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Zero polynomial -> vanishing polynomial

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Dankrad Feist 2023-12-23 15:08:02 +00:00
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14
specs/deneb/polynomial-commitments-sampling.md
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@ -27,7 +27,7 @@
- [`divide_polynomialcoeff`](#divide_polynomialcoeff)
- [`shift_polynomialcoeff`](#shift_polynomialcoeff)
- [`interpolate_polynomialcoeff`](#interpolate_polynomialcoeff)
- [`zero_polynomialcoeff`](#zero_polynomialcoeff)
- [`vanishing_polynomialcoeff`](#vanishing_polynomialcoeff)
- [`evaluate_polynomialcoeff`](#evaluate_polynomialcoeff)
- [KZG multiproofs](#kzg-multiproofs)
- [`compute_kzg_proof_multi_impl`](#compute_kzg_proof_multi_impl)
@ -266,12 +266,12 @@ def interpolate_polynomialcoeff(xs: Sequence[BLSFieldElement], ys: Sequence[BLSF
return r
```
#### `zero_polynomialcoeff`
#### `vanishing_polynomialcoeff`
```python
def zero_polynomialcoeff(xs: Sequence[BLSFieldElement]) -> PolynomialCoeff:
def vanishing_polynomialcoeff(xs: Sequence[BLSFieldElement]) -> PolynomialCoeff:
"""
Compute a zero polynomial on ``xs`` (in coefficient form)
Compute the vanishing polynomial on ``xs`` (in coefficient form)
"""
p = [1]
for x in xs:
@ -312,7 +312,7 @@ def compute_kzg_proof_multi_impl(
polynomial_shifted = add_polynomialcoeff(polynomial_coeff, neg_polynomialcoeff(interpolation_polynomial))
# For all x_i, compute (x_i - z)
denominator_poly = zero_polynomialcoeff(zs)
denominator_poly = vanishing_polynomialcoeff(zs)
# Compute the quotient polynomial directly in evaluation form
quotient_polynomial = divide_polynomialcoeff(polynomial_shifted, denominator_poly)
@ -330,7 +330,7 @@ def verify_kzg_proof_multi_impl(commitment: KZGCommitment,
"""
Helper function that verifies a KZG multiproof
"""
zero_poly = g2_lincomb(KZG_SETUP_G2[:len(zs) + 1], zero_polynomialcoeff(zs))
zero_poly = g2_lincomb(KZG_SETUP_G2[:len(zs) + 1], vanishing_polynomialcoeff(zs))
interpolated_poly = g1_lincomb(KZG_SETUP_G1[:len(zs)], interpolate_polynomialcoeff(zs, ys))
return (bls.pairing_check([
@ -468,7 +468,7 @@ def recover_cells(cells: Sequence[Tuple[int, ByteVector[BYTES_PER_CELL]]]) -> Po
assert len(cells) >= CELLS_PER_BLOB // 2
cell_ids = [cell_id for cell_id, _ in cells]
missing_cell_ids = [cell_id for cell_id in range(CELLS_PER_BLOB) if cell_id not in cell_ids]
short_zero_poly = zero_polynomialcoeff([ROOTS_OF_UNITY_REDUCED[reverse_bits(cell_id, CELLS_PER_BLOB)] for cell_id in missing_cell_ids])
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: