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# -*- coding: utf-8 -*-
#
# PublicKey/DSA.py : DSA signature primitive
#
# Written in 2008 by Dwayne C. Litzenberger <dlitz@dlitz.net>
#
# ===================================================================
# The contents of this file are dedicated to the public domain. To
# the extent that dedication to the public domain is not available,
# everyone is granted a worldwide, perpetual, royalty-free,
# non-exclusive license to exercise all rights associated with the
# contents of this file for any purpose whatsoever.
# No rights are reserved.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# ===================================================================
__all__ = ['generate', 'construct', 'DsaKey', 'import_key' ]
import binascii
import struct
import itertools
from Cryptodome.Util.py3compat import bchr, bord, tobytes, tostr, iter_range
from Cryptodome import Random
from Cryptodome.IO import PKCS8, PEM
from Cryptodome.Hash import SHA256
from Cryptodome.Util.asn1 import (
DerObject, DerSequence,
DerInteger, DerObjectId,
DerBitString,
)
from Cryptodome.Math.Numbers import Integer
from Cryptodome.Math.Primality import (test_probable_prime, COMPOSITE,
PROBABLY_PRIME)
from Cryptodome.PublicKey import (_expand_subject_public_key_info,
_create_subject_public_key_info,
_extract_subject_public_key_info)
# ; The following ASN.1 types are relevant for DSA
#
# SubjectPublicKeyInfo ::= SEQUENCE {
# algorithm AlgorithmIdentifier,
# subjectPublicKey BIT STRING
# }
#
# id-dsa ID ::= { iso(1) member-body(2) us(840) x9-57(10040) x9cm(4) 1 }
#
# ; See RFC3279
# Dss-Parms ::= SEQUENCE {
# p INTEGER,
# q INTEGER,
# g INTEGER
# }
#
# DSAPublicKey ::= INTEGER
#
# DSSPrivatKey_OpenSSL ::= SEQUENCE
# version INTEGER,
# p INTEGER,
# q INTEGER,
# g INTEGER,
# y INTEGER,
# x INTEGER
# }
#
class DsaKey(object):
r"""Class defining an actual DSA key.
Do not instantiate directly.
Use :func:`generate`, :func:`construct` or :func:`import_key` instead.
:ivar p: DSA modulus
:vartype p: integer
:ivar q: Order of the subgroup
:vartype q: integer
:ivar g: Generator
:vartype g: integer
:ivar y: Public key
:vartype y: integer
:ivar x: Private key
:vartype x: integer
:undocumented: exportKey, publickey
"""
_keydata = ['y', 'g', 'p', 'q', 'x']
def __init__(self, key_dict):
input_set = set(key_dict.keys())
public_set = set(('y' , 'g', 'p', 'q'))
if not public_set.issubset(input_set):
raise ValueError("Some DSA components are missing = %s" %
str(public_set - input_set))
extra_set = input_set - public_set
if extra_set and extra_set != set(('x',)):
raise ValueError("Unknown DSA components = %s" %
str(extra_set - set(('x',))))
self._key = dict(key_dict)
def _sign(self, m, k):
if not self.has_private():
raise TypeError("DSA public key cannot be used for signing")
if not (1 < k < self.q):
raise ValueError("k is not between 2 and q-1")
x, q, p, g = [self._key[comp] for comp in ['x', 'q', 'p', 'g']]
blind_factor = Integer.random_range(min_inclusive=1,
max_exclusive=q)
inv_blind_k = (blind_factor * k).inverse(q)
blind_x = x * blind_factor
r = pow(g, k, p) % q # r = (g**k mod p) mod q
s = (inv_blind_k * (blind_factor * m + blind_x * r)) % q
return map(int, (r, s))
def _verify(self, m, sig):
r, s = sig
y, q, p, g = [self._key[comp] for comp in ['y', 'q', 'p', 'g']]
if not (0 < r < q) or not (0 < s < q):
return False
w = Integer(s).inverse(q)
u1 = (w * m) % q
u2 = (w * r) % q
v = (pow(g, u1, p) * pow(y, u2, p) % p) % q
return v == r
def has_private(self):
"""Whether this is a DSA private key"""
return 'x' in self._key
def can_encrypt(self): # legacy
return False
def can_sign(self): # legacy
return True
def public_key(self):
"""A matching DSA public key.
Returns:
a new :class:`DsaKey` object
"""
public_components = dict((k, self._key[k]) for k in ('y', 'g', 'p', 'q'))
return DsaKey(public_components)
def __eq__(self, other):
if bool(self.has_private()) != bool(other.has_private()):
return False
result = True
for comp in self._keydata:
result = result and (getattr(self._key, comp, None) ==
getattr(other._key, comp, None))
return result
def __ne__(self, other):
return not self.__eq__(other)
def __getstate__(self):
# DSA key is not pickable
from pickle import PicklingError
raise PicklingError
def domain(self):
"""The DSA domain parameters.
Returns
tuple : (p,q,g)
"""
return [int(self._key[comp]) for comp in ('p', 'q', 'g')]
def __repr__(self):
attrs = []
for k in self._keydata:
if k == 'p':
bits = Integer(self.p).size_in_bits()
attrs.append("p(%d)" % (bits,))
elif hasattr(self, k):
attrs.append(k)
if self.has_private():
attrs.append("private")
# PY3K: This is meant to be text, do not change to bytes (data)
return "<%s @0x%x %s>" % (self.__class__.__name__, id(self), ",".join(attrs))
def __getattr__(self, item):
try:
return int(self._key[item])
except KeyError:
raise AttributeError(item)
def export_key(self, format='PEM', pkcs8=None, passphrase=None,
protection=None, randfunc=None):
"""Export this DSA key.
Args:
format (string):
The encoding for the output:
- *'PEM'* (default). ASCII as per `RFC1421`_/ `RFC1423`_.
- *'DER'*. Binary ASN.1 encoding.
- *'OpenSSH'*. ASCII one-liner as per `RFC4253`_.
Only suitable for public keys, not for private keys.
passphrase (string):
*Private keys only*. The pass phrase to protect the output.
pkcs8 (boolean):
*Private keys only*. If ``True`` (default), the key is encoded
with `PKCS#8`_. If ``False``, it is encoded in the custom
OpenSSL/OpenSSH container.
protection (string):
*Only in combination with a pass phrase*.
The encryption scheme to use to protect the output.
If :data:`pkcs8` takes value ``True``, this is the PKCS#8
algorithm to use for deriving the secret and encrypting
the private DSA key.
For a complete list of algorithms, see :mod:`Cryptodome.IO.PKCS8`.
The default is *PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC*.
If :data:`pkcs8` is ``False``, the obsolete PEM encryption scheme is
used. It is based on MD5 for key derivation, and Triple DES for
encryption. Parameter :data:`protection` is then ignored.
The combination ``format='DER'`` and ``pkcs8=False`` is not allowed
if a passphrase is present.
randfunc (callable):
A function that returns random bytes.
By default it is :func:`Cryptodome.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 OpenSSL/OpenSSH.
.. 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
.. _RFC4253: http://www.ietf.org/rfc/rfc4253.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':
tup1 = [self._key[x].to_bytes() for x in ('p', 'q', 'g', 'y')]
def func(x):
if (bord(x[0]) & 0x80):
return bchr(0) + x
else:
return x
tup2 = [func(x) for x in tup1]
keyparts = [b'ssh-dss'] + tup2
keystring = b''.join(
[struct.pack(">I", len(kp)) + kp for kp in keyparts]
)
return b'ssh-dss ' + binascii.b2a_base64(keystring)[:-1]
# DER format is always used, even in case of PEM, which simply
# encodes it into BASE64.
params = DerSequence([self.p, self.q, self.g])
if self.has_private():
if pkcs8 is None:
pkcs8 = True
if pkcs8:
if not protection:
protection = 'PBKDF2WithHMAC-SHA1AndDES-EDE3-CBC'
private_key = DerInteger(self.x).encode()
binary_key = PKCS8.wrap(
private_key, oid, passphrase,
protection, key_params=params,
randfunc=randfunc
)
if passphrase:
key_type = 'ENCRYPTED PRIVATE'
else:
key_type = 'PRIVATE'
passphrase = None
else:
if format != 'PEM' and passphrase:
raise ValueError("DSA private key cannot be encrypted")
ints = [0, self.p, self.q, self.g, self.y, self.x]
binary_key = DerSequence(ints).encode()
key_type = "DSA PRIVATE"
else:
if pkcs8:
raise ValueError("PKCS#8 is only meaningful for private keys")
binary_key = _create_subject_public_key_info(oid,
DerInteger(self.y), params)
key_type = "PUBLIC"
if format == 'DER':
return binary_key
if format == 'PEM':
pem_str = PEM.encode(
binary_key, key_type + " KEY",
passphrase, randfunc
)
return tobytes(pem_str)
raise ValueError("Unknown key format '%s'. Cannot export the DSA key." % format)
# Backward-compatibility
exportKey = export_key
publickey = public_key
# Methods defined in PyCryptodome that we don't support anymore
def sign(self, M, K):
raise NotImplementedError("Use module Cryptodome.Signature.DSS instead")
def verify(self, M, signature):
raise NotImplementedError("Use module Cryptodome.Signature.DSS instead")
def encrypt(self, plaintext, K):
raise NotImplementedError
def decrypt(self, ciphertext):
raise NotImplementedError
def blind(self, M, B):
raise NotImplementedError
def unblind(self, M, B):
raise NotImplementedError
def size(self):
raise NotImplementedError
def _generate_domain(L, randfunc):
"""Generate a new set of DSA domain parameters"""
N = { 1024:160, 2048:224, 3072:256 }.get(L)
if N is None:
raise ValueError("Invalid modulus length (%d)" % L)
outlen = SHA256.digest_size * 8
n = (L + outlen - 1) // outlen - 1 # ceil(L/outlen) -1
b_ = L - 1 - (n * outlen)
# Generate q (A.1.1.2)
q = Integer(4)
upper_bit = 1 << (N - 1)
while test_probable_prime(q, randfunc) != PROBABLY_PRIME:
seed = randfunc(64)
U = Integer.from_bytes(SHA256.new(seed).digest()) & (upper_bit - 1)
q = U | upper_bit | 1
assert(q.size_in_bits() == N)
# Generate p (A.1.1.2)
offset = 1
upper_bit = 1 << (L - 1)
while True:
V = [ SHA256.new(seed + Integer(offset + j).to_bytes()).digest()
for j in iter_range(n + 1) ]
V = [ Integer.from_bytes(v) for v in V ]
W = sum([V[i] * (1 << (i * outlen)) for i in iter_range(n)],
(V[n] & ((1 << b_) - 1)) * (1 << (n * outlen)))
X = Integer(W + upper_bit) # 2^{L-1} < X < 2^{L}
assert(X.size_in_bits() == L)
c = X % (q * 2)
p = X - (c - 1) # 2q divides (p-1)
if p.size_in_bits() == L and \
test_probable_prime(p, randfunc) == PROBABLY_PRIME:
break
offset += n + 1
# Generate g (A.2.3, index=1)
e = (p - 1) // q
for count in itertools.count(1):
U = seed + b"ggen" + bchr(1) + Integer(count).to_bytes()
W = Integer.from_bytes(SHA256.new(U).digest())
g = pow(W, e, p)
if g != 1:
break
return (p, q, g, seed)
def generate(bits, randfunc=None, domain=None):
"""Generate a new DSA key pair.
The algorithm follows Appendix A.1/A.2 and B.1 of `FIPS 186-4`_,
respectively for domain generation and key pair generation.
Args:
bits (integer):
Key length, or size (in bits) of the DSA modulus *p*.
It must be 1024, 2048 or 3072.
randfunc (callable):
Random number generation function; it accepts a single integer N
and return a string of random data N bytes long.
If not specified, :func:`Cryptodome.Random.get_random_bytes` is used.
domain (tuple):
The DSA domain parameters *p*, *q* and *g* as a list of 3
integers. Size of *p* and *q* must comply to `FIPS 186-4`_.
If not specified, the parameters are created anew.
Returns:
:class:`DsaKey` : a new DSA key object
Raises:
ValueError : when **bits** is too little, too big, or not a multiple of 64.
.. _FIPS 186-4: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
"""
if randfunc is None:
randfunc = Random.get_random_bytes
if domain:
p, q, g = map(Integer, domain)
## Perform consistency check on domain parameters
# P and Q must be prime
fmt_error = test_probable_prime(p) == COMPOSITE
fmt_error |= test_probable_prime(q) == COMPOSITE
# Verify Lagrange's theorem for sub-group
fmt_error |= ((p - 1) % q) != 0
fmt_error |= g <= 1 or g >= p
fmt_error |= pow(g, q, p) != 1
if fmt_error:
raise ValueError("Invalid DSA domain parameters")
else:
p, q, g, _ = _generate_domain(bits, randfunc)
L = p.size_in_bits()
N = q.size_in_bits()
if L != bits:
raise ValueError("Mismatch between size of modulus (%d)"
" and 'bits' parameter (%d)" % (L, bits))
if (L, N) not in [(1024, 160), (2048, 224),
(2048, 256), (3072, 256)]:
raise ValueError("Lengths of p and q (%d, %d) are not compatible"
"to FIPS 186-3" % (L, N))
if not 1 < g < p:
raise ValueError("Incorrent DSA generator")
# B.1.1
c = Integer.random(exact_bits=N + 64, randfunc=randfunc)
x = c % (q - 1) + 1 # 1 <= x <= q-1
y = pow(g, x, p)
key_dict = { 'y':y, 'g':g, 'p':p, 'q':q, 'x':x }
return DsaKey(key_dict)
def construct(tup, consistency_check=True):
"""Construct a DSA key from a tuple of valid DSA components.
Args:
tup (tuple):
A tuple of long integers, with 4 or 5 items
in the following order:
1. Public key (*y*).
2. Sub-group generator (*g*).
3. Modulus, finite field order (*p*).
4. Sub-group order (*q*).
5. Private key (*x*). Optional.
consistency_check (boolean):
If ``True``, the library will verify that the provided components
fulfil the main DSA properties.
Raises:
ValueError: when the key being imported fails the most basic DSA validity checks.
Returns:
:class:`DsaKey` : a DSA key object
"""
key_dict = dict(zip(('y', 'g', 'p', 'q', 'x'), map(Integer, tup)))
key = DsaKey(key_dict)
fmt_error = False
if consistency_check:
# P and Q must be prime
fmt_error = test_probable_prime(key.p) == COMPOSITE
fmt_error |= test_probable_prime(key.q) == COMPOSITE
# Verify Lagrange's theorem for sub-group
fmt_error |= ((key.p - 1) % key.q) != 0
fmt_error |= key.g <= 1 or key.g >= key.p
fmt_error |= pow(key.g, key.q, key.p) != 1
# Public key
fmt_error |= key.y <= 0 or key.y >= key.p
if hasattr(key, 'x'):
fmt_error |= key.x <= 0 or key.x >= key.q
fmt_error |= pow(key.g, key.x, key.p) != key.y
if fmt_error:
raise ValueError("Invalid DSA key components")
return key
# Dss-Parms ::= SEQUENCE {
# p OCTET STRING,
# q OCTET STRING,
# g OCTET STRING
# }
# DSAPublicKey ::= INTEGER -- public key, y
def _import_openssl_private(encoded, passphrase, params):
if params:
raise ValueError("DSA private key already comes with parameters")
der = DerSequence().decode(encoded, nr_elements=6, only_ints_expected=True)
if der[0] != 0:
raise ValueError("No version found")
tup = [der[comp] for comp in (4, 3, 1, 2, 5)]
return construct(tup)
def _import_subjectPublicKeyInfo(encoded, passphrase, params):
algoid, encoded_key, emb_params = _expand_subject_public_key_info(encoded)
if algoid != oid:
raise ValueError("No DSA subjectPublicKeyInfo")
if params and emb_params:
raise ValueError("Too many DSA parameters")
y = DerInteger().decode(encoded_key).value
p, q, g = list(DerSequence().decode(params or emb_params))
tup = (y, g, p, q)
return construct(tup)
def _import_x509_cert(encoded, passphrase, params):
sp_info = _extract_subject_public_key_info(encoded)
return _import_subjectPublicKeyInfo(sp_info, None, params)
def _import_pkcs8(encoded, passphrase, params):
if params:
raise ValueError("PKCS#8 already includes parameters")
k = PKCS8.unwrap(encoded, passphrase)
if k[0] != oid:
raise ValueError("No PKCS#8 encoded DSA key")
x = DerInteger().decode(k[1]).value
p, q, g = list(DerSequence().decode(k[2]))
tup = (pow(g, x, p), g, p, q, x)
return construct(tup)
def _import_key_der(key_data, passphrase, params):
"""Import a DSA key (public or private half), encoded in DER form."""
decodings = (_import_openssl_private,
_import_subjectPublicKeyInfo,
_import_x509_cert,
_import_pkcs8)
for decoding in decodings:
try:
return decoding(key_data, passphrase, params)
except ValueError:
pass
raise ValueError("DSA key format is not supported")
def import_key(extern_key, passphrase=None):
"""Import a DSA key.
Args:
extern_key (string or byte string):
The DSA key to import.
The following formats are supported for a DSA **public** key:
- X.509 certificate (binary DER or PEM)
- X.509 ``subjectPublicKeyInfo`` (binary DER or PEM)
- OpenSSH (ASCII one-liner, see `RFC4253`_)
The following formats are supported for a DSA **private** key:
- `PKCS#8`_ ``PrivateKeyInfo`` or ``EncryptedPrivateKeyInfo``
DER SEQUENCE (binary or PEM)
- OpenSSL/OpenSSH custom format (binary or PEM)
For details about the PEM encoding, see `RFC1421`_/`RFC1423`_.
passphrase (string):
In case of an encrypted private key, this is the pass phrase
from which the decryption key is derived.
Encryption may be applied either at the `PKCS#8`_ or at the PEM level.
Returns:
:class:`DsaKey` : a DSA key object
Raises:
ValueError : 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
.. _RFC4253: http://www.ietf.org/rfc/rfc4253.txt
.. _PKCS#8: http://www.ietf.org/rfc/rfc5208.txt
"""
extern_key = tobytes(extern_key)
if passphrase is not None:
passphrase = tobytes(passphrase)
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_key_der(der, passphrase, None)
if extern_key.startswith(b'ssh-dss '):
# This is probably a public 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:]
if keyparts[0] == b"ssh-dss":
tup = [Integer.from_bytes(keyparts[x]) for x in (4, 3, 1, 2)]
return construct(tup)
if len(extern_key) > 0 and bord(extern_key[0]) == 0x30:
# This is probably a DER encoded key
return _import_key_der(extern_key, passphrase, None)
raise ValueError("DSA key format is not supported")
# Backward compatibility
importKey = import_key
#: `Object ID`_ for a DSA key.
#:
#: id-dsa ID ::= { iso(1) member-body(2) us(840) x9-57(10040) x9cm(4) 1 }
#:
#: .. _`Object ID`: http://www.alvestrand.no/objectid/1.2.840.10040.4.1.html
oid = "1.2.840.10040.4.1"