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number of cells in an extended blob

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Kevaundray Wedderburn 2024-04-18 17:38:04 +01:00
parent 477fa0e3ca
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specs/_features/eip7594/polynomial-commitments-sampling.md
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@ -84,7 +84,7 @@ Cells are the smallest unit of blob data that can come with their own KZG proofs
| `FIELD_ELEMENTS_PER_EXT_BLOB` | `2 * FIELD_ELEMENTS_PER_BLOB` | Number of field elements in a Reed-Solomon extended blob | | `FIELD_ELEMENTS_PER_EXT_BLOB` | `2 * FIELD_ELEMENTS_PER_BLOB` | Number of field elements in a Reed-Solomon extended blob |
| `FIELD_ELEMENTS_PER_CELL` | `uint64(64)` | Number of field elements in a cell | | `FIELD_ELEMENTS_PER_CELL` | `uint64(64)` | Number of field elements in a cell |
| `BYTES_PER_CELL` | `FIELD_ELEMENTS_PER_CELL * BYTES_PER_FIELD_ELEMENT` | The number of bytes in a cell | | `BYTES_PER_CELL` | `FIELD_ELEMENTS_PER_CELL * BYTES_PER_FIELD_ELEMENT` | The number of bytes in a cell |
| `CELLS_PER_BLOB` | `FIELD_ELEMENTS_PER_EXT_BLOB // FIELD_ELEMENTS_PER_CELL` | The number of cells in a blob | | `CELLS_PER_EXT_BLOB` | `FIELD_ELEMENTS_PER_EXT_BLOB // FIELD_ELEMENTS_PER_CELL` | The number of cells in an extended blob |
| `RANDOM_CHALLENGE_KZG_CELL_BATCH_DOMAIN` | `b'RCKZGCBATCH__V1_'` | | `RANDOM_CHALLENGE_KZG_CELL_BATCH_DOMAIN` | `b'RCKZGCBATCH__V1_'` |
## Helper functions ## Helper functions
@ -359,7 +359,7 @@ def coset_for_cell(cell_id: CellID) -> Cell:
""" """
Get the coset for a given ``cell_id`` Get the coset for a given ``cell_id``
""" """
assert cell_id < CELLS_PER_BLOB assert cell_id < CELLS_PER_EXT_BLOB
roots_of_unity_brp = bit_reversal_permutation( roots_of_unity_brp = bit_reversal_permutation(
compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB) compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB)
) )
@ -374,8 +374,8 @@ def coset_for_cell(cell_id: CellID) -> Cell:
```python ```python
def compute_cells_and_proofs(blob: Blob) -> Tuple[ def compute_cells_and_proofs(blob: Blob) -> Tuple[
Vector[Cell, CELLS_PER_BLOB], Vector[Cell, CELLS_PER_EXT_BLOB],
Vector[KZGProof, CELLS_PER_BLOB]]: Vector[KZGProof, CELLS_PER_EXT_BLOB]]:
""" """
Compute all the cell proofs for one blob. This is an inefficient O(n^2) algorithm, Compute all the cell proofs for one blob. This is an inefficient O(n^2) algorithm,
for performant implementation the FK20 algorithm that runs in O(n log n) should be for performant implementation the FK20 algorithm that runs in O(n log n) should be
@ -389,7 +389,7 @@ def compute_cells_and_proofs(blob: Blob) -> Tuple[
cells = [] cells = []
proofs = [] proofs = []
for i in range(CELLS_PER_BLOB): for i in range(CELLS_PER_EXT_BLOB):
coset = coset_for_cell(i) coset = coset_for_cell(i)
proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset) proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset)
cells.append(ys) cells.append(ys)
@ -401,7 +401,7 @@ def compute_cells_and_proofs(blob: Blob) -> Tuple[
#### `compute_cells` #### `compute_cells`
```python ```python
def compute_cells(blob: Blob) -> Vector[Cell, CELLS_PER_BLOB]: def compute_cells(blob: Blob) -> Vector[Cell, CELLS_PER_EXT_BLOB]:
""" """
Compute the cell data for a blob (without computing the proofs). Compute the cell data for a blob (without computing the proofs).
@ -414,7 +414,7 @@ def compute_cells(blob: Blob) -> Vector[Cell, CELLS_PER_BLOB]:
compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB)) compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB))
extended_data_rbo = bit_reversal_permutation(extended_data) extended_data_rbo = bit_reversal_permutation(extended_data)
return [extended_data_rbo[i * FIELD_ELEMENTS_PER_CELL:(i + 1) * FIELD_ELEMENTS_PER_CELL] return [extended_data_rbo[i * FIELD_ELEMENTS_PER_CELL:(i + 1) * FIELD_ELEMENTS_PER_CELL]
for i in range(CELLS_PER_BLOB)] for i in range(CELLS_PER_EXT_BLOB)]
``` ```
### Cell verification ### Cell verification
@ -491,11 +491,11 @@ def construct_vanishing_polynomial(missing_cell_ids: Sequence[CellID]) -> Tuple[
corresponds to a missing field element. corresponds to a missing field element.
""" """
# Get the small domain # Get the small domain
roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_BLOB) roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_EXT_BLOB)
# Compute polynomial that vanishes at all the missing cells (over the small domain) # Compute polynomial that vanishes at all the missing cells (over the small domain)
short_zero_poly = vanishing_polynomialcoeff([ short_zero_poly = vanishing_polynomialcoeff([
roots_of_unity_reduced[reverse_bits(missing_cell_id, CELLS_PER_BLOB)] roots_of_unity_reduced[reverse_bits(missing_cell_id, CELLS_PER_EXT_BLOB)]
for missing_cell_id in missing_cell_ids for missing_cell_id in missing_cell_ids
]) ])
@ -510,7 +510,7 @@ def construct_vanishing_polynomial(missing_cell_ids: Sequence[CellID]) -> Tuple[
zero_poly_eval_brp = bit_reversal_permutation(zero_poly_eval) zero_poly_eval_brp = bit_reversal_permutation(zero_poly_eval)
# Sanity check # Sanity check
for cell_id in range(CELLS_PER_BLOB): for cell_id in range(CELLS_PER_EXT_BLOB):
start = cell_id * FIELD_ELEMENTS_PER_CELL start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
if cell_id in missing_cell_ids: if cell_id in missing_cell_ids:
@ -605,7 +605,7 @@ def recover_polynomial(cell_ids: Sequence[CellID],
""" """
assert len(cell_ids) == len(cells_bytes) assert len(cell_ids) == len(cells_bytes)
# Check we have enough cells to be able to perform the reconstruction # Check we have enough cells to be able to perform the reconstruction
assert CELLS_PER_BLOB / 2 <= len(cell_ids) <= CELLS_PER_BLOB assert CELLS_PER_EXT_BLOB / 2 <= len(cell_ids) <= CELLS_PER_EXT_BLOB
# Check for duplicates # Check for duplicates
assert len(cell_ids) == len(set(cell_ids)) assert len(cell_ids) == len(set(cell_ids))
@ -615,7 +615,7 @@ def recover_polynomial(cell_ids: Sequence[CellID],
# Convert from bytes to cells # Convert from bytes to cells
cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes] cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes]
missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_BLOB) if cell_id not in cell_ids] missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_EXT_BLOB) if cell_id not in cell_ids]
zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp = construct_vanishing_polynomial(missing_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( eval_shifted_extended_evaluation, eval_shifted_zero_poly, shift_inv = recover_shifted_data(