diff -uNr a/oauth2client/_pure_python_crypt.py b/oauth2client/_pure_python_crypt.py
--- a/oauth2client/_pure_python_crypt.py	2016-10-14 19:53:53.000000000 +0200
+++ b/oauth2client/_pure_python_crypt.py	2018-06-21 15:40:25.216478384 +0200
@@ -23,7 +23,10 @@
 from pyasn1_modules import pem
 from pyasn1_modules.rfc2459 import Certificate
 from pyasn1_modules.rfc5208 import PrivateKeyInfo
-import rsa
+from cryptography.hazmat.primitives import serialization, hashes
+from cryptography.hazmat.primitives.asymmetric import padding
+from cryptography import x509
+from cryptography.hazmat.backends import default_backend
 import six
 
 from oauth2client import _helpers
@@ -70,7 +73,8 @@
     """
 
     def __init__(self, pubkey):
-        self._pubkey = pubkey
+        self._pubkey = serialization.load_pem_public_key(pubkey,
+            backend=default_backend())
 
     def verify(self, message, signature):
         """Verifies a message against a signature.
@@ -87,8 +91,9 @@
         """
         message = _helpers._to_bytes(message, encoding='utf-8')
         try:
-            return rsa.pkcs1.verify(message, signature, self._pubkey)
-        except (ValueError, rsa.pkcs1.VerificationError):
+            return self._pubkey.verify(signature, message, padding.PKCS1v15(),
+                hashes.SHA256())
+        except (ValueError, TypeError, InvalidSignature):
             return False
 
     @classmethod
@@ -112,16 +117,18 @@
         """
         key_pem = _helpers._to_bytes(key_pem)
         if is_x509_cert:
-            der = rsa.pem.load_pem(key_pem, 'CERTIFICATE')
+            der = x509.load_pem_x509_certificate(pem_data, default_backend())
             asn1_cert, remaining = decoder.decode(der, asn1Spec=Certificate())
             if remaining != b'':
                 raise ValueError('Unused bytes', remaining)
 
             cert_info = asn1_cert['tbsCertificate']['subjectPublicKeyInfo']
             key_bytes = _bit_list_to_bytes(cert_info['subjectPublicKey'])
-            pubkey = rsa.PublicKey.load_pkcs1(key_bytes, 'DER')
+            pubkey = serialization.load_der_public_key(decoded_key,
+                backend=default_backend())
         else:
-            pubkey = rsa.PublicKey.load_pkcs1(key_pem, 'PEM')
+            pubkey = serialization.load_pem_public_key(decoded_key,
+                backend=default_backend())
         return cls(pubkey)
 
 
@@ -134,6 +141,8 @@
 
     def __init__(self, pkey):
         self._key = pkey
+        self._pubkey = serialization.load_pem_private_key(pkey,
+            backend=default_backend())
 
     def sign(self, message):
         """Signs a message.
@@ -145,7 +154,7 @@
             string, The signature of the message for the given key.
         """
         message = _helpers._to_bytes(message, encoding='utf-8')
-        return rsa.pkcs1.sign(message, self._key, 'SHA-256')
+        return self._key.sign(message, padding.PKCS1v15(), hashes.SHA256())
 
     @classmethod
     def from_string(cls, key, password='notasecret'):
@@ -168,16 +177,19 @@
             six.StringIO(key), _PKCS1_MARKER, _PKCS8_MARKER)
 
         if marker_id == 0:
-            pkey = rsa.key.PrivateKey.load_pkcs1(key_bytes,
-                                                 format='DER')
+            pkey = serialization.load_der_private_key(
+                key_bytes, password=None,
+                backend=default_backend())
+
         elif marker_id == 1:
             key_info, remaining = decoder.decode(
                 key_bytes, asn1Spec=_PKCS8_SPEC)
             if remaining != b'':
                 raise ValueError('Unused bytes', remaining)
             pkey_info = key_info.getComponentByName('privateKey')
-            pkey = rsa.key.PrivateKey.load_pkcs1(pkey_info.asOctets(),
-                                                 format='DER')
+            pkey = serialization.load_der_private_key(
+                pkey_info.asOctets(), password=None,
+                backend=default_backend())
         else:
             raise ValueError('No key could be detected.')