## Reconstruction
### `construct_vanishing_polynomial`
```python
def construct_vanishing_polynomial(cell_ids: Sequence[CellID],
cells: Sequence[Cell]) -> Tuple[
Sequence[BLSFieldElement],
Sequence[BLSFieldElement]]:
missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_BLOB) if cell_id not in cell_ids]
roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_BLOB)
short_zero_poly = vanishing_polynomialcoeff([
roots_of_unity_reduced[reverse_bits(cell_id, CELLS_PER_BLOB)]
for cell_id in missing_cell_ids
])
zero_poly_coeff = []
for i in short_zero_poly:
zero_poly_coeff.append(i)
zero_poly_coeff.extend([0] * (FIELD_ELEMENTS_PER_CELL - 1))
zero_poly_coeff = zero_poly_coeff + [0] * (2 * FIELD_ELEMENTS_PER_BLOB - len(zero_poly_coeff))
zero_poly_eval = fft_field(zero_poly_coeff,
compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB))
zero_poly_eval_brp = bit_reversal_permutation(zero_poly_eval)
for cell_id in missing_cell_ids:
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
assert zero_poly_eval_brp[start:end] == [0] * FIELD_ELEMENTS_PER_CELL
for cell_id in cell_ids:
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
assert all(a != 0 for a in zero_poly_eval_brp[start:end])
return zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp
```
### `recover_shifted_data`
### `recover_original_data`
### `recover_polynomial`
```python
@ -488,32 +527,9 @@ def recover_polynomial(cell_ids: Sequence[CellID],
assert len(cell_ids) == len(cells_bytes)
cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes]
assert len(cells) >= CELLS_PER_BLOB // 2
missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_BLOB) if cell_id not in cell_ids]
roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_BLOB)
short_zero_poly = vanishing_polynomialcoeff([
roots_of_unity_reduced[reverse_bits(cell_id, CELLS_PER_BLOB)]
for cell_id in missing_cell_ids
])
full_zero_poly = []
for i in short_zero_poly:
full_zero_poly.append(i)
full_zero_poly.extend([0] * (FIELD_ELEMENTS_PER_CELL - 1))
full_zero_poly = full_zero_poly + [0] * (2 * FIELD_ELEMENTS_PER_BLOB - len(full_zero_poly))
zero_poly_eval = fft_field(full_zero_poly,
compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB))
zero_poly_eval_brp = bit_reversal_permutation(zero_poly_eval)
for cell_id in missing_cell_ids:
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
assert zero_poly_eval_brp[start:end] == [0] * FIELD_ELEMENTS_PER_CELL
for cell_id in cell_ids:
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
assert all(a != 0 for a in zero_poly_eval_brp[start:end])
zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp = construct_vanishing_polynomial(cell_ids, cells)
extended_evaluation_rbo = [0] * (FIELD_ELEMENTS_PER_BLOB * 2)
for cell_id, cell in zip(cell_ids, cells):
@ -533,7 +549,7 @@ def recover_polynomial(cell_ids: Sequence[CellID],
shift_inv = div(BLSFieldElement(1), shift_factor)
shifted_extended_evaluation = shift_polynomialcoeff(extended_evaluations_fft, shift_factor)
shifted_zero_poly = shift_polynomialcoeff(full_zero_poly, shift_factor)
shifted_zero_poly = shift_polynomialcoeff(zero_poly_coeff, shift_factor)
eval_shifted_extended_evaluation = fft_field(shifted_extended_evaluation, roots_of_unity_extended)
eval_shifted_zero_poly = fft_field(shifted_zero_poly, roots_of_unity_extended)