status-im
/
eth2.0-specs
mirror of https://github.com/status-im/eth2.0-specs.git
2
0
Fork 0
Code Issues Projects Releases Wiki Activity

Small improvements on construct_vanishing_polynomial()

This commit is contained in:
George Kadianakis 2024-01-31 13:32:23 +02:00
parent 4d01d50437
commit 212c1fe624
1 changed files with 30 additions and 21 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

51
specs/_features/eip7594/polynomial-commitments-sampling.md
View File

@ -477,34 +477,40 @@ def verify_cell_proof_batch(row_commitments_bytes: Sequence[Bytes48],
### `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]
def construct_vanishing_polynomial(missing_cell_ids: Sequence[CellID]) -> Tuple[
Sequence[BLSFieldElement],
Sequence[BLSFieldElement]]:
"""
Given the cells that are missing from the data, compute the polynomial that vanishes at every point that
corresponds to a missing field element
"""
# Get the small domain
roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_BLOB)
# Compute polynomial that vanishes at all the missing cells (over the small domain)
short_zero_poly = vanishing_polynomialcoeff([
roots_of_unity_reduced[reverse_bits(cell_id, CELLS_PER_BLOB)]
for cell_id in missing_cell_ids
roots_of_unity_reduced[reverse_bits(missing_cell_id, CELLS_PER_BLOB)]
for missing_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))
# Extend vanishing polynomial to full domain using the closed form of the vanishing polynomial over a coset
zero_poly_coeff = [0] * (FIELD_ELEMENTS_PER_BLOB * 2)
for (i, coeff) in enumerate(short_zero_poly):
zero_poly_coeff[i * FIELD_ELEMENTS_PER_CELL] = coeff
# Compute evaluations of the extended vanishing polynomial
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:
# Sanity check
for cell_id in range(CELLS_PER_BLOB):
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])
if cell_id in missing_cell_ids:
assert zero_poly_eval_brp[start:end] == [0] * FIELD_ELEMENTS_PER_CELL
else: # cell_id in cell_ids
assert all(a != 0 for a in zero_poly_eval_brp[start:end])
return zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp
```
@ -593,12 +599,15 @@ def recover_polynomial(cell_ids: Sequence[CellID],
"""
assert len(cell_ids) == len(cells_bytes)
# Get the extended domain
roots_of_unity_extended = compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB)
# Convert from bytes to cells
cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes]
assert len(cells) >= CELLS_PER_BLOB // 2
roots_of_unity_extended = compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB)
zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp = construct_vanishing_polynomial(cell_ids, cells)
missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_BLOB) if cell_id not in cell_ids]
zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp = construct_vanishing_polynomial(missing_cell_ids)
eval_shifted_extended_evaluation, eval_shifted_zero_poly, shift_inv = \
recover_shifted_data(cell_ids, cells, zero_poly_eval, zero_poly_coeff, roots_of_unity_extended)