diff --git a/EIPS/eip-4844.md b/EIPS/eip-4844.md
index 719b81048c76e1..ca4934b1420efb 100644
--- a/EIPS/eip-4844.md
+++ b/EIPS/eip-4844.md
@@ -79,15 +79,17 @@ Compared to full data sharding, this EIP has a reduced cap on the number of thes
 Converts a blob to its corresponding KZG point:
 
 ```python
+def lincomb(points: List[KZGCommitment], scalars: List[BLSFieldElement]) -> KZGCommitment:
+    """
+    BLS multiscalar multiplication. This function can be optimized using Pippenger's algorithm and variants.
+    """
+    r = bls.Z1
+    for x, a in zip(points, scalars):
+        r = bls.add(r, bls.multiply(x, a))
+    return r
+
 def blob_to_kzg(blob: Blob) -> KZGCommitment:
-    computed_kzg = bls.Z1
-    for value, point_kzg in zip(blob, KZG_SETUP_LAGRANGE):
-        assert value < BLS_MODULUS
-        computed_kzg = bls.add(
-            computed_kzg,
-            bls.multiply(point_kzg, value)
-        )
-    return computed_kzg
+    return lincomb(blob, KZG_SETUP_LAGRANGE)
 ```
 
 Converts a KZG point into a versioned hash:
@@ -379,6 +381,24 @@ def hash_to_bls_field(x: Container) -> BLSFieldElement:
     return int.from_bytes(hash_tree_root(x), "little") % BLS_MODULUS
 
 
+def compute_powers(x: BLSFieldElement, n: uint64) -> List[BLSFieldElement]:
+    current_power = 1
+    powers = []
+    for _ in range(n):
+        powers.append(BLSFieldElement(current_power))
+        current_power = current_power * int(x) % BLS_MODULUS
+    return powers
+
+def vector_lincomb(vectors: List[List[BLSFieldElement]], scalars: List[BLSFieldElement]) -> List[BLSFieldElement]:
+    """
+    Given a list of vectors, compute the linear combination of each column with `scalars`, and return the resulting
+    vector.
+    """
+    r = [0]*len(vectors[0])
+    for v, a in zip(vectors, scalars):
+        for i, x in enumerate(v):
+            r[i] = (r[i] + a * x) % BLS_MODULUS
+    return [BLSFieldElement(x) for x in r]
 
 def validate_blob_transaction_wrapper(wrapper: BlobTransactionNetworkWrapper):
     versioned_hashes = wrapper.tx.message.blob_versioned_hashes