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RSA.py
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# -*- coding: utf-8 -*- # =================================================================== # # Copyright (c) 2016, Legrandin <helderijs@gmail.com> # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in # the documentation and/or other materials provided with the # distribution. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE # COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, # INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, # BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER # CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT # LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN # ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. # =================================================================== __all__ = ['generate', 'construct', 'import_key', 'RsaKey', 'oid'] import binascii import struct from Crypto import Random from Crypto.Util.py3compat import tobytes, bord, tostr from Crypto.Util.asn1 import DerSequence, DerNull from Crypto.Math.Numbers import Integer from Crypto.Math.Primality import (test_probable_prime, generate_probable_prime, COMPOSITE) from Crypto.PublicKey import (_expand_subject_public_key_info, _create_subject_public_key_info, _extract_subject_public_key_info) class RsaKey(object): r"""Class defining an actual RSA key. Do not instantiate directly. Use :func:`generate`, :func:`construct` or :func:`import_key` instead. :ivar n: RSA modulus :vartype n: integer :ivar e: RSA public exponent :vartype e: integer :ivar d: RSA private exponent :vartype d: integer :ivar p: First factor of the RSA modulus :vartype p: integer :ivar q: Second factor of the RSA modulus :vartype q: integer :ivar invp: Chinese remainder component (:math:`p^{-1} \text{mod } q`) :vartype invp: integer :ivar invq: Chinese remainder component (:math:`q^{-1} \text{mod } p`) :vartype invq: integer :ivar u: Same as ``invp`` :vartype u: integer :undocumented: exportKey, publickey """ def __init__(self, **kwargs): """Build an RSA key. :Keywords: n : integer The modulus. e : integer The public exponent. d : integer The private exponent. Only required for private keys. p : integer The first factor of the modulus. Only required for private keys. q : integer The second factor of the modulus. Only required for private keys. u : integer The CRT coefficient (inverse of p modulo q). Only required for private keys. """ input_set = set(kwargs.keys()) public_set = set(('n', 'e')) private_set = public_set | set(('p', 'q', 'd', 'u')) if input_set not in (private_set, public_set): raise ValueError("Some RSA components are missing") for component, value in kwargs.items(): setattr(self, "_" + component, value) if input_set == private_set: self._dp = self._d % (self._p - 1) # = (e⁻¹) mod (p-1) self._dq = self._d % (self._q - 1) # = (e⁻¹) mod (q-1) self._invq = None # will be computed on demand @property def n(self): return int(self._n) @property def e(self): return int(self._e) @property def d(self): if not self.has_private(): raise AttributeError("No private exponent available for public keys") return int(self._d) @property def p(self): if not self.has_private(): raise AttributeError("No CRT component 'p' available for public keys") return int(self._p) @property def q(self): if not self.has_private(): raise AttributeError("No CRT component 'q' available for public keys") return int(self._q) @property def dp(self): if not self.has_private(): raise AttributeError("No CRT component 'dp' available for public keys") return int(self._dp) @property def dq(self): if not self.has_private(): raise AttributeError("No CRT component 'dq' available for public keys") return int(self._dq) @property def invq(self): if not self.has_private(): raise AttributeError("No CRT component 'invq' available for public keys") if self._invq is None: self._invq = self._q.inverse(self._p) return int(self._invq) @property def invp(self): return self.u @property def u(self): if not self.has_private(): raise AttributeError("No CRT component 'u' available for public keys") return int(self._u) def size_in_bits(self): """Size of the RSA modulus in bits""" return self._n.size_in_bits() def size_in_bytes(self): """The minimal amount of bytes that can hold the RSA modulus""" return (self._n.size_in_bits() - 1) // 8 + 1 def _encrypt(self, plaintext): if not 0 <= plaintext < self._n: raise ValueError("Plaintext too large") return int(pow(Integer(plaintext), self._e, self._n)) def _decrypt(self, ciphertext): if not 0 <= ciphertext < self._n: raise ValueError("Ciphertext too large") if not self.has_private(): raise TypeError("This is not a private key") # Blinded RSA decryption (to prevent timing attacks): # Step 1: Generate random secret blinding factor r, # such that 0 < r < n-1 r = Integer.random_range(min_inclusive=1, max_exclusive=self._n) # Step 2: Compute c' = c * r**e mod n cp = Integer(ciphertext) * pow(r, self._e, self._n) % self._n # Step 3: Compute m' = c'**d mod n (normal RSA decryption) m1 = pow(cp, self._dp, self._p) m2 = pow(cp, self._dq, self._q) h = ((m2 - m1) * self._u) % self._q mp = h * self._p + m1 # Step 4: Compute m = m' * (r**(-1)) mod n result = (r.inverse(self._n) * mp) % self._n # Verify no faults occurred if ciphertext != pow(result, self._e, self._n): raise ValueError("Fault detected in RSA decryption") return result def has_private(self): """Whether this is an RSA private key""" return hasattr(self, "_d") def can_encrypt(self): # legacy return True def can_sign(self): # legacy return True def public_key(self): """A matching RSA public key. Returns: a new :class:`RsaKey` object """ return RsaKey(n=self._n, e=self._e) def __eq__(self, other): if self.has_private() != other.has_private(): return False if self.n != other.n or self.e != other.e: return False if not self.has_private(): return True return (self.d == other.d) def __ne__(self, other): return not (self == other) def __getstate__(self): # RSA key is not pickable from pickle import PicklingError raise PicklingError def __repr__(self): if self.has_private(): extra = ", d=%d, p=%d, q=%d, u=%d" % (int(self._d), int(self._p), int(self._q), int(self._u)) else: extra = "" return "RsaKey(n=%d, e=%d%s)" % (int(self._n), int(self._e), extra) def __str__(self): if self.has_private(): key_type = "Private" else: key_type = "Public" return "%s RSA key at 0x%X" % (key_type, id(self)) def export_key(self, format='PEM', passphrase=None, pkcs=1, protection=None, randfunc=None): """Export this RSA key. Args: format (string): The format to use for wrapping the key: - *'PEM'*. (*Default*) Text encoding, done according to `RFC1421`_/`RFC1423`_. - *'DER'*. Binary encoding. - *'OpenSSH'*. Textual encoding, done according to OpenSSH specification. Only suitable for public keys (not private keys). passphrase (string): (*For private keys only*) The pass phrase used for protecting the output. pkcs (integer): (*For private keys only*) The ASN.1 structure to use for serializing the key. Note that even in case of PEM encoding, there is an inner ASN.1 DER structure. With ``pkcs=1`` (*default*), the private key is encoded in a simple `PKCS#1`_ structure (``RSAPrivateKey``). With ``pkcs=8``, the private key is encoded in a `PKCS#8`_ structure (``PrivateKeyInfo``). .. note:: This parameter is ignored for a public key. For DER and PEM, an ASN.1 DER ``SubjectPublicKeyInfo`` structure is always used. protection (string): (*For private keys only*) The encryption scheme to use for protecting the private key. If ``None`` (default), the behavior depends on :attr:`format`: - For *'DER'*, the *PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC* scheme is used. The following operations are performed: 1. A 16 byte Triple DES key is derived from the passphrase using :func:`Crypto.Protocol.KDF.PBKDF2` with 8 bytes salt, and 1 000 iterations of :mod:`Crypto.Hash.HMAC`. 2. The private key is encrypted using CBC. 3. The encrypted key is encoded according to PKCS#8. - For *'PEM'*, the obsolete PEM encryption scheme is used. It is based on MD5 for key derivation, and Triple DES for encryption. Specifying a value for :attr:`protection` is only meaningful for PKCS#8 (that is, ``pkcs=8``) and only if a pass phrase is present too. The supported schemes for PKCS#8 are listed in the :mod:`Crypto.IO.PKCS8` module (see :attr:`wrap_algo` parameter). randfunc (callable): A function that provides random bytes. Only used for PEM encoding. The default is :func:`Crypto.Random.get_random_bytes`. Returns: byte string: the encoded key Raises: ValueError:when the format is unknown or when you try to encrypt a private key with *DER* format and PKCS#1. .. warning:: If you don't provide a pass phrase, the private key will be exported in the clear! .. _RFC1421: http://www.ietf.org/rfc/rfc1421.txt .. _RFC1423: http://www.ietf.org/rfc/rfc1423.txt .. _`PKCS#1`: http://www.ietf.org/rfc/rfc3447.txt .. _`PKCS#8`: http://www.ietf.org/rfc/rfc5208.txt """ if passphrase is not None: passphrase = tobytes(passphrase) if randfunc is None: randfunc = Random.get_random_bytes if format == 'OpenSSH': e_bytes, n_bytes = [x.to_bytes() for x in (self._e, self._n)] if bord(e_bytes[0]) & 0x80: e_bytes = b'\x00' + e_bytes if bord(n_bytes[0]) & 0x80: n_bytes = b'\x00' + n_bytes keyparts = [b'ssh-rsa', e_bytes, n_bytes] keystring = b''.join([struct.pack(">I", len(kp)) + kp for kp in keyparts]) return b'ssh-rsa ' + binascii.b2a_base64(keystring)[:-1] # DER format is always used, even in case of PEM, which simply # encodes it into BASE64. if self.has_private(): binary_key = DerSequence([0, self.n, self.e, self.d, self.p, self.q, self.d % (self.p-1), self.d % (self.q-1), Integer(self.q).inverse(self.p) ]).encode() if pkcs == 1: key_type = 'RSA PRIVATE KEY' if format == 'DER' and passphrase: raise ValueError("PKCS#1 private key cannot be encrypted") else: # PKCS#8 from Crypto.IO import PKCS8 if format == 'PEM' and protection is None: key_type = 'PRIVATE KEY' binary_key = PKCS8.wrap(binary_key, oid, None, key_params=DerNull()) else: key_type = 'ENCRYPTED PRIVATE KEY' if not protection: protection = 'PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC' binary_key = PKCS8.wrap(binary_key, oid, passphrase, protection, key_params=DerNull()) passphrase = None else: key_type = "PUBLIC KEY" binary_key = _create_subject_public_key_info(oid, DerSequence([self.n, self.e]), DerNull() ) if format == 'DER': return binary_key if format == 'PEM': from Crypto.IO import PEM pem_str = PEM.encode(binary_key, key_type, passphrase, randfunc) return tobytes(pem_str) raise ValueError("Unknown key format '%s'. Cannot export the RSA key." % format) # Backward compatibility exportKey = export_key publickey = public_key # Methods defined in PyCrypto that we don't support anymore def sign(self, M, K): raise NotImplementedError("Use module Crypto.Signature.pkcs1_15 instead") def verify(self, M, signature): raise NotImplementedError("Use module Crypto.Signature.pkcs1_15 instead") def encrypt(self, plaintext, K): raise NotImplementedError("Use module Crypto.Cipher.PKCS1_OAEP instead") def decrypt(self, ciphertext): raise NotImplementedError("Use module Crypto.Cipher.PKCS1_OAEP instead") def blind(self, M, B): raise NotImplementedError def unblind(self, M, B): raise NotImplementedError def size(self): raise NotImplementedError def generate(bits, randfunc=None, e=65537): """Create a new RSA key pair. The algorithm closely follows NIST `FIPS 186-4`_ in its sections B.3.1 and B.3.3. The modulus is the product of two non-strong probable primes. Each prime passes a suitable number of Miller-Rabin tests with random bases and a single Lucas test. Args: bits (integer): Key length, or size (in bits) of the RSA modulus. It must be at least 1024, but **2048 is recommended.** The FIPS standard only defines 1024, 2048 and 3072. randfunc (callable): Function that returns random bytes. The default is :func:`Crypto.Random.get_random_bytes`. e (integer): Public RSA exponent. It must be an odd positive integer. It is typically a small number with very few ones in its binary representation. The FIPS standard requires the public exponent to be at least 65537 (the default). Returns: an RSA key object (:class:`RsaKey`, with private key). .. _FIPS 186-4: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf """ if bits < 1024: raise ValueError("RSA modulus length must be >= 1024") if e % 2 == 0 or e < 3: raise ValueError("RSA public exponent must be a positive, odd integer larger than 2.") if randfunc is None: randfunc = Random.get_random_bytes d = n = Integer(1) e = Integer(e) while n.size_in_bits() != bits and d < (1 << (bits // 2)): # Generate the prime factors of n: p and q. # By construciton, their product is always # 2^{bits-1} < p*q < 2^bits. size_q = bits // 2 size_p = bits - size_q min_p = min_q = (Integer(1) << (2 * size_q - 1)).sqrt() if size_q != size_p: min_p = (Integer(1) << (2 * size_p - 1)).sqrt() def filter_p(candidate): return candidate > min_p and (candidate - 1).gcd(e) == 1 p = generate_probable_prime(exact_bits=size_p, randfunc=randfunc, prime_filter=filter_p) min_distance = Integer(1) << (bits // 2 - 100) def filter_q(candidate): return (candidate > min_q and (candidate - 1).gcd(e) == 1 and abs(candidate - p) > min_distance) q = generate_probable_prime(exact_bits=size_q, randfunc=randfunc, prime_filter=filter_q) n = p * q lcm = (p - 1).lcm(q - 1) d = e.inverse(lcm) if p > q: p, q = q, p u = p.inverse(q) return RsaKey(n=n, e=e, d=d, p=p, q=q, u=u) def construct(rsa_components, consistency_check=True): r"""Construct an RSA key from a tuple of valid RSA components. The modulus **n** must be the product of two primes. The public exponent **e** must be odd and larger than 1. In case of a private key, the following equations must apply: .. math:: \begin{align} p*q &= n \\ e*d &\equiv 1 ( \text{mod lcm} [(p-1)(q-1)]) \\ p*u &\equiv 1 ( \text{mod } q) \end{align} Args: rsa_components (tuple): A tuple of integers, with at least 2 and no more than 6 items. The items come in the following order: 1. RSA modulus *n*. 2. Public exponent *e*. 3. Private exponent *d*. Only required if the key is private. 4. First factor of *n* (*p*). Optional, but the other factor *q* must also be present. 5. Second factor of *n* (*q*). Optional. 6. CRT coefficient *q*, that is :math:`p^{-1} \text{mod }q`. Optional. consistency_check (boolean): If ``True``, the library will verify that the provided components fulfil the main RSA properties. Raises: ValueError: when the key being imported fails the most basic RSA validity checks. Returns: An RSA key object (:class:`RsaKey`). """ class InputComps(object): pass input_comps = InputComps() for (comp, value) in zip(('n', 'e', 'd', 'p', 'q', 'u'), rsa_components): setattr(input_comps, comp, Integer(value)) n = input_comps.n e = input_comps.e if not hasattr(input_comps, 'd'): key = RsaKey(n=n, e=e) else: d = input_comps.d if hasattr(input_comps, 'q'): p = input_comps.p q = input_comps.q else: # Compute factors p and q from the private exponent d. # We assume that n has no more than two factors. # See 8.2.2(i) in Handbook of Applied Cryptography. ktot = d * e - 1 # The quantity d*e-1 is a multiple of phi(n), even, # and can be represented as t*2^s. t = ktot while t % 2 == 0: t //= 2 # Cycle through all multiplicative inverses in Zn. # The algorithm is non-deterministic, but there is a 50% chance # any candidate a leads to successful factoring. # See "Digitalized Signatures and Public Key Functions as Intractable # as Factorization", M. Rabin, 1979 spotted = False a = Integer(2) while not spotted and a < 100: k = Integer(t) # Cycle through all values a^{t*2^i}=a^k while k < ktot: cand = pow(a, k, n) # Check if a^k is a non-trivial root of unity (mod n) if cand != 1 and cand != (n - 1) and pow(cand, 2, n) == 1: # We have found a number such that (cand-1)(cand+1)=0 (mod n). # Either of the terms divides n. p = Integer(n).gcd(cand + 1) spotted = True break k *= 2 # This value was not any good... let's try another! a += 2 if not spotted: raise ValueError("Unable to compute factors p and q from exponent d.") # Found ! assert ((n % p) == 0) q = n // p if hasattr(input_comps, 'u'): u = input_comps.u else: u = p.inverse(q) # Build key object key = RsaKey(n=n, e=e, d=d, p=p, q=q, u=u) # Verify consistency of the key if consistency_check: # Modulus and public exponent must be coprime if e <= 1 or e >= n: raise ValueError("Invalid RSA public exponent") if Integer(n).gcd(e) != 1: raise ValueError("RSA public exponent is not coprime to modulus") # For RSA, modulus must be odd if not n & 1: raise ValueError("RSA modulus is not odd") if key.has_private(): # Modulus and private exponent must be coprime if d <= 1 or d >= n: raise ValueError("Invalid RSA private exponent") if Integer(n).gcd(d) != 1: raise ValueError("RSA private exponent is not coprime to modulus") # Modulus must be product of 2 primes if p * q != n: raise ValueError("RSA factors do not match modulus") if test_probable_prime(p) == COMPOSITE: raise ValueError("RSA factor p is composite") if test_probable_prime(q) == COMPOSITE: raise ValueError("RSA factor q is composite") # See Carmichael theorem phi = (p - 1) * (q - 1) lcm = phi // (p - 1).gcd(q - 1) if (e * d % int(lcm)) != 1: raise ValueError("Invalid RSA condition") if hasattr(key, 'u'): # CRT coefficient if u <= 1 or u >= q: raise ValueError("Invalid RSA component u") if (p * u % q) != 1: raise ValueError("Invalid RSA component u with p") return key def _import_pkcs1_private(encoded, *kwargs): # 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 # } # # Version ::= INTEGER der = DerSequence().decode(encoded, nr_elements=9, only_ints_expected=True) if der[0] != 0: raise ValueError("No PKCS#1 encoding of an RSA private key") return construct(der[1:6] + [Integer(der[4]).inverse(der[5])]) def _import_pkcs1_public(encoded, *kwargs): # RSAPublicKey ::= SEQUENCE { # modulus INTEGER, -- n # publicExponent INTEGER -- e # } der = DerSequence().decode(encoded, nr_elements=2, only_ints_expected=True) return construct(der) def _import_subjectPublicKeyInfo(encoded, *kwargs): algoid, encoded_key, params = _expand_subject_public_key_info(encoded) if algoid != oid or params is not None: raise ValueError("No RSA subjectPublicKeyInfo") return _import_pkcs1_public(encoded_key) def _import_x509_cert(encoded, *kwargs): sp_info = _extract_subject_public_key_info(encoded) return _import_subjectPublicKeyInfo(sp_info) def _import_pkcs8(encoded, passphrase): from Crypto.IO import PKCS8 k = PKCS8.unwrap(encoded, passphrase) if k[0] != oid: raise ValueError("No PKCS#8 encoded RSA key") return _import_keyDER(k[1], passphrase) def _import_keyDER(extern_key, passphrase): """Import an RSA key (public or private half), encoded in DER form.""" decodings = (_import_pkcs1_private, _import_pkcs1_public, _import_subjectPublicKeyInfo, _import_x509_cert, _import_pkcs8) for decoding in decodings: try: return decoding(extern_key, passphrase) except ValueError: pass raise ValueError("RSA key format is not supported") def _import_openssh_private_rsa(data, password): from ._openssh import (import_openssh_private_generic, read_bytes, read_string, check_padding) ssh_name, decrypted = import_openssh_private_generic(data, password) if ssh_name != "ssh-rsa": raise ValueError("This SSH key is not RSA") n, decrypted = read_bytes(decrypted) e, decrypted = read_bytes(decrypted) d, decrypted = read_bytes(decrypted) iqmp, decrypted = read_bytes(decrypted) p, decrypted = read_bytes(decrypted) q, decrypted = read_bytes(decrypted) _, padded = read_string(decrypted) # Comment check_padding(padded) build = [Integer.from_bytes(x) for x in (n, e, d, q, p, iqmp)] return construct(build) def import_key(extern_key, passphrase=None): """Import an RSA key (public or private). Args: extern_key (string or byte string): The RSA key to import. The following formats are supported for an RSA **public key**: - X.509 certificate (binary or PEM format) - X.509 ``subjectPublicKeyInfo`` DER SEQUENCE (binary or PEM encoding) - `PKCS#1`_ ``RSAPublicKey`` DER SEQUENCE (binary or PEM encoding) - An OpenSSH line (e.g. the content of ``~/.ssh/id_ecdsa``, ASCII) The following formats are supported for an RSA **private key**: - PKCS#1 ``RSAPrivateKey`` DER SEQUENCE (binary or PEM encoding) - `PKCS#8`_ ``PrivateKeyInfo`` or ``EncryptedPrivateKeyInfo`` DER SEQUENCE (binary or PEM encoding) - OpenSSH (text format, introduced in `OpenSSH 6.5`_) For details about the PEM encoding, see `RFC1421`_/`RFC1423`_. passphrase (string or byte string): For private keys only, the pass phrase that encrypts the key. Returns: An RSA key object (:class:`RsaKey`). Raises: ValueError/IndexError/TypeError: When the given key cannot be parsed (possibly because the pass phrase is wrong). .. _RFC1421: http://www.ietf.org/rfc/rfc1421.txt .. _RFC1423: http://www.ietf.org/rfc/rfc1423.txt .. _`PKCS#1`: http://www.ietf.org/rfc/rfc3447.txt .. _`PKCS#8`: http://www.ietf.org/rfc/rfc5208.txt .. _`OpenSSH 6.5`: https://flak.tedunangst.com/post/new-openssh-key-format-and-bcrypt-pbkdf """ from Crypto.IO import PEM extern_key = tobytes(extern_key) if passphrase is not None: passphrase = tobytes(passphrase) if extern_key.startswith(b'-----BEGIN OPENSSH PRIVATE KEY'): text_encoded = tostr(extern_key) openssh_encoded, marker, enc_flag = PEM.decode(text_encoded, passphrase) result = _import_openssh_private_rsa(openssh_encoded, passphrase) return result if extern_key.startswith(b'-----'): # This is probably a PEM encoded key. (der, marker, enc_flag) = PEM.decode(tostr(extern_key), passphrase) if enc_flag: passphrase = None return _import_keyDER(der, passphrase) if extern_key.startswith(b'ssh-rsa '): # This is probably an OpenSSH key keystring = binascii.a2b_base64(extern_key.split(b' ')[1]) keyparts = [] while len(keystring) > 4: length = struct.unpack(">I", keystring[:4])[0] keyparts.append(keystring[4:4 + length]) keystring = keystring[4 + length:] e = Integer.from_bytes(keyparts[1]) n = Integer.from_bytes(keyparts[2]) return construct([n, e]) if len(extern_key) > 0 and bord(extern_key[0]) == 0x30: # This is probably a DER encoded key return _import_keyDER(extern_key, passphrase) raise ValueError("RSA key format is not supported") # Backward compatibility importKey = import_key #: `Object ID`_ for the RSA encryption algorithm. This OID often indicates #: a generic RSA key, even when such key will be actually used for digital #: signatures. #: #: .. _`Object ID`: http://www.alvestrand.no/objectid/1.2.840.113549.1.1.1.html oid = "1.2.840.113549.1.1.1"