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+# Copyright 2016 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#      http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Pure-Python RSA cryptography implementation.
+
+Uses the ``rsa``, ``pyasn1`` and ``pyasn1_modules`` packages
+to parse PEM files storing PKCS#1 or PKCS#8 keys as well as
+certificates. There is no support for p12 files.
+"""
+
+from __future__ import absolute_import
+
+import io
+
+from pyasn1.codec.der import decoder  # type: ignore
+from pyasn1_modules import pem  # type: ignore
+from pyasn1_modules.rfc2459 import Certificate  # type: ignore
+from pyasn1_modules.rfc5208 import PrivateKeyInfo  # type: ignore
+import rsa  # type: ignore
+
+from google.auth import _helpers
+from google.auth import exceptions
+from google.auth.crypt import base
+
+_POW2 = (128, 64, 32, 16, 8, 4, 2, 1)
+_CERTIFICATE_MARKER = b"-----BEGIN CERTIFICATE-----"
+_PKCS1_MARKER = ("-----BEGIN RSA PRIVATE KEY-----", "-----END RSA PRIVATE KEY-----")
+_PKCS8_MARKER = ("-----BEGIN PRIVATE KEY-----", "-----END PRIVATE KEY-----")
+_PKCS8_SPEC = PrivateKeyInfo()
+
+
+def _bit_list_to_bytes(bit_list):
+    """Converts an iterable of 1s and 0s to bytes.
+
+    Combines the list 8 at a time, treating each group of 8 bits
+    as a single byte.
+
+    Args:
+        bit_list (Sequence): Sequence of 1s and 0s.
+
+    Returns:
+        bytes: The decoded bytes.
+    """
+    num_bits = len(bit_list)
+    byte_vals = bytearray()
+    for start in range(0, num_bits, 8):
+        curr_bits = bit_list[start : start + 8]
+        char_val = sum(val * digit for val, digit in zip(_POW2, curr_bits))
+        byte_vals.append(char_val)
+    return bytes(byte_vals)
+
+
+class RSAVerifier(base.Verifier):
+    """Verifies RSA cryptographic signatures using public keys.
+
+    Args:
+        public_key (rsa.key.PublicKey): The public key used to verify
+            signatures.
+    """
+
+    def __init__(self, public_key):
+        self._pubkey = public_key
+
+    @_helpers.copy_docstring(base.Verifier)
+    def verify(self, message, signature):
+        message = _helpers.to_bytes(message)
+        try:
+            return rsa.pkcs1.verify(message, signature, self._pubkey)
+        except (ValueError, rsa.pkcs1.VerificationError):
+            return False
+
+    @classmethod
+    def from_string(cls, public_key):
+        """Construct an Verifier instance from a public key or public
+        certificate string.
+
+        Args:
+            public_key (Union[str, bytes]): The public key in PEM format or the
+                x509 public key certificate.
+
+        Returns:
+            google.auth.crypt._python_rsa.RSAVerifier: The constructed verifier.
+
+        Raises:
+            ValueError: If the public_key can't be parsed.
+        """
+        public_key = _helpers.to_bytes(public_key)
+        is_x509_cert = _CERTIFICATE_MARKER in public_key
+
+        # If this is a certificate, extract the public key info.
+        if is_x509_cert:
+            der = rsa.pem.load_pem(public_key, "CERTIFICATE")
+            asn1_cert, remaining = decoder.decode(der, asn1Spec=Certificate())
+            if remaining != b"":
+                raise exceptions.InvalidValue("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")
+        else:
+            pubkey = rsa.PublicKey.load_pkcs1(public_key, "PEM")
+        return cls(pubkey)
+
+
+class RSASigner(base.Signer, base.FromServiceAccountMixin):
+    """Signs messages with an RSA private key.
+
+    Args:
+        private_key (rsa.key.PrivateKey): The private key to sign with.
+        key_id (str): Optional key ID used to identify this private key. This
+            can be useful to associate the private key with its associated
+            public key or certificate.
+    """
+
+    def __init__(self, private_key, key_id=None):
+        self._key = private_key
+        self._key_id = key_id
+
+    @property  # type: ignore
+    @_helpers.copy_docstring(base.Signer)
+    def key_id(self):
+        return self._key_id
+
+    @_helpers.copy_docstring(base.Signer)
+    def sign(self, message):
+        message = _helpers.to_bytes(message)
+        return rsa.pkcs1.sign(message, self._key, "SHA-256")
+
+    @classmethod
+    def from_string(cls, key, key_id=None):
+        """Construct an Signer instance from a private key in PEM format.
+
+        Args:
+            key (str): Private key in PEM format.
+            key_id (str): An optional key id used to identify the private key.
+
+        Returns:
+            google.auth.crypt.Signer: The constructed signer.
+
+        Raises:
+            ValueError: If the key cannot be parsed as PKCS#1 or PKCS#8 in
+                PEM format.
+        """
+        key = _helpers.from_bytes(key)  # PEM expects str in Python 3
+        marker_id, key_bytes = pem.readPemBlocksFromFile(
+            io.StringIO(key), _PKCS1_MARKER, _PKCS8_MARKER
+        )
+
+        # Key is in pkcs1 format.
+        if marker_id == 0:
+            private_key = rsa.key.PrivateKey.load_pkcs1(key_bytes, format="DER")
+        # Key is in pkcs8.
+        elif marker_id == 1:
+            key_info, remaining = decoder.decode(key_bytes, asn1Spec=_PKCS8_SPEC)
+            if remaining != b"":
+                raise exceptions.InvalidValue("Unused bytes", remaining)
+            private_key_info = key_info.getComponentByName("privateKey")
+            private_key = rsa.key.PrivateKey.load_pkcs1(
+                private_key_info.asOctets(), format="DER"
+            )
+        else:
+            raise exceptions.MalformedError("No key could be detected.")
+
+        return cls(private_key, key_id=key_id)