[catapult] - Copy Telemetry's gsutilz over to third_party.

third_party/gsutil/third_party/rsa/rsa/key.py

Index: third_party/gsutil/third_party/rsa/rsa/key.py
diff --git a/third_party/gsutil/third_party/rsa/rsa/key.py b/third_party/gsutil/third_party/rsa/rsa/key.py
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+# -*- coding: utf-8 -*-
+#
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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.
+
+'''RSA key generation code.
+
+Create new keys with the newkeys() function. It will give you a PublicKey and a
+PrivateKey object.
+
+Loading and saving keys requires the pyasn1 module. This module is imported as
+late as possible, such that other functionality will remain working in absence
+of pyasn1.
+
+'''
+
+import logging
+from rsa._compat import b, bytes_type
+
+import rsa.prime
+import rsa.pem
+import rsa.common
+
+log = logging.getLogger(__name__)
+
+
+
+class AbstractKey(object):
+    '''Abstract superclass for private and public keys.'''
+
+    @classmethod
+    def load_pkcs1(cls, keyfile, format='PEM'):
+        r'''Loads a key in PKCS#1 DER or PEM format.
+
+        :param keyfile: contents of a DER- or PEM-encoded file that contains
+            the public key.
+        :param format: the format of the file to load; 'PEM' or 'DER'
+
+        :return: a PublicKey object
+
+        '''
+
+        methods = {
+            'PEM': cls._load_pkcs1_pem,
+            'DER': cls._load_pkcs1_der,
+        }
+
+        if format not in methods:
+            formats = ', '.join(sorted(methods.keys()))
+            raise ValueError('Unsupported format: %r, try one of %s' % (format,
+                formats))
+
+        method = methods[format]
+        return method(keyfile)
+
+    def save_pkcs1(self, format='PEM'):
+        '''Saves the public key in PKCS#1 DER or PEM format.
+
+        :param format: the format to save; 'PEM' or 'DER'
+        :returns: the DER- or PEM-encoded public key.
+
+        '''
+
+        methods = {
+            'PEM': self._save_pkcs1_pem,
+            'DER': self._save_pkcs1_der,
+        }
+
+        if format not in methods:
+            formats = ', '.join(sorted(methods.keys()))
+            raise ValueError('Unsupported format: %r, try one of %s' % (format,
+                formats))
+
+        method = methods[format]
+        return method()
+
+class PublicKey(AbstractKey):
+    '''Represents a public RSA key.
+
+    This key is also known as the 'encryption key'. It contains the 'n' and 'e'
+    values.
+
+    Supports attributes as well as dictionary-like access. Attribute accesss is
+    faster, though.
+
+    >>> PublicKey(5, 3)
+    PublicKey(5, 3)
+
+    >>> key = PublicKey(5, 3)
+    >>> key.n
+    5
+    >>> key['n']
+    5
+    >>> key.e
+    3
+    >>> key['e']
+    3
+
+    '''
+
+    __slots__ = ('n', 'e')
+
+    def __init__(self, n, e):
+        self.n = n
+        self.e = e
+
+    def __getitem__(self, key):
+        return getattr(self, key)
+
+    def __repr__(self):
+        return 'PublicKey(%i, %i)' % (self.n, self.e)
+
+    def __eq__(self, other):
+        if other is None:
+            return False
+
+        if not isinstance(other, PublicKey):
+            return False
+
+        return self.n == other.n and self.e == other.e
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    @classmethod
+    def _load_pkcs1_der(cls, keyfile):
+        r'''Loads a key in PKCS#1 DER format.
+
+        @param keyfile: contents of a DER-encoded file that contains the public
+            key.
+        @return: a PublicKey object
+
+        First let's construct a DER encoded key:
+
+        >>> import base64
+        >>> b64der = 'MAwCBQCNGmYtAgMBAAE='
+        >>> der = base64.decodestring(b64der)
+
+        This loads the file:
+
+        >>> PublicKey._load_pkcs1_der(der)
+        PublicKey(2367317549, 65537)
+
+        '''
+
+        from pyasn1.codec.der import decoder
+        from rsa.asn1 import AsnPubKey
+        
+        (priv, _) = decoder.decode(keyfile, asn1Spec=AsnPubKey())
+        return cls(n=int(priv['modulus']), e=int(priv['publicExponent']))
+
+    def _save_pkcs1_der(self):
+        '''Saves the public key in PKCS#1 DER format.
+
+        @returns: the DER-encoded public key.
+        '''
+
+        from pyasn1.codec.der import encoder
+        from rsa.asn1 import AsnPubKey
+
+        # Create the ASN object
+        asn_key = AsnPubKey()
+        asn_key.setComponentByName('modulus', self.n)
+        asn_key.setComponentByName('publicExponent', self.e)
+
+        return encoder.encode(asn_key)
+
+    @classmethod
+    def _load_pkcs1_pem(cls, keyfile):
+        '''Loads a PKCS#1 PEM-encoded public key file.
+
+        The contents of the file before the "-----BEGIN RSA PUBLIC KEY-----" and
+        after the "-----END RSA PUBLIC KEY-----" lines is ignored.
+
+        @param keyfile: contents of a PEM-encoded file that contains the public
+            key.
+        @return: a PublicKey object
+        '''
+
+        der = rsa.pem.load_pem(keyfile, 'RSA PUBLIC KEY')
+        return cls._load_pkcs1_der(der)
+
+    def _save_pkcs1_pem(self):
+        '''Saves a PKCS#1 PEM-encoded public key file.
+
+        @return: contents of a PEM-encoded file that contains the public key.
+        '''
+
+        der = self._save_pkcs1_der()
+        return rsa.pem.save_pem(der, 'RSA PUBLIC KEY')
+
+    @classmethod
+    def load_pkcs1_openssl_pem(cls, keyfile):
+        '''Loads a PKCS#1.5 PEM-encoded public key file from OpenSSL.
+        
+        These files can be recognised in that they start with BEGIN PUBLIC KEY
+        rather than BEGIN RSA PUBLIC KEY.
+        
+        The contents of the file before the "-----BEGIN PUBLIC KEY-----" and
+        after the "-----END PUBLIC KEY-----" lines is ignored.
+
+        @param keyfile: contents of a PEM-encoded file that contains the public
+            key, from OpenSSL.
+        @return: a PublicKey object
+        '''
+
+        der = rsa.pem.load_pem(keyfile, 'PUBLIC KEY')
+        return cls.load_pkcs1_openssl_der(der)
+
+    @classmethod
+    def load_pkcs1_openssl_der(cls, keyfile):
+        '''Loads a PKCS#1 DER-encoded public key file from OpenSSL.
+
+        @param keyfile: contents of a DER-encoded file that contains the public
+            key, from OpenSSL.
+        @return: a PublicKey object
+        '''
+    
+        from rsa.asn1 import OpenSSLPubKey
+        from pyasn1.codec.der import decoder
+        from pyasn1.type import univ
+        
+        (keyinfo, _) = decoder.decode(keyfile, asn1Spec=OpenSSLPubKey())
+        
+        if keyinfo['header']['oid'] != univ.ObjectIdentifier('1.2.840.113549.1.1.1'):
+            raise TypeError("This is not a DER-encoded OpenSSL-compatible public key")
+                
+        return cls._load_pkcs1_der(keyinfo['key'][1:])
+        
+        
+
+
+class PrivateKey(AbstractKey):
+    '''Represents a private RSA key.
+
+    This key is also known as the 'decryption key'. It contains the 'n', 'e',
+    'd', 'p', 'q' and other values.
+
+    Supports attributes as well as dictionary-like access. Attribute accesss is
+    faster, though.
+
+    >>> PrivateKey(3247, 65537, 833, 191, 17)
+    PrivateKey(3247, 65537, 833, 191, 17)
+
+    exp1, exp2 and coef don't have to be given, they will be calculated:
+
+    >>> pk = PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
+    >>> pk.exp1
+    55063
+    >>> pk.exp2
+    10095
+    >>> pk.coef
+    50797
+
+    If you give exp1, exp2 or coef, they will be used as-is:
+
+    >>> pk = PrivateKey(1, 2, 3, 4, 5, 6, 7, 8)
+    >>> pk.exp1
+    6
+    >>> pk.exp2
+    7
+    >>> pk.coef
+    8
+
+    '''
+
+    __slots__ = ('n', 'e', 'd', 'p', 'q', 'exp1', 'exp2', 'coef')
+
+    def __init__(self, n, e, d, p, q, exp1=None, exp2=None, coef=None):
+        self.n = n
+        self.e = e
+        self.d = d
+        self.p = p
+        self.q = q
+
+        # Calculate the other values if they aren't supplied
+        if exp1 is None:
+            self.exp1 = int(d % (p - 1))
+        else:
+            self.exp1 = exp1
+
+        if exp1 is None:
+            self.exp2 = int(d % (q - 1))
+        else:
+            self.exp2 = exp2
+
+        if coef is None:
+            self.coef = rsa.common.inverse(q, p)
+        else:
+            self.coef = coef
+
+    def __getitem__(self, key):
+        return getattr(self, key)
+
+    def __repr__(self):
+        return 'PrivateKey(%(n)i, %(e)i, %(d)i, %(p)i, %(q)i)' % self
+
+    def __eq__(self, other):
+        if other is None:
+            return False
+
+        if not isinstance(other, PrivateKey):
+            return False
+
+        return (self.n == other.n and
+            self.e == other.e and
+            self.d == other.d and
+            self.p == other.p and
+            self.q == other.q and
+            self.exp1 == other.exp1 and
+            self.exp2 == other.exp2 and
+            self.coef == other.coef)
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    @classmethod
+    def _load_pkcs1_der(cls, keyfile):
+        r'''Loads a key in PKCS#1 DER format.
+
+        @param keyfile: contents of a DER-encoded file that contains the private
+            key.
+        @return: a PrivateKey object
+
+        First let's construct a DER encoded key:
+
+        >>> import base64
+        >>> b64der = 'MC4CAQACBQDeKYlRAgMBAAECBQDHn4npAgMA/icCAwDfxwIDANcXAgInbwIDAMZt'
+        >>> der = base64.decodestring(b64der)
+
+        This loads the file:
+
+        >>> PrivateKey._load_pkcs1_der(der)
+        PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
+
+        '''
+
+        from pyasn1.codec.der import decoder
+        (priv, _) = decoder.decode(keyfile)
+
+        # ASN.1 contents of DER encoded private key:
+        #
+        # RSAPrivateKey ::= SEQUENCE {
+        #     version           Version, 
+        #     modulus           INTEGER,  -- n
+        #     publicExponent    INTEGER,  -- e
+        #     privateExponent   INTEGER,  -- d
+        #     prime1            INTEGER,  -- p
+        #     prime2            INTEGER,  -- q
+        #     exponent1         INTEGER,  -- d mod (p-1)
+        #     exponent2         INTEGER,  -- d mod (q-1) 
+        #     coefficient       INTEGER,  -- (inverse of q) mod p
+        #     otherPrimeInfos   OtherPrimeInfos OPTIONAL 
+        # }
+
+        if priv[0] != 0:
+            raise ValueError('Unable to read this file, version %s != 0' % priv[0])
+
+        as_ints = tuple(int(x) for x in priv[1:9])
+        return cls(*as_ints)
+
+    def _save_pkcs1_der(self):
+        '''Saves the private key in PKCS#1 DER format.
+
+        @returns: the DER-encoded private key.
+        '''
+
+        from pyasn1.type import univ, namedtype
+        from pyasn1.codec.der import encoder
+
+        class AsnPrivKey(univ.Sequence):
+            componentType = namedtype.NamedTypes(
+                namedtype.NamedType('version', univ.Integer()),
+                namedtype.NamedType('modulus', univ.Integer()),
+                namedtype.NamedType('publicExponent', univ.Integer()),
+                namedtype.NamedType('privateExponent', univ.Integer()),
+                namedtype.NamedType('prime1', univ.Integer()),
+                namedtype.NamedType('prime2', univ.Integer()),
+                namedtype.NamedType('exponent1', univ.Integer()),
+                namedtype.NamedType('exponent2', univ.Integer()),
+                namedtype.NamedType('coefficient', univ.Integer()),
+            )
+
+        # Create the ASN object
+        asn_key = AsnPrivKey()
+        asn_key.setComponentByName('version', 0)
+        asn_key.setComponentByName('modulus', self.n)
+        asn_key.setComponentByName('publicExponent', self.e)
+        asn_key.setComponentByName('privateExponent', self.d)
+        asn_key.setComponentByName('prime1', self.p)
+        asn_key.setComponentByName('prime2', self.q)
+        asn_key.setComponentByName('exponent1', self.exp1)
+        asn_key.setComponentByName('exponent2', self.exp2)
+        asn_key.setComponentByName('coefficient', self.coef)
+
+        return encoder.encode(asn_key)
+
+    @classmethod
+    def _load_pkcs1_pem(cls, keyfile):
+        '''Loads a PKCS#1 PEM-encoded private key file.
+
+        The contents of the file before the "-----BEGIN RSA PRIVATE KEY-----" and
+        after the "-----END RSA PRIVATE KEY-----" lines is ignored.
+
+        @param keyfile: contents of a PEM-encoded file that contains the private
+            key.
+        @return: a PrivateKey object
+        '''
+
+        der = rsa.pem.load_pem(keyfile, b('RSA PRIVATE KEY'))
+        return cls._load_pkcs1_der(der)
+
+    def _save_pkcs1_pem(self):
+        '''Saves a PKCS#1 PEM-encoded private key file.
+
+        @return: contents of a PEM-encoded file that contains the private key.
+        '''
+
+        der = self._save_pkcs1_der()
+        return rsa.pem.save_pem(der, b('RSA PRIVATE KEY'))
+
+def find_p_q(nbits, getprime_func=rsa.prime.getprime, accurate=True):
+    ''''Returns a tuple of two different primes of nbits bits each.
+    
+    The resulting p * q has exacty 2 * nbits bits, and the returned p and q
+    will not be equal.
+
+    :param nbits: the number of bits in each of p and q.
+    :param getprime_func: the getprime function, defaults to
+        :py:func:`rsa.prime.getprime`.
+
+        *Introduced in Python-RSA 3.1*
+
+    :param accurate: whether to enable accurate mode or not.
+    :returns: (p, q), where p > q
+
+    >>> (p, q) = find_p_q(128)
+    >>> from rsa import common
+    >>> common.bit_size(p * q)
+    256
+
+    When not in accurate mode, the number of bits can be slightly less
+
+    >>> (p, q) = find_p_q(128, accurate=False)
+    >>> from rsa import common
+    >>> common.bit_size(p * q) <= 256
+    True
+    >>> common.bit_size(p * q) > 240
+    True
+    
+    '''
+    
+    total_bits = nbits * 2
+
+    # Make sure that p and q aren't too close or the factoring programs can
+    # factor n.
+    shift = nbits // 16
+    pbits = nbits + shift
+    qbits = nbits - shift
+    
+    # Choose the two initial primes
+    log.debug('find_p_q(%i): Finding p', nbits)
+    p = getprime_func(pbits)
+    log.debug('find_p_q(%i): Finding q', nbits)
+    q = getprime_func(qbits)
+
+    def is_acceptable(p, q):
+        '''Returns True iff p and q are acceptable:
+            
+            - p and q differ
+            - (p * q) has the right nr of bits (when accurate=True)
+        '''
+
+        if p == q:
+            return False
+
+        if not accurate:
+            return True
+
+        # Make sure we have just the right amount of bits
+        found_size = rsa.common.bit_size(p * q)
+        return total_bits == found_size
+
+    # Keep choosing other primes until they match our requirements.
+    change_p = False
+    while not is_acceptable(p, q):
+        # Change p on one iteration and q on the other
+        if change_p:
+            p = getprime_func(pbits)
+        else:
+            q = getprime_func(qbits)
+
+        change_p = not change_p
+
+    # We want p > q as described on
+    # http://www.di-mgt.com.au/rsa_alg.html#crt
+    return (max(p, q), min(p, q))
+
+def calculate_keys(p, q, nbits):
+    '''Calculates an encryption and a decryption key given p and q, and
+    returns them as a tuple (e, d)
+
+    '''
+
+    phi_n = (p - 1) * (q - 1)
+
+    # A very common choice for e is 65537
+    e = 65537
+
+    try:
+        d = rsa.common.inverse(e, phi_n)
+    except ValueError:
+        raise ValueError("e (%d) and phi_n (%d) are not relatively prime" %
+                (e, phi_n))
+
+    if (e * d) % phi_n != 1:
+        raise ValueError("e (%d) and d (%d) are not mult. inv. modulo "
+                "phi_n (%d)" % (e, d, phi_n))
+
+    return (e, d)
+
+def gen_keys(nbits, getprime_func, accurate=True):
+    '''Generate RSA keys of nbits bits. Returns (p, q, e, d).
+
+    Note: this can take a long time, depending on the key size.
+    
+    :param nbits: the total number of bits in ``p`` and ``q``. Both ``p`` and
+        ``q`` will use ``nbits/2`` bits.
+    :param getprime_func: either :py:func:`rsa.prime.getprime` or a function
+        with similar signature.
+    '''
+
+    (p, q) = find_p_q(nbits // 2, getprime_func, accurate)
+    (e, d) = calculate_keys(p, q, nbits // 2)
+
+    return (p, q, e, d)
+
+def newkeys(nbits, accurate=True, poolsize=1):
+    '''Generates public and private keys, and returns them as (pub, priv).
+
+    The public key is also known as the 'encryption key', and is a
+    :py:class:`rsa.PublicKey` object. The private key is also known as the
+    'decryption key' and is a :py:class:`rsa.PrivateKey` object.
+
+    :param nbits: the number of bits required to store ``n = p*q``.
+    :param accurate: when True, ``n`` will have exactly the number of bits you
+        asked for. However, this makes key generation much slower. When False,
+        `n`` may have slightly less bits.
+    :param poolsize: the number of processes to use to generate the prime
+        numbers. If set to a number > 1, a parallel algorithm will be used.
+        This requires Python 2.6 or newer.
+
+    :returns: a tuple (:py:class:`rsa.PublicKey`, :py:class:`rsa.PrivateKey`)
+
+    The ``poolsize`` parameter was added in *Python-RSA 3.1* and requires
+    Python 2.6 or newer.
+    
+    '''
+
+    if nbits < 16:
+        raise ValueError('Key too small')
+
+    if poolsize < 1:
+        raise ValueError('Pool size (%i) should be >= 1' % poolsize)
+
+    # Determine which getprime function to use
+    if poolsize > 1:
+        from rsa import parallel
+        import functools
+
+        getprime_func = functools.partial(parallel.getprime, poolsize=poolsize)
+    else: getprime_func = rsa.prime.getprime
+
+    # Generate the key components
+    (p, q, e, d) = gen_keys(nbits, getprime_func)
+    
+    # Create the key objects
+    n = p * q
+
+    return (
+        PublicKey(n, e),
+        PrivateKey(n, e, d, p, q)
+    )
+
+__all__ = ['PublicKey', 'PrivateKey', 'newkeys']
+
+if __name__ == '__main__':
+    import doctest
+    
+    try:
+        for count in range(100):
+            (failures, tests) = doctest.testmod()
+            if failures:
+                break
+
+            if (count and count % 10 == 0) or count == 1:
+                print('%i times' % count)
+    except KeyboardInterrupt:
+        print('Aborted')
+    else:
+        print('Doctests done')