From 233129122bd289316f9aa5afbeefa25392618aa5 Mon Sep 17 00:00:00 2001 From: kevaundray Date: Wed, 17 Jul 2024 14:23:59 +0100 Subject: [PATCH] Replace `recover_data` with `recover_polynomialcoeff` (#3820) * chore: remove recover_data * make it look closer to final code * Improve comments * Fix lint issue * Fix tests & clean things up a bit * Replace a couple uses of "monomial" with "coefficient" * Revert "Replace a couple uses of "monomial" with "coefficient"" This reverts commit c9a1a757d1a09190eee78767b3d36b2a84066e42. * Only replace "monomial" with "coefficient" --------- Co-authored-by: Justin Traglia <95511699+jtraglia@users.noreply.github.com> Co-authored-by: Justin Traglia --- .../polynomial-commitments-sampling.md | 97 ++++++++----------- 1 file changed, 41 insertions(+), 56 deletions(-) diff --git a/specs/_features/eip7594/polynomial-commitments-sampling.md b/specs/_features/eip7594/polynomial-commitments-sampling.md index 2993d50bf9..7fec2a52d7 100644 --- a/specs/_features/eip7594/polynomial-commitments-sampling.md +++ b/specs/_features/eip7594/polynomial-commitments-sampling.md @@ -39,12 +39,13 @@ - [`coset_for_cell`](#coset_for_cell) - [Cells](#cells-1) - [Cell computation](#cell-computation) + - [`compute_cells_and_kzg_proofs_polynomialcoeff`](#compute_cells_and_kzg_proofs_polynomialcoeff) - [`compute_cells_and_kzg_proofs`](#compute_cells_and_kzg_proofs) - [Cell verification](#cell-verification) - [`verify_cell_kzg_proof_batch`](#verify_cell_kzg_proof_batch) - [Reconstruction](#reconstruction) - [`construct_vanishing_polynomial`](#construct_vanishing_polynomial) - - [`recover_data`](#recover_data) + - [`recover_polynomialcoeff`](#recover_polynomialcoeff) - [`recover_cells_and_kzg_proofs`](#recover_cells_and_kzg_proofs) @@ -555,6 +556,24 @@ def coset_for_cell(cell_index: CellIndex) -> Coset: ### Cell computation +#### `compute_cells_and_kzg_proofs_polynomialcoeff` + +```python +def compute_cells_and_kzg_proofs_polynomialcoeff(polynomial_coeff: PolynomialCoeff) -> Tuple[ + Vector[Cell, CELLS_PER_EXT_BLOB], + Vector[KZGProof, CELLS_PER_EXT_BLOB]]: + """ + Helper function which computes cells/proofs for a polynomial in coefficient form. + """ + cells, proofs = [], [] + for i in range(CELLS_PER_EXT_BLOB): + coset = coset_for_cell(CellIndex(i)) + proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset) + cells.append(coset_evals_to_cell(ys)) + proofs.append(proof) + return cells, proofs +``` + #### `compute_cells_and_kzg_proofs` ```python @@ -572,17 +591,7 @@ def compute_cells_and_kzg_proofs(blob: Blob) -> Tuple[ polynomial = blob_to_polynomial(blob) polynomial_coeff = polynomial_eval_to_coeff(polynomial) - - cells = [] - proofs = [] - - for i in range(CELLS_PER_EXT_BLOB): - coset = coset_for_cell(CellIndex(i)) - proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset) - cells.append(coset_evals_to_cell(ys)) - proofs.append(proof) - - return cells, proofs + return compute_cells_and_kzg_proofs_polynomialcoeff(polynomial_coeff) ``` ### Cell verification @@ -668,21 +677,19 @@ def construct_vanishing_polynomial(missing_cell_indices: Sequence[CellIndex]) -> return zero_poly_coeff ``` -### `recover_data` +### `recover_polynomialcoeff` ```python -def recover_data(cell_indices: Sequence[CellIndex], - cells: Sequence[Cell], - ) -> Sequence[BLSFieldElement]: +def recover_polynomialcoeff(cell_indices: Sequence[CellIndex], + cells: Sequence[Cell]) -> Sequence[BLSFieldElement]: """ - Recover the missing evaluations for the extended blob, given at least half of the evaluations. + Recover the polynomial in coefficient form that when evaluated at the roots of unity will give the extended blob. """ - - # Get the extended domain. This will be referred to as the FFT domain. + # Get the extended domain. This will be referred to as the FFT domain roots_of_unity_extended = compute_roots_of_unity(FIELD_ELEMENTS_PER_EXT_BLOB) - # Flatten the cells into evaluations. - # If a cell is missing, then its evaluation is zero. + # Flatten the cells into evaluations + # If a cell is missing, then its evaluation is zero extended_evaluation_rbo = [0] * FIELD_ELEMENTS_PER_EXT_BLOB for cell_index, cell in zip(cell_indices, cells): start = cell_index * FIELD_ELEMENTS_PER_CELL @@ -690,7 +697,7 @@ def recover_data(cell_indices: Sequence[CellIndex], extended_evaluation_rbo[start:end] = cell extended_evaluation = bit_reversal_permutation(extended_evaluation_rbo) - # Compute Z(x) in monomial form + # Compute Z(x) in coefficient form # Z(x) is the polynomial which vanishes on all of the evaluations which are missing missing_cell_indices = [CellIndex(cell_index) for cell_index in range(CELLS_PER_EXT_BLOB) if cell_index not in cell_indices] @@ -703,7 +710,7 @@ def recover_data(cell_indices: Sequence[CellIndex], extended_evaluation_times_zero = [BLSFieldElement(int(a) * int(b) % BLS_MODULUS) for a, b in zip(zero_poly_eval, extended_evaluation)] - # Convert (E*Z)(x) to monomial form + # Convert (E*Z)(x) to coefficient form extended_evaluation_times_zero_coeffs = fft_field(extended_evaluation_times_zero, roots_of_unity_extended, inv=True) # Convert (E*Z)(x) to evaluation form over a coset of the FFT domain @@ -713,18 +720,12 @@ def recover_data(cell_indices: Sequence[CellIndex], zero_poly_over_coset = coset_fft_field(zero_poly_coeff, roots_of_unity_extended) # Compute Q_3(x) = (E*Z)(x) / Z(x) in evaluation form over a coset of the FFT domain - reconstructed_poly_over_coset = [ - div(a, b) - for a, b in zip(extended_evaluations_over_coset, zero_poly_over_coset) - ] + reconstructed_poly_over_coset = [div(a, b) for a, b in zip(extended_evaluations_over_coset, zero_poly_over_coset)] - # Convert Q_3(x) to monomial form + # Convert Q_3(x) to coefficient form reconstructed_poly_coeff = coset_fft_field(reconstructed_poly_over_coset, roots_of_unity_extended, inv=True) - # Convert Q_3(x) to evaluation form over the FFT domain and bit reverse the result - reconstructed_data = bit_reversal_permutation(fft_field(reconstructed_poly_coeff, roots_of_unity_extended)) - - return reconstructed_data + return reconstructed_poly_coeff[:FIELD_ELEMENTS_PER_BLOB] ``` ### `recover_cells_and_kzg_proofs` @@ -735,7 +736,7 @@ def recover_cells_and_kzg_proofs(cell_indices: Sequence[CellIndex], Vector[Cell, CELLS_PER_EXT_BLOB], Vector[KZGProof, CELLS_PER_EXT_BLOB]]: """ - Given at least 50% of cells/proofs for a blob, recover all the cells/proofs. + Given at least 50% of cells for a blob, recover all the cells/proofs. 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 @@ -745,6 +746,7 @@ def recover_cells_and_kzg_proofs(cell_indices: Sequence[CellIndex], Public method. """ + # Check we have the same number of cells and indices assert len(cell_indices) == len(cells) # Check we have enough cells to be able to perform the reconstruction assert CELLS_PER_EXT_BLOB / 2 <= len(cell_indices) <= CELLS_PER_EXT_BLOB @@ -757,29 +759,12 @@ def recover_cells_and_kzg_proofs(cell_indices: Sequence[CellIndex], for cell in cells: assert len(cell) == BYTES_PER_CELL - # Convert cells to coset evals + # Convert cells to coset evaluations cosets_evals = [cell_to_coset_evals(cell) for cell in cells] - reconstructed_data = recover_data(cell_indices, cosets_evals) - - for cell_index, coset_evals in zip(cell_indices, cosets_evals): - start = cell_index * FIELD_ELEMENTS_PER_CELL - end = (cell_index + 1) * FIELD_ELEMENTS_PER_CELL - assert reconstructed_data[start:end] == coset_evals - - recovered_cells = [ - coset_evals_to_cell(reconstructed_data[i * FIELD_ELEMENTS_PER_CELL:(i + 1) * FIELD_ELEMENTS_PER_CELL]) - for i in range(CELLS_PER_EXT_BLOB)] - - polynomial_eval = reconstructed_data[:FIELD_ELEMENTS_PER_BLOB] - polynomial_coeff = polynomial_eval_to_coeff(polynomial_eval) - recovered_proofs = [None] * CELLS_PER_EXT_BLOB - - for i in range(CELLS_PER_EXT_BLOB): - coset = coset_for_cell(CellIndex(i)) - proof, ys = compute_kzg_proof_multi_impl(polynomial_coeff, coset) - assert coset_evals_to_cell(ys) == recovered_cells[i] - recovered_proofs[i] = proof - - return recovered_cells, recovered_proofs + # Given the coset evaluations, recover the polynomial in coefficient form + polynomial_coeff = recover_polynomialcoeff(cell_indices, cosets_evals) + + # Recompute all cells/proofs + return compute_cells_and_kzg_proofs_polynomialcoeff(polynomial_coeff) ```