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Add helpers: recover_shifted_data() and recover_original_data()

This commit is contained in:
George Kadianakis 2024-01-23 18:22:05 +02:00
parent 8b3ac46a2d
commit be5e5c5a75
1 changed files with 61 additions and 31 deletions
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92
specs/_features/eip7594/polynomial-commitments-sampling.md
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@ -42,6 +42,9 @@
- [`verify_cell_proof`](#verify_cell_proof)
- [`verify_cell_proof_batch`](#verify_cell_proof_batch)
- [Reconstruction](#reconstruction)
- [`construct_vanishing_polynomial`](#construct_vanishing_polynomial)
- [`recover_shifted_data`](#recover_shifted_data)
- [`recover_original_data`](#recover_original_data)
- [`recover_polynomial`](#recover_polynomial)
<!-- END doctoc generated TOC please keep comment here to allow auto update -->
@ -508,8 +511,60 @@ def construct_vanishing_polynomial(cell_ids: Sequence[CellID],
### `recover_shifted_data`
```python
def recover_shifted_data(cell_ids: Sequence[CellID],
cells: Sequence[Cell],
zero_poly_eval: Sequence[BLSFieldElement],
zero_poly_coeff: Sequence[BLSFieldElement],
roots_of_unity_extended: Sequence[BLSFieldElement]) -> Tuple[
Sequence[BLSFieldElement],
Sequence[BLSFieldElement],
BLSFieldElement]:
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
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
extended_evaluation_rbo[start:end] = cell
extended_evaluation = bit_reversal_permutation(extended_evaluation_rbo)
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)
shifted_extended_evaluation = shift_polynomialcoeff(extended_evaluations_fft, 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)
return eval_shifted_extended_evaluation, eval_shifted_zero_poly, shift_inv
```
### `recover_original_data`
```python
def recover_original_data(eval_shifted_extended_evaluation: Sequence[BLSFieldElement],
eval_shifted_zero_poly: Sequence[BLSFieldElement],
shift_inv: BLSFieldElement,
roots_of_unity_extended: Sequence[BLSFieldElement]) -> Sequence[BLSFieldElement]:
eval_shifted_reconstructed_poly = [
div(a, b)
for a, b in zip(eval_shifted_extended_evaluation, eval_shifted_zero_poly)
]
shifted_reconstructed_poly = fft_field(eval_shifted_reconstructed_poly, roots_of_unity_extended, inv=True)
reconstructed_poly = shift_polynomialcoeff(shifted_reconstructed_poly, shift_inv)
reconstructed_data = bit_reversal_permutation(fft_field(reconstructed_poly, roots_of_unity_extended))
return reconstructed_data
```
### `recover_polynomial`
```python
@ -529,41 +584,16 @@ def recover_polynomial(cell_ids: Sequence[CellID],
cells = [bytes_to_cell(cell_bytes) for cell_bytes in cells_bytes]
assert len(cells) >= CELLS_PER_BLOB // 2
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):
start = cell_id * FIELD_ELEMENTS_PER_CELL
end = (cell_id + 1) * FIELD_ELEMENTS_PER_CELL
extended_evaluation_rbo[start:end] = cell
extended_evaluation = bit_reversal_permutation(extended_evaluation_rbo)
extended_evaluation_times_zero = [BLSFieldElement(int(a) * int(b) % BLS_MODULUS)
for a, b in zip(zero_poly_eval, extended_evaluation)]
roots_of_unity_extended = compute_roots_of_unity(2 * FIELD_ELEMENTS_PER_BLOB)
extended_evaluations_fft = fft_field(extended_evaluation_times_zero, roots_of_unity_extended, inv=True)
zero_poly_coeff, zero_poly_eval, zero_poly_eval_brp = construct_vanishing_polynomial(cell_ids, cells)
shift_factor = BLSFieldElement(PRIMITIVE_ROOT_OF_UNITY)
shift_inv = div(BLSFieldElement(1), shift_factor)
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)
shifted_extended_evaluation = shift_polynomialcoeff(extended_evaluations_fft, 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)
eval_shifted_reconstructed_poly = [
div(a, b)
for a, b in zip(eval_shifted_extended_evaluation, eval_shifted_zero_poly)
]
shifted_reconstructed_poly = fft_field(eval_shifted_reconstructed_poly, roots_of_unity_extended, inv=True)
reconstructed_poly = shift_polynomialcoeff(shifted_reconstructed_poly, shift_inv)
reconstructed_data = bit_reversal_permutation(fft_field(reconstructed_poly, roots_of_unity_extended))
reconstructed_data = \
recover_original_data(eval_shifted_extended_evaluation, eval_shifted_zero_poly, shift_inv,
roots_of_unity_extended)
for cell_id, cell in zip(cell_ids, cells):
start = cell_id * FIELD_ELEMENTS_PER_CELL