diff --git a/bip32/bip32.py b/bip32/bip32.py
index 7dcc026..ba68366 100644
--- a/bip32/bip32.py
+++ b/bip32/bip32.py
@@ -12,6 +12,8 @@
     _hardened_index_in_path,
     _privkey_to_pubkey,
     _deriv_path_str_to_list,
+    _pubkey_is_valid,
+    _privkey_is_valid,
 )
 
 
@@ -28,6 +30,11 @@ def __init__(self, message):
         self.message = message
 
 
+class ParsingError(ValueError):
+    def __init__(self, message):
+        self.message = message
+
+
 class BIP32:
     def __init__(
         self,
@@ -65,9 +72,13 @@ def __init__(
         if privkey is not None:
             if not isinstance(privkey, bytes):
                 raise InvalidInputError("'privkey' must be bytes")
+            if not _privkey_is_valid(privkey):
+                raise InvalidInputError("Invalid secp256k1 private key")
         if pubkey is not None:
             if not isinstance(pubkey, bytes):
                 raise InvalidInputError("'pubkey' must be bytes")
+            if not _pubkey_is_valid(pubkey):
+                raise InvalidInputError("Invalid secp256k1 public key")
         else:
             pubkey = _privkey_to_pubkey(privkey)
 
@@ -268,6 +279,23 @@ def from_xpriv(cls, xpriv):
             chaincode,
             key,
         ) = _unserialize_extended_key(extended_key)
+
+        if key[0] != 0:
+            raise ParsingError("Invalid xpriv: private key prefix must be 0")
+
+        if depth == 0:
+            if fingerprint != b"\x00\x00\x00\x00":
+                raise ParsingError(
+                    "Invalid xpriv: fingerprint must be 0 if depth is 0 (master xpriv)"
+                )
+            if index != 0:
+                raise ParsingError(
+                    "Invalid xpriv: index must be 0 if depth is 0 (master xpriv)"
+                )
+
+        if network is None:
+            raise ParsingError("Invalid xpriv: unknown network")
+
         # We need to remove the trailing `0` before the actual private key !!
         return BIP32(chaincode, key[1:], None, fingerprint, depth, index, network)
 
@@ -289,7 +317,24 @@ def from_xpub(cls, xpub):
             chaincode,
             key,
         ) = _unserialize_extended_key(extended_key)
-        return BIP32(chaincode, None, key, fingerprint, depth, index, network)
+
+        if depth == 0:
+            if fingerprint != b"\x00\x00\x00\x00":
+                raise ParsingError(
+                    "Invalid xpub: fingerprint must be 0 if depth is 0 (master xpub)"
+                )
+            if index != 0:
+                raise ParsingError(
+                    "Invalid xpub: index must be 0 if depth is 0 (master xpub)"
+                )
+
+        if network is None:
+            raise ParsingError("Invalid xpub: unknown network")
+
+        try:
+            return BIP32(chaincode, None, key, fingerprint, depth, index, network)
+        except InvalidInputError as e:
+            raise ParsingError(f"Invalid xpub: '{e}'")
 
     @classmethod
     def from_seed(cls, seed, network="main"):
diff --git a/bip32/utils.py b/bip32/utils.py
index 6c1ce41..9601992 100644
--- a/bip32/utils.py
+++ b/bip32/utils.py
@@ -22,6 +22,24 @@ class BIP32DerivationError(Exception):
     """We derived an invalid (secret > N or point(secret) is infinity) key!"""
 
 
+def _privkey_is_valid(privkey):
+    """Takes bytes and returns True if it's a valid secp256k1 privkey"""
+    try:
+        coincurve.PrivateKey(privkey)
+        return True
+    except ValueError:
+        return False
+
+
+def _pubkey_is_valid(pubkey):
+    """Takes bytes and returns True if it's a valid secp256k1 pubkey"""
+    try:
+        coincurve.PublicKey(pubkey)
+        return True
+    except ValueError:
+        return False
+
+
 def _privkey_to_pubkey(privkey):
     """Takes a 32 bytes privkey and returns a 33 bytes secp256k1 pubkey"""
     return coincurve.PublicKey.from_secret(privkey).format()
@@ -167,9 +185,10 @@ def _unserialize_extended_key(extended_key):
     """
     assert isinstance(extended_key, bytes) and len(extended_key) == 78
     prefix = int.from_bytes(extended_key[:4], "big")
+    network = None
     if prefix in list(ENCODING_PREFIX["main"].values()):
         network = "main"
-    else:
+    elif prefix in list(ENCODING_PREFIX["test"].values()):
         network = "test"
     depth = extended_key[4]
     fingerprint = extended_key[5:9]
diff --git a/tests/test_bip32.py b/tests/test_bip32.py
index 7cd93ff..fc04b8f 100644
--- a/tests/test_bip32.py
+++ b/tests/test_bip32.py
@@ -272,6 +272,38 @@ def test_vector_4():
     )
 
 
+def test_vector_5():
+    invalid_xpubs = [
+        "xpub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6LBpB85b3D2yc8sfvZU521AAwdZafEz7mnzBBsz4wKY5fTtTQBm",
+        "xpub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6Txnt3siSujt9RCVYsx4qHZGc62TG4McvMGcAUjeuwZdduYEvFn",
+        "xpub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6N8ZMMXctdiCjxTNq964yKkwrkBJJwpzZS4HS2fxvyYUA4q2Xe4",
+        "xpub661no6RGEX3uJkY4bNnPcw4URcQTrSibUZ4NqJEw5eBkv7ovTwgiT91XX27VbEXGENhYRCf7hyEbWrR3FewATdCEebj6znwMfQkhRYHRLpJ",
+        "xpub661MyMwAuDcm6CRQ5N4qiHKrJ39Xe1R1NyfouMKTTWcguwVcfrZJaNvhpebzGerh7gucBvzEQWRugZDuDXjNDRmXzSZe4c7mnTK97pTvGS8",
+        "DMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHGMQzT7ayAmfo4z3gY5KfbrZWZ6St24UVf2Qgo6oujFktLHdHY4",
+        "DMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHPmHJiEDXkTiJTVV9rHEBUem2mwVbbNfvT2MTcAqj3nesx8uBf9",
+        "xpub661MyMwAqRbcEYS8w7XLSVeEsBXy79zSzH1J8vCdxAZningWLdN3zgtU6Q5JXayek4PRsn35jii4veMimro1xefsM58PgBMrvdYre8QyULY",
+    ]
+    for xpub in invalid_xpubs:
+        with pytest.raises(ValueError):
+            BIP32.from_xpub(xpub)
+
+    invalid_xprivs = [
+        "xprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHL",
+        "xprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzF93Y5wvzdUayhgkkFoicQZcP3y52uPPxFnfoLZB21Teqt1VvEHx",
+        "xprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFAzHGBP2UuGCqWLTAPLcMtD5SDKr24z3aiUvKr9bJpdrcLg1y3G",
+        "xprv9s21ZrQH4r4TsiLvyLXqM9P7k1K3EYhA1kkD6xuquB5i39AU8KF42acDyL3qsDbU9NmZn6MsGSUYZEsuoePmjzsB3eFKSUEh3Gu1N3cqVUN",
+        "xprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFAzHGBP2UuGCqWLTAPLcMtD9y5gkZ6Eq3Rjuahrv17fEQ3Qen6J",
+        "xprv9s2SPatNQ9Vc6GTbVMFPFo7jsaZySyzk7L8n2uqKXJen3KUmvQNTuLh3fhZMBoG3G4ZW1N2kZuHEPY53qmbZzCHshoQnNf4GvELZfqTUrcv",
+        "xprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFGpWnsj83BHtEy5Zt8CcDr1UiRXuWCmTQLxEK9vbz5gPstX92JQ",
+        "xprv9s21ZrQH143K24Mfq5zL5MhWK9hUhhGbd45hLXo2Pq2oqzMMo63oStZzFGTQQD3dC4H2D5GBj7vWvSQaaBv5cxi9gafk7NF3pnBju6dwKvH",
+        "DMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHGMQzT7ayAmfo4z3gY5KfbrZWZ6St24UVf2Qgo6oujFktLHdHY4",
+        "DMwo58pR1QLEFihHiXPVykYB6fJmsTeHvyTp7hRThAtCX8CvYzgPcn8XnmdfHPmHJiEDXkTiJTVV9rHEBUem2mwVbbNfvT2MTcAqj3nesx8uBf9",
+    ]
+    for xpriv in invalid_xprivs:
+        with pytest.raises(ValueError):
+            BIP32.from_xpriv(xpriv)
+
+
 def test_sanity_checks():
     seed = bytes.fromhex(
         "1077a46dc8545d372f22d9e110ae6c5c2bf7620fe9c4c911f5404d112233e1aa270567dd3554092e051ba3ba86c303590b0309116ac89964ff284db2219d7511"