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Minor fixes

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This commit is contained in:
Hsiao-Wei Wang
2023-12-13 00:25:30 +08:00
parent 0d4007a6d9
commit f0af688fbd
2 changed files with 28 additions and 24 deletions
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50
specs/deneb/polynomial-commitments-sampling.md
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@@ -75,16 +75,16 @@ Public functions MUST accept raw bytes as input and perform the required cryptog
| - | - | - |
| `FIELD_ELEMENTS_PER_SAMPLE` | `uint64(64)` | Number of field elements in a sample |
| `BYTES_PER_SAMPLE` | `FIELD_ELEMENTS_PER_SAMPLE * BYTES_PER_FIELD_ELEMENT` | The number of bytes in a sample |
| `SAMPLES_PER_BLOB` | `(2 * FIELD_ELEMENTS_PER_BLOB) / FIELD_ELEMENTS_PER_SAMPLE` | The number of samples for a blob |
| `SAMPLES_PER_BLOB` | `((2 * FIELD_ELEMENTS_PER_BLOB) // FIELD_ELEMENTS_PER_SAMPLE)` | The number of samples for a blob |
### Crypto
| Name | Value | Description |
| - | - | - |
| `ROOT_OF_UNITY2` | `pow(PRIMITIVE_ROOT_OF_UNITY, (BLS_MODULUS - 1) // int(FIELD_ELEMENTS_PER_BLOB * 2), BLS_MODULUS)` | Root of unity of order FIELD_ELEMENTS_PER_BLOB * 2 over the BLS12-381 field |
| `ROOTS_OF_UNITY2` | `[pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(FIELD_ELEMENTS_PER_BLOB * 2)]` | Roots of unity of order FIELD_ELEMENTS_PER_BLOB * 2 over the BLS12-381 field |
| `ROOTS_OF_UNITY2` | `([pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(FIELD_ELEMENTS_PER_BLOB * 2)])` | Roots of unity of order FIELD_ELEMENTS_PER_BLOB * 2 over the BLS12-381 field |
| `ROOT_OF_UNITY_S` | `pow(PRIMITIVE_ROOT_OF_UNITY, (BLS_MODULUS - 1) // int(SAMPLES_PER_BLOB), BLS_MODULUS)` | Root of unity of order SAMPLES_PER_BLOB over the BLS12-381 field |
| `ROOTS_OF_UNITY_S` | `[pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(SAMPLES_PER_BLOB)]` | Roots of unity of order SAMPLES_PER_BLOB over the BLS12-381 field |
| `ROOTS_OF_UNITY_S` | `([pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(SAMPLES_PER_BLOB)])` | Roots of unity of order SAMPLES_PER_BLOB over the BLS12-381 field |
## Helper functions
@@ -313,8 +313,9 @@ Extended KZG functions for multiproofs
#### `compute_kzg_proof_multi_impl`
```python
def compute_kzg_proof_multi_impl(polynomial_coeff: PolynomialCoeff,
zs: Sequence[BLSFieldElement]) -> Tuple[KZGProof, Sequence[BLSFieldElement]]:
def compute_kzg_proof_multi_impl(
polynomial_coeff: PolynomialCoeff,
zs: Sequence[BLSFieldElement]) -> Tuple[KZGProof, Sequence[BLSFieldElement]]:
"""
Helper function that computes multi-evaluation KZG proofs.
"""
@@ -343,17 +344,16 @@ 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))
interpolated_poly = g1_lincomb(KZG_SETUP_G1[:len(zs)], interpolate_polynomialcoeff(zs, ys))
return (
bls.pairing_check(
[[bls.bytes48_to_G1(proof), bls.bytes96_to_G2(zero_poly)],
[bls.add(bls.bytes48_to_G1(commitment), bls.neg(bls.bytes48_to_G1(interpolated_poly))),
bls.neg(bls.bytes96_to_G2(KZG_SETUP_G2[0]))]]
)
)
return (bls.pairing_check([
[bls.bytes48_to_G1(proof), bls.bytes96_to_G2(zero_poly)],
[
bls.add(bls.bytes48_to_G1(commitment), bls.neg(bls.bytes48_to_G1(interpolated_poly))),
bls.neg(bls.bytes96_to_G2(KZG_SETUP_G2[0])),
],
]))
```
### Sample cosets
@@ -394,9 +394,9 @@ def compute_samples_and_proofs(blob: Blob) -> Tuple[
proofs = []
for i in range(SAMPLES_PER_BLOB):
samples.append(ys)
coset = coset_for_sample(i)
proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset)
samples.append(ys)
proofs.append(proof)
return samples, proofs
@@ -411,7 +411,8 @@ def compute_samples(blob: Blob) -> Vector[Vector[BLSFieldElement, FIELD_ELEMENTS
extended_data = fft_field(polynomial_coeff + [0] * FIELD_ELEMENTS_PER_BLOB, ROOTS_OF_UNITY2)
extended_data_rbo = bit_reversal_permutation(extended_data)
return [extended_data_rbo[i * FIELD_ELEMENTS_PER_SAMPLE:(i + 1) * FIELD_ELEMENTS_PER_SAMPLE] for i in range(SAMPLES_PER_BLOB)]
return [extended_data_rbo[i * FIELD_ELEMENTS_PER_SAMPLE:(i + 1) * FIELD_ELEMENTS_PER_SAMPLE]
for i in range(SAMPLES_PER_BLOB)]
```
### Sample verification
@@ -420,8 +421,9 @@ def compute_samples(blob: Blob) -> Vector[Vector[BLSFieldElement, FIELD_ELEMENTS
```python
def verify_sample_proof(commitment: KZGCommitment,
sample_id: int,
data: Vector[BLSFieldElement]) -> bool:
sample_id: int,
data: Vector[BLSFieldElement],
proof: KZGProof) -> bool:
"""
Check a sample proof
"""
@@ -498,15 +500,17 @@ def recover_samples_impl(samples: Sequence[Tuple[int, Sequence[BLSFieldElement]]
shifted_extended_evaluation = shift_polynomialcoeff(extended_evaluations_fft, shift_factor)
shifted_zero_poly = shift_polynomialcoeff(full_zero_poly, shift_factor)
eval_shifted_extended_evaluation = fft_field(shifted_extended_evaluation, ROOTS_OF_UNITY2)
eval_shifted_zero_poly = fft_field(shifted_zero_poly, ROOTS_OF_UNITY2)
eval_shifted_reconstructed_poly = [div(a, b) for a, b in
zip(eval_shifted_extended_evaluation, eval_shifted_zero_poly)]
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_UNITY2, inv=True)
reconstructed_poly = shift_polynomialcoeff(shifted_reconstructed_poly, shift_inv)
reconstructed_data = bit_reversal_permutation(fft_field(reconstructed_poly, ROOTS_OF_UNITY2))
@@ -516,4 +520,4 @@ def recover_samples_impl(samples: Sequence[Tuple[int, Sequence[BLSFieldElement]]
sample_data
return reconstructed_data
```
```

2
specs/deneb/polynomial-commitments.md
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@@ -97,7 +97,7 @@ Public functions MUST accept raw bytes as input and perform the required cryptog
| Name | Value | Notes |
| - | - | - |
| `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (BLS_MODULUS - 1) // int(FIELD_ELEMENTS_PER_BLOB), BLS_MODULUS)` | Root of unity of order FIELD_ELEMENTS_PER_BLOB over the BLS12-381 field |
| `ROOTS_OF_UNITY` | `[pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(FIELD_ELEMENTS_PER_BLOB)]` | Roots of unity of order FIELD_ELEMENTS_PER_BLOB over the BLS12-381 field |
| `ROOTS_OF_UNITY` | `([pow(ROOT_OF_UNITY, i, BLS_MODULUS) for i in range(FIELD_ELEMENTS_PER_BLOB)])` | Roots of unity of order FIELD_ELEMENTS_PER_BLOB over the BLS12-381 field |
### Trusted setup