diff --git a/setup.py b/setup.py
index 350f4aedd..451da1b73 100644
--- a/setup.py
+++ b/setup.py
@@ -537,7 +537,7 @@ setup(
         "eth-typing>=2.1.0,<3.0.0",
         "pycryptodome==3.9.4",
         "py_ecc==5.0.0",
-        "milagro_bls_binding==1.3.0",
+        "milagro_bls_binding==1.4.0",
         "dataclasses==0.6",
         "remerkleable==0.1.17",
         "ruamel.yaml==0.16.5",
diff --git a/tests/core/pyspec/eth2spec/utils/bls.py b/tests/core/pyspec/eth2spec/utils/bls.py
index dd3172b4b..88edbac61 100644
--- a/tests/core/pyspec/eth2spec/utils/bls.py
+++ b/tests/core/pyspec/eth2spec/utils/bls.py
@@ -10,6 +10,7 @@ bls = py_ecc_bls
 
 STUB_SIGNATURE = b'\x11' * 96
 STUB_PUBKEY = b'\x22' * 48
+Z1_PUBKEY = b'\xc0' + b'\x00' * 47
 Z2_SIGNATURE = b'\xc0' + b'\x00' * 95
 STUB_COORDINATES = _signature_to_G2(Z2_SIGNATURE)
 
@@ -66,6 +67,11 @@ def AggregateVerify(pubkeys, messages, signature):
 
 @only_with_bls(alt_return=True)
 def FastAggregateVerify(pubkeys, message, signature):
+    # TODO: remove it when milagro_bls_binding is fixed
+    # https://github.com/ChihChengLiang/milagro_bls_binding/issues/19
+    if Z1_PUBKEY in pubkeys:
+        return False
+
     try:
         result = bls.FastAggregateVerify(list(pubkeys), message, signature)
     except Exception:
@@ -81,6 +87,9 @@ def Aggregate(signatures):
 
 @only_with_bls(alt_return=STUB_SIGNATURE)
 def Sign(SK, message):
+    # TODO: remove it when https://github.com/sigp/milagro_bls/issues/39 is fixed
+    if SK == 0:
+        raise Exception("SK should not be zero")
     if bls == py_ecc_bls:
         return bls.Sign(SK, message)
     else:
diff --git a/tests/generators/bls/main.py b/tests/generators/bls/main.py
index 32edc1c41..8cdc2a94b 100644
--- a/tests/generators/bls/main.py
+++ b/tests/generators/bls/main.py
@@ -83,7 +83,8 @@ def case01_sign():
             }
     # Edge case: privkey == 0
     expect_exception(bls.Sign, ZERO_PRIVKEY, message)
-    # expect_exception(milagro_bls.Sign, ZERO_PRIVKEY_BYTES, message)  # TODO: enable it when milagro is ready
+    # TODO enable it when milagro_bls is ready for IETF BLS draft 04
+    # expect_exception(milagro_bls.Sign, ZERO_PRIVKEY_BYTES, message)
     yield f'sign_case_zero_privkey', {
         'input': {
             'privkey': encode_hex(ZERO_PRIVKEY_BYTES),
@@ -147,7 +148,7 @@ def case02_verify():
 
     # Invalid pubkey and signature with the point at infinity
     assert not bls.Verify(Z1_PUBKEY, SAMPLE_MESSAGE, Z2_SIGNATURE)
-    # assert not milagro_bls.Verify(Z1_PUBKEY, SAMPLE_MESSAGE, Z2_SIGNATURE)  # TODO: enable it when milagro is ready
+    assert not milagro_bls.Verify(Z1_PUBKEY, SAMPLE_MESSAGE, Z2_SIGNATURE)
     yield f'verify_infinity_pubkey_and_infinity_signature', {
         'input': {
             'pubkey': encode_hex(Z1_PUBKEY),
@@ -266,7 +267,7 @@ def case04_fast_aggregate_verify():
     signatures = [bls.Sign(privkey, SAMPLE_MESSAGE) for privkey in PRIVKEYS]
     aggregate_signature = bls.Aggregate(signatures)
     assert not bls.FastAggregateVerify(pubkeys_with_infinity, SAMPLE_MESSAGE, aggregate_signature)
-    # TODO: enable it when milagro is ready
+    # TODO enable it when milagro_bls is ready for IETF BLS draft 04
     # assert not milagro_bls.FastAggregateVerify(pubkeys_with_infinity, SAMPLE_MESSAGE, aggregate_signature)
     yield f'fast_aggregate_verify_infinity_pubkey', {
         'input': {
@@ -345,8 +346,7 @@ def case05_aggregate_verify():
     pubkeys_with_infinity = pubkeys + [Z1_PUBKEY]
     messages_with_sample = messages + [SAMPLE_MESSAGE]
     assert not bls.AggregateVerify(pubkeys_with_infinity, messages_with_sample, aggregate_signature)
-    # TODO: enable it when milagro is ready
-    # assert not milagro_bls.AggregateVerify(pubkeys_with_infinity, messages_with_sample, aggregate_signature)
+    assert not milagro_bls.AggregateVerify(pubkeys_with_infinity, messages_with_sample, aggregate_signature)
     yield f'aggregate_verify_infinity_pubkey', {
         'input': {
             'pubkeys': [encode_hex(pubkey) for pubkey in pubkeys_with_infinity],