EIP4844: Refactor Fiat-Shamir logic to handle empty sidecars (#3093)

Additionally, it makes the Fiat-Shamir hashing logic more robust by making the challenges independent of each other. It also makes it more efficient to implement by moving both challenge computations to a single function needing a single transcript hash.

Co-authored-by: George Kadianakis <desnacked@riseup.net>
Co-authored-by: Dankrad Feist <mail@dankradfeist.de>

specs/eip4844/polynomial-commitments.md

@@ -21,7 +21,7 @@
   - [BLS12-381 helpers](#bls12-381-helpers)
     - [`bytes_to_bls_field`](#bytes_to_bls_field)
     - [`blob_to_polynomial`](#blob_to_polynomial)
-    - [`hash_to_bls_field`](#hash_to_bls_field)
+    - [`compute_challenges`](#compute_challenges)
     - [`bls_modular_inverse`](#bls_modular_inverse)
     - [`div`](#div)
     - [`g1_lincomb`](#g1_lincomb)
@@ -41,7 +41,6 @@
 <!-- END doctoc generated TOC please keep comment here to allow auto update -->
 <!-- /TOC -->
 
-
 ## Introduction
 
 This document specifies basic polynomial operations and KZG polynomial commitment operations as they are needed for the EIP-4844 specification. The implementations are not optimized for performance, but readability. All practical implementations should optimize the polynomial operations.
@@ -163,31 +162,44 @@ def blob_to_polynomial(blob: Blob) -> Polynomial:
     return polynomial
 ```
 
-#### `hash_to_bls_field`
+#### `compute_challenges`
 
 ```python
-def hash_to_bls_field(polys: Sequence[Polynomial],
+def compute_challenges(polynomials: Sequence[Polynomial],
-                      comms: Sequence[KZGCommitment]) -> BLSFieldElement:
+                       commitments: Sequence[KZGCommitment]) -> BLSFieldElement:
     """
-    Compute 32-byte hash of serialized polynomials and commitments concatenated.
+    Return the Fiat-Shamir challenges required by the rest of the protocol.
-    This hash is then converted to a BLS field element, where the result is not uniform over the BLS field.
+    The Fiat-Shamir logic works as per the following pseudocode:
-    Return the BLS field element.
+
+       hashed_data = hash(DOMAIN_SEPARATOR, polynomials, commitments)
+       r = hash(hashed_data, 0)
+       r_powers = [r, r**2, r**3, ...]
+       eval_challenge = hash(hashed_data, 1)
+
+    Then return `r_powers` and `eval_challenge` after converting them to BLS field elements.
+    The resulting field elements are not uniform over the BLS field.
     """
     # Append the number of polynomials and the degree of each polynomial as a domain separator
-    num_polys = int.to_bytes(len(polys), 8, ENDIANNESS)
+    num_polynomials = int.to_bytes(len(polynomials), 8, ENDIANNESS)
     degree_poly = int.to_bytes(FIELD_ELEMENTS_PER_BLOB, 8, ENDIANNESS)
-    data = FIAT_SHAMIR_PROTOCOL_DOMAIN + degree_poly + num_polys
+    data = FIAT_SHAMIR_PROTOCOL_DOMAIN + degree_poly + num_polynomials
 
     # Append each polynomial which is composed by field elements
-    for poly in polys:
+    for poly in polynomials:
         for field_element in poly:
             data += int.to_bytes(field_element, BYTES_PER_FIELD_ELEMENT, ENDIANNESS)
 
     # Append serialized G1 points
-    for commitment in comms:
+    for commitment in commitments:
         data += commitment
 
-    return bytes_to_bls_field(hash(data))
+    # Transcript has been prepared: time to create the challenges
+    hashed_data = hash(data)
+    r = hash(hashed_data + b'\x00')
+    r_powers = compute_powers(bytes_to_bls_field(r), len(commitments))
+    eval_challenge = hash(hashed_data + b'\x01')
+
+    return r_powers, bytes_to_bls_field(eval_challenge)
 ```
 
 #### `bls_modular_inverse`
@@ -234,7 +246,8 @@ def poly_lincomb(polys: Sequence[Polynomial],
     Given a list of ``polynomials``, interpret it as a 2D matrix and compute the linear combination
     of each column with `scalars`: return the resulting polynomials.
     """
-    result = [0] * len(polys[0])
+    assert len(polys) == len(scalars)
+    result = [0] * FIELD_ELEMENTS_PER_BLOB
     for v, s in zip(polys, scalars):
         for i, x in enumerate(v):
             result[i] = (result[i] + int(s) * int(x)) % BLS_MODULUS
@@ -256,6 +269,7 @@ def compute_powers(x: BLSFieldElement, n: uint64) -> Sequence[BLSFieldElement]:
     return powers
 ```
 
+
 ### Polynomials
 
 #### `evaluate_polynomial_in_evaluation_form`
@@ -367,14 +381,15 @@ def compute_aggregated_poly_and_commitment(
     """
     Return (1) the aggregated polynomial, (2) the aggregated KZG commitment,
     and (3) the polynomial evaluation random challenge.
+    This function should also work with blobs == [] and kzg_commitments == []
     """
+    assert len(blobs) == len(kzg_commitments)
+
     # Convert blobs to polynomials
     polynomials = [blob_to_polynomial(blob) for blob in blobs]
 
-    # Generate random linear combination challenges
+    # Generate random linear combination and evaluation challenges
-    r = hash_to_bls_field(polynomials, kzg_commitments)
+    r_powers, evaluation_challenge = compute_challenges(polynomials, kzg_commitments)
-    r_powers = compute_powers(r, len(kzg_commitments))
-    evaluation_challenge = int(r_powers[-1]) * r % BLS_MODULUS
 
     # Create aggregated polynomial in evaluation form
     aggregated_poly = Polynomial(poly_lincomb(polynomials, r_powers))
@@ -390,6 +405,7 @@ def compute_aggregated_poly_and_commitment(
 ```python
 def compute_aggregate_kzg_proof(blobs: Sequence[Blob]) -> KZGProof:
     """
+    Given a list of blobs, return the aggregated KZG proof that is used to verify them against their commitments.
     Public method.
     """
     commitments = [blob_to_kzg_commitment(blob) for blob in blobs]
@@ -407,6 +423,8 @@ def verify_aggregate_kzg_proof(blobs: Sequence[Blob],
                                expected_kzg_commitments: Sequence[KZGCommitment],
                                kzg_aggregated_proof: KZGProof) -> bool:
     """
+    Given a list of blobs and an aggregated KZG proof, verify that they correspond to the provided commitments.
+    
     Public method.
     """
     aggregated_poly, aggregated_poly_commitment, evaluation_challenge = compute_aggregated_poly_and_commitment(

tests/core/pyspec/eth2spec/test/eip4844/unittests/validator/test_validator.py

@@ -25,6 +25,12 @@ def _run_validate_blobs_sidecar_test(spec, state, blob_count):
     spec.validate_blobs_sidecar(block.slot, block.hash_tree_root(), expected_commitments, blobs_sidecar)
 
 
+@with_eip4844_and_later
+@spec_state_test
+def test_validate_blobs_sidecar_zero_blobs(spec, state):
+    _run_validate_blobs_sidecar_test(spec, state, blob_count=0)
+
+
 @with_eip4844_and_later
 @spec_state_test
 def test_validate_blobs_sidecar_one_blob(spec, state):