chore: (ben) add code to generate the vanishing polynomial when all c…

…ells are missing

specs/_features/eip7594/polynomial-commitments-sampling.md

@@ -576,6 +576,20 @@ def construct_vanishing_polynomial(missing_cell_ids: Sequence[CellID]) -> Sequen
     Given the cells IDs that are missing from the data, compute the polynomial that vanishes at every point that
     corresponds to a missing field element.
     """
+
+    # If all of the cells are missing, then the vanishing polynomial
+    # can be computed as Z(x) = x^n - 1, where `n` is FIELD_ELEMENTS_PER_EXT_BLOB
+    # 
+    # Note: this makes the function complete on all inputs, however this code path should not 
+    # be hit since this method is used for data recovery and if all of the
+    # cells are missing, then we can return early.  
+    if len(missing_cell_ids) == CELLS_PER_EXT_BLOB:
+        z_x = [BLSFieldElement(0)] * (FIELD_ELEMENTS_PER_EXT_BLOB + 1)
+        z_x[0] = BLS_MODULUS - 1
+        z_x[-1] = 1
+
+        return z_x
+
     # Get the small domain
     roots_of_unity_reduced = compute_roots_of_unity(CELLS_PER_EXT_BLOB)
 
@@ -618,11 +632,10 @@ def recover_data(cell_ids: Sequence[CellID],
     # Compute Z(x) in monomial form
     # Z(x) is the polynomial which vanishes on all of the evaluations which are missing
     missing_cell_ids = [CellID(cell_id) for cell_id in range(CELLS_PER_EXT_BLOB) if cell_id not in cell_ids]
-    zero_poly_coeff = construct_vanishing_polynomial(missing_cell_ids)
 
+    zero_poly_coeff = construct_vanishing_polynomial(missing_cell_ids)
     # Convert Z(x) to evaluation form over the FFT domain
     zero_poly_eval = fft_field(zero_poly_coeff, roots_of_unity_extended)
-
     # Compute (E*Z)(x) = E(x) * Z(x) in evaluation form over the FFT domain
     extended_evaluation_times_zero = [BLSFieldElement(int(a) * int(b) % BLS_MODULUS)
                                       for a, b in zip(zero_poly_eval, extended_evaluation)]

tests/core/pyspec/eth2spec/test/eip7594/unittests/polynomial_commitments/test_polynomial_commitments.py

@@ -69,6 +69,20 @@ def test_construct_vanishing_polynomial(spec):
             assert all(a != 0 for a in zero_poly_eval_brp[start:end])
 
 
+@with_eip7594_and_later
+@spec_test
+@single_phase
+def test_construct_vanishing_polynomial_all_missing_zeros(spec):
+
+    all_cell_ids = range(spec.CELLS_PER_EXT_BLOB)
+
+    zero_poly_coeff = spec.construct_vanishing_polynomial(all_cell_ids)
+    roots_of_unity = spec.compute_roots_of_unity(spec.FIELD_ELEMENTS_PER_EXT_BLOB)
+    zero_poly_eval = spec.fft_field(zero_poly_coeff, roots_of_unity)
+
+    assert all(a == 0 for a in zero_poly_eval)
+
+
 @with_eip7594_and_later
 @spec_test
 @single_phase