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New FIELD_ELEMENTS_PER_EXT_BLOB: number of cells in an extended blob

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George Kadianakis
2024-02-05 16:53:59 +02:00
parent e3b83d5450
commit 1e41a6bc69
1 changed files with 9 additions and 8 deletions
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17
specs/_features/eip7594/polynomial-commitments-sampling.md
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@@ -79,9 +79,10 @@ Cells are the smallest unit of blob data that can come with their own KZG proofs
| Name | Value | Description |
| - | - | - |
| `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 |
| `BYTES_PER_CELL` | `FIELD_ELEMENTS_PER_CELL * BYTES_PER_FIELD_ELEMENT` | The number of bytes in a cell |
| `CELLS_PER_BLOB` | `((2 * FIELD_ELEMENTS_PER_BLOB) // FIELD_ELEMENTS_PER_CELL)` | The number of cells in a blob |
| `CELLS_PER_BLOB` | `FIELD_ELEMENTS_PER_EXT_BLOB // FIELD_ELEMENTS_PER_CELL` | The number of cells in a blob |
| `RANDOM_CHALLENGE_KZG_CELL_BATCH_DOMAIN` | `b'RCKZGCBATCH__V1_'` |
## Helper functions
@@ -355,7 +356,7 @@ def coset_for_cell(cell_id: CellID) -> Cell:
"""
assert cell_id < CELLS_PER_BLOB
roots_of_unity_brp = bit_reversal_permutation(
compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB)
compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB)
)
return Cell(roots_of_unity_brp[FIELD_ELEMENTS_PER_CELL * cell_id:FIELD_ELEMENTS_PER_CELL * (cell_id + 1)])
```
@@ -405,7 +406,7 @@ def compute_cells(blob: Blob) -> Vector[Cell, CELLS_PER_BLOB]:
polynomial_coeff = polynomial_eval_to_coeff(polynomial)
extended_data = fft_field(polynomial_coeff + [0] * FIELD_ELEMENTS_PER_BLOB,
compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB))
compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB))
extended_data_rbo = bit_reversal_permutation(extended_data)
return [extended_data_rbo[i * FIELD_ELEMENTS_PER_CELL:(i + 1) * FIELD_ELEMENTS_PER_CELL]
for i in range(CELLS_PER_BLOB)]
@@ -494,13 +495,13 @@ def construct_vanishing_polynomial(missing_cell_ids: Sequence[CellID]) -> Tuple[
])
# 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)
zero_poly_coeff = [0] * (FIELD_ELEMENTS_PER_EXT_BLOB)
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))
compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB))
zero_poly_eval_brp = bit_reversal_permutation(zero_poly_eval)
# Sanity check
@@ -532,7 +533,7 @@ def recover_shifted_data(cell_ids: Sequence[CellID],
shift_factor = BLSFieldElement(PRIMITIVE_ROOT_OF_UNITY)
shift_inv = div(BLSFieldElement(1), shift_factor)
extended_evaluation_rbo = [0] * (FIELD_ELEMENTS_PER_BLOB * 2)
extended_evaluation_rbo = [0] * (FIELD_ELEMENTS_PER_EXT_BLOB)
for cell_id, cell in zip(cell_ids, cells):
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
@@ -588,7 +589,7 @@ 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:
"""
Recover original polynomial from 2 * FIELD_ELEMENTS_PER_CELL evaluations, half of which can be missing. This
Recover original polynomial from FIELD_ELEMENTS_PER_EXT_BLOB 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
@@ -604,7 +605,7 @@ def recover_polynomial(cell_ids: Sequence[CellID],
assert len(cell_ids) == len(set(cell_ids))
# Get the extended domain
roots_of_unity_extended = compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB)
roots_of_unity_extended = compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB)
# Convert from bytes to cells
cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes]