def make_valid_rsa_key(priv_key, pub_key):
"""Generate a valid private key, with N close to the N from pub_key"""
# Attempt to make the key valid by finding a Q which multiplies with P to
# form something close to N
n = pub_key.public_numbers().n
e = pub_key.public_numbers().e
p = priv_key.private_numbers().p
q = close_prime(n // p)
assert is_prime(e)
assert is_prime(p)
assert is_prime(q)
# Compute D from the new P&Q
phi = (p - 1) * (q - 1)
return rsa.RSAPrivateNumbers(
public_numbers=rsa.RSAPublicNumbers(e, p * q),
p=p,
q=q,
d=rsa.rsa_crt_iqmp(phi, e),
dmp1=rsa.rsa_crt_dmp1(e, p),
dmq1=rsa.rsa_crt_dmp1(e, q),
iqmp=rsa.rsa_crt_iqmp(p, q),
).private_key(BACKEND)
def convert_key(cls, packet, private=False):
if isinstance(packet, RSAPrivateKey) or isinstance(packet, RSAPublicKey) or isinstance(packet, DSAPublicKey) or isinstance(packet, DSAPrivateKey):
if (not private) and (isinstance(packet, DSAPrivateKey) or isinstance(packet, RSAPrivateKey)):
return packet.public_key()
else:
return packet
packet = cls._parse_packet(packet)
if isinstance(packet, OpenPGP.Message):
packet = packet[0]
if packet.key_algorithm_name() == 'DSA':
params = dsa.DSAParameterNumbers(
cls._bytes_to_long(packet.key['p']),
cls._bytes_to_long(packet.key['q']),
cls._bytes_to_long(packet.key['g']))
public = dsa.DSAPublicNumbers(
cls._bytes_to_long(packet.key['y']),
params)
if private:
return dsa.DSAPrivateNumbers(cls._bytes_to_long(packet.key['x']), public).private_key(openssl.backend)
else:
return public.public_key(openssl.backend)
else: # RSA
public = rsa.RSAPublicNumbers(cls._bytes_to_long(packet.key['e']), cls._bytes_to_long(packet.key['n']))
if private:
d = cls._bytes_to_long(packet.key['d'])
p = cls._bytes_to_long(packet.key['q'])
q = cls._bytes_to_long(packet.key['p'])
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmp1(d, q)
u = cls._bytes_to_long(packet.key['u'])
return rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, u, public).private_key(default_backend())
else:
return public.public_key(default_backend())
def fields_from_json(cls, jobj):
# pylint: disable=invalid-name
n, e = (cls._decode_param(jobj[x]) for x in ('n', 'e'))
public_numbers = rsa.RSAPublicNumbers(e=e, n=n)
if 'd' not in jobj: # public key
key = public_numbers.public_key(default_backend())
else: # private key
d = cls._decode_param(jobj['d'])
if ('p' in jobj or 'q' in jobj or 'dp' in jobj or
'dq' in jobj or 'qi' in jobj or 'oth' in jobj):
# "If the producer includes any of the other private
# key parameters, then all of the others MUST be
# present, with the exception of "oth", which MUST
# only be present when more than two prime factors
# were used."
p, q, dp, dq, qi, = all_params = tuple(
jobj.get(x) for x in ('p', 'q', 'dp', 'dq', 'qi'))
if tuple(param for param in all_params if param is None):
raise errors.Error(
"Some private parameters are missing: {0}".format(
all_params))
p, q, dp, dq, qi = tuple(cls._decode_param(x) for x in all_params)
# TODO: check for oth
else:
p, q = rsa.rsa_recover_prime_factors(n, e, d) # cryptography>=0.8
dp = rsa.rsa_crt_dmp1(d, p)
dq = rsa.rsa_crt_dmq1(d, q)
qi = rsa.rsa_crt_iqmp(p, q)
key = rsa.RSAPrivateNumbers(
p, q, d, dp, dq, qi, public_numbers).private_key(default_backend())
return cls(key=key)
def generateKeyPair(keySize):
p = generateLargePrime(keySize)
print('Generating q prime...')
q = generateLargePrime(keySize)
n = p * q
# Step 2: Create a number e that is relatively prime to (p-1)*(q-1).
print('Generating e that is relatively prime to (p-1)*(q-1)...')
while True:
e = random.randrange(2 ** (keySize - 1), 2 ** (keySize))
if gcd(e, (p - 1) * (q - 1)) == 1:
break
# Step 3: Calculate d, the mod inverse of e.
print('Calculating d that is mod inverse of e...')
d = findModInverse(e, (p - 1) * (q - 1))
iqmp = rsa.rsa_crt_iqmp(p, q)
dmp1 = rsa.rsa_crt_dmp1(d,p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
public_key_numbers = rsa.RSAPublicNumbers(e,n)
publicKey = public_key_numbers.public_key(default_backend());
private_key_numbers = rsa.RSAPrivateNumbers(
p,
q,
d,
dmp1,
dmq1,
iqmp,
public_key_numbers
)
privateKey = private_key_numbers.private_key(default_backend())
print('Public key:', publicKey)
print('Private key:', privateKey)
return (publicKey, privateKey, str(p))
def compute_rsa_private_key(cls, p, q, e, n, d):
"""
Computes RSA private key based on provided RSA semi-primes
and returns cryptography lib instance.
@developer: tnanoba
:param p: int
:param q: int
:param e: int
:param n: int
:param d: int
:return: object
"""
# Computes: d % (p - 1)
dmp1 = rsa.rsa_crt_dmp1(d, p)
# Computes: d % (q - 1)
dmq1 = rsa.rsa_crt_dmq1(d, q)
# Modular inverse q of p, (q ^ -1 mod p)
iqmp = rsa.rsa_crt_iqmp(p, q)
public_numbers = rsa.RSAPublicNumbers(e, n)
return rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp,
public_numbers).private_key(
default_backend())
def _convert_rsa_private_key(keypair):
backend = Backend()
def _trim_bn_to_int(s):
binary = s.lstrip(b'\x00')
bn_ptr = backend._lib.BN_bin2bn(binary, len(binary), backend._ffi.NULL)
try:
return backend._bn_to_int(bn_ptr)
finally:
backend._lib.OPENSSL_free(bn_ptr)
(n, e, d, iqmp, p, q) = [
_trim_bn_to_int(value)
for value in _read_KEY_RSA(io.BytesIO(keypair.private_key))
]
numbers = RSAPrivateNumbers(
d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=RSAPublicNumbers(e=e, n=n),
)
return numbers.private_key(backend)
def from_jwk(jwk):
try:
obj = json.loads(jwk)
except ValueError:
raise InvalidKeyError('Key is not valid JSON')
if obj.get != 'RSA':
raise InvalidKeyError('Not an RSA key')
if 'd' in obj and 'e' in obj and 'n' in obj:
# Private key
if 'oth' in obj:
raise InvalidKeyError(
'Unsupported RSA private key: > 2 primes not supported'
)
other_props = ['p', 'q', 'dp', 'dq', 'qi']
props_found = [prop in obj for prop in other_props]
any_props_found = any(props_found)
if any_props_found and not all(props_found):
raise InvalidKeyError(
'RSA key must include all parameters if any are present besides d'
)
public_numbers = RSAPublicNumbers(
from_base64url_uint(obj['e']),
from_base64url_uint(obj['n']))
if any_props_found:
numbers = RSAPrivateNumbers(
d=from_base64url_uint(obj['d']),
p=from_base64url_uint(obj['p']),
q=from_base64url_uint(obj['q']),
dmp1=from_base64url_uint(obj['dp']),
dmq1=from_base64url_uint(obj['dq']),
iqmp=from_base64url_uint(obj['qi']),
public_numbers=public_numbers)
else:
d = from_base64url_uint(obj['d'])
p, q = rsa_recover_prime_factors(public_numbers.n, d,
public_numbers.e)
numbers = RSAPrivateNumbers(d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=public_numbers)
return numbers.private_key(default_backend())
elif 'n' in obj and 'e' in obj:
# Public key
numbers = RSAPublicNumbers(from_base64url_uint(obj['e']),
from_base64url_uint(obj['n']))
return numbers.public_key(default_backend())
else:
raise InvalidKeyError('Not a public or private key')
def _deserialize_rsa_private_key(stream: typing.BinaryIO) -> rsa.RSAPrivateKey:
rsa_n = _sshbuf_get_bignum2(stream)
rsa_e = _sshbuf_get_bignum2(stream)
rsa_d = _sshbuf_get_bignum2(stream)
rsa_iqmp = _sshbuf_get_bignum2(stream)
rsa_p = _sshbuf_get_bignum2(stream)
rsa_q = _sshbuf_get_bignum2(stream)
# Calculate Chinese remainder theorem coefficients
# used to speed up calculations.
# Luckily, our library provides functions to calculate these...
rsa_dmp1 = rsa.rsa_crt_dmp1(rsa_d, rsa_p) # dmp1 = d mod (p - 1)
rsa_dmq1 = rsa.rsa_crt_dmq1(rsa_d, rsa_q) # dmp2 = d mod (q - 1)
public_numbers = rsa.RSAPublicNumbers(e=rsa_e, n=rsa_n)
private_numbers = rsa.RSAPrivateNumbers(
p=rsa_p,
q=rsa_q,
d=rsa_d,
dmp1=rsa_dmp1,
dmq1=rsa_dmq1,
iqmp=rsa_iqmp,
public_numbers=public_numbers,
)
return private_numbers.private_key(backend=default_backend())
def convert_to_pem(jwks_keys):
pem_keys = []
for jwk_key in jwks_keys:
e = jwk_key.get('e')
n = jwk_key.get('n')
d = jwk_key.get('d')
# We don't have p, q, dp, dq and qi but you can recover it with knowledge of d
# if you have p and q you wouldn't need the d but could calculate d from this.
(p, q) = rsa.rsa_recover_prime_factors(n, e, d)
dp = rsa.rsa_crt_dmp1(d, p)
dq = rsa.rsa_crt_dmq1(d, q)
qi = rsa.rsa_crt_iqmp(p, q)
public_numbers = rsa.RSAPublicNumbers(e=e, n=n)
key = rsa.RSAPrivateNumbers(
p, q, d, dp, dq, qi, public_numbers).private_key(default_backend())
pem_string = key.private_bytes(
encoding=serialization.Encoding.PEM,
format=serialization.PrivateFormat.TraditionalOpenSSL,
encryption_algorithm=serialization.NoEncryption())
pem_keys.append(pem_string.decode('ascii'))
return pem_keys
def build_rsa_private(n,
public,
private,
p=-1,
q=-1,
dmp1=-1,
dmq1=-1,
iqmp=-1):
"""A wrapper function to create an RSA private key from given parameters.
Keyword arguments:
n -- the modulus
public -- the public exponent
private -- the private exponent
p -- (optional) prime 1
q -- (optional) prime 2
dmp1 -- (optional) CRT exponent 1
dmq1 -- (optional) CRT exponent 2
iqmp --- (optional) CRT coefficient
"""
if p == -1 or q == -1:
p, q = rsa.recover_prime_factors(n, public, private)
if dmp1 == -1:
dmp1 = rsa.rsa_crt_dmp1(private, p)
if dmq1 == -1:
dmq1 = rsa.rsa_crt_dmq1(private, q)
if iqmp == -1:
iqmp = rsa.rsa_crt_iqmp(p, q)
pubNum = rsa.RSAPublicNumbers(public, n)
privNum = rsa.RSAPrivateNumbers(p, q, private, dmp1, dmq1, iqmp, pubNum)
return default_backend().load_rsa_private_numbers(privNum)
def load_private_key(self):
obj = self._dict_data
if 'oth' in obj: # pragma: no cover
# https://tools.ietf.org/html/rfc7518#section-6.3.2.7
raise ValueError('"oth" is not supported yet')
public_numbers = RSAPublicNumbers(base64_to_int(obj['e']),
base64_to_int(obj['n']))
if has_all_prime_factors(obj):
numbers = RSAPrivateNumbers(d=base64_to_int(obj['d']),
p=base64_to_int(obj['p']),
q=base64_to_int(obj['q']),
dmp1=base64_to_int(obj['dp']),
dmq1=base64_to_int(obj['dq']),
iqmp=base64_to_int(obj['qi']),
public_numbers=public_numbers)
else:
d = base64_to_int(obj['d'])
p, q = rsa_recover_prime_factors(public_numbers.n, d,
public_numbers.e)
numbers = RSAPrivateNumbers(d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=public_numbers)
return numbers.private_key(default_backend())
def load_jwks(jwks_obj):
"""
Given a JWKS-formatted dictionary representing a private key,
return a python-cryptography private key object
"""
if jwks_obj['kty'] == "RSA":
n = long_from_bytes(jwks_obj['n'])
e = long_from_bytes(jwks_obj['e'])
d = long_from_bytes(jwks_obj['d'])
public_key_numbers = rsa.RSAPublicNumbers(
e = e,
n = n,
)
# If loading a partial key, we'll have to recalculate a
# few of the relevant constants
if ('p' not in jwks_obj) or ('q' not in jwks_obj):
p, q = rsa.rsa_recover_prime_factors(n, e, d)
else:
p = long_from_bytes(jwks_obj['p'])
q = long_from_bytes(jwks_obj['q'])
if 'qi' not in jwks_obj:
qi = rsa.rsa_crt_iqmp(p, q)
else:
qi = long_from_bytes(jwks_obj['qi'])
if 'dp' not in jwks_obj:
dmp1 = rsa.rsa_crt_dmp1(d, p)
else:
dmp1 = long_from_bytes(jwks_obj['dp'])
if 'dq' not in jwks_obj:
dmq1 = rsa.rsa_crt_dmq1(d, q)
else:
dmq1 = long_from_bytes(jwks_obj['dq'])
private_key_numbers = rsa.RSAPrivateNumbers(
p = p,
q = q,
d = d,
dmp1 = dmp1,
dmq1 = dmq1,
iqmp = qi,
public_numbers = public_key_numbers
)
return private_key_numbers.private_key(default_backend())
elif jwks_obj['kty'] == 'EC':
public_key_numbers = ec.EllipticCurvePublicNumbers(
long_from_bytes(jwks_obj['x']),
long_from_bytes(jwks_obj['y']),
ec.SECP256R1()
)
private_key_numbers = ec.EllipticCurvePrivateNumbers(
long_from_bytes(jwks_obj['d']),
public_key_numbers
)
return private_key_numbers.private_key(default_backend())
else:
raise scitokens.scitokens.UnsupportedKeyException("Issuer public key not supported.")
def __init__(
self,
n: str,
e: str,
d: Optional[str] = None,
p: Optional[str] = None,
q: Optional[str] = None,
dp: Optional[str] = None,
dq: Optional[str] = None,
qi: Optional[str] = None,
**ignore,
) -> None:
self._private = None
self._public = None
modulus = b64_to_int(n)
public_exponent = b64_to_int(e)
public = rsa.RSAPublicNumbers(public_exponent, modulus)
self._public: RSA_PUBLIC = public.public_key(default_backend())
if d:
private_exponent = b64_to_int(d)
first_prime = b64_to_int(p)
second_prime = b64_to_int(q)
first_prime_crt = b64_to_int(dp)
second_prime_crt = b64_to_int(dq)
crt_coefficient = b64_to_int(qi)
if not first_prime or not second_prime:
first_prime, second_prime = rsa.rsa_recover_prime_factors(
modulus, public_exponent, private_exponent)
if not first_prime_crt:
first_prime_crt = rsa.rsa_crt_dmp1(private_exponent,
first_prime)
if not second_prime_crt:
second_prime_crt = rsa.rsa_crt_dmq1(private_exponent,
second_prime)
if not crt_coefficient:
crt_coefficient = rsa.rsa_crt_iqmp(first_prime, second_prime)
private = rsa.RSAPrivateNumbers(
first_prime,
second_prime,
private_exponent,
first_prime_crt,
second_prime_crt,
crt_coefficient,
public,
)
self._private: RSA_PRIVATE = private.private_key(default_backend())
def _check_rsa_private_numbers(skey):
assert skey
pkey = skey.public_numbers
assert pkey
assert pkey.e
assert pkey.n
assert skey.d
assert skey.p * skey.q == pkey.n
assert skey.dmp1 == rsa.rsa_crt_dmp1(skey.d, skey.p)
assert skey.dmq1 == rsa.rsa_crt_dmq1(skey.d, skey.q)
assert skey.iqmp == rsa.rsa_crt_iqmp(skey.p, skey.q)
def make_privkey(p, q, e=65537):
n = p * q
d = number.inverse(e, (p - 1) * (q - 1))
iqmp = rsa.rsa_crt_iqmp(p, q)
dmp1 = rsa.rsa_crt_dmp1(e, p)
dmq1 = rsa.rsa_crt_dmq1(e, q)
pub = rsa.RSAPublicNumbers(e, n)
priv = rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp, pub)
pubkey = pub.public_key(default_backend())
privkey = priv.private_key(default_backend())
return privkey, pubkey
def __init__(self, p: int, n: int, e: int, pubnums: rsa.RSAPublicNumbers):
q = n // p
d = _MyRSAPrivateNumbers._generate_d(p, q, e, n)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
iqmp = rsa.rsa_crt_iqmp(p, q)
super().__init__(p, q, d, dmp1, dmq1, iqmp, pubnums)
def _check_rsa_private_numbers(skey):
assert skey
pkey = skey.public_numbers
assert pkey
assert pkey.e
assert pkey.n
assert skey.d
assert skey.p * skey.q == pkey.n
assert skey.dmp1 == rsa.rsa_crt_dmp1(skey.d, skey.p)
assert skey.dmq1 == rsa.rsa_crt_dmq1(skey.d, skey.q)
assert skey.iqmp == rsa.rsa_crt_iqmp(skey.p, skey.q)
def from_jwk(jwk):
if not isinstance(jwk, JsonWebKey):
raise TypeError('The specified jwk must be a JsonWebKey')
if jwk.kty != 'RSA' and jwk.kty != 'RSA-HSM':
raise ValueError(
'The specified jwk must have a key type of "RSA" or "RSA-HSM"')
if not jwk.n or not jwk.e:
raise ValueError(
'Invalid RSA jwk, both n and e must be have values')
rsa_key = _RsaKey()
rsa_key.kid = jwk.kid
rsa_key.kty = jwk.kty
rsa_key.key_ops = jwk.key_ops
pub = RSAPublicNumbers(n=_bytes_to_int(jwk.n), e=_bytes_to_int(jwk.e))
# if the private key values are specified construct a private key
# only the secret primes and private exponent are needed as other fields can be calculated
if jwk.p and jwk.q and jwk.d:
# convert the values of p, q, and d from bytes to int
p = _bytes_to_int(jwk.p)
q = _bytes_to_int(jwk.q)
d = _bytes_to_int(jwk.d)
# convert or compute the remaining private key numbers
dmp1 = _bytes_to_int(jwk.dp) if jwk.dp else rsa_crt_dmp1(
private_exponent=d, p=p)
dmq1 = _bytes_to_int(jwk.dq) if jwk.dq else rsa_crt_dmq1(
private_exponent=d, q=q)
iqmp = _bytes_to_int(jwk.qi) if jwk.qi else rsa_crt_iqmp(p=p, q=q)
# create the private key from the jwk key values
priv = RSAPrivateNumbers(p=p,
q=q,
d=d,
dmp1=dmp1,
dmq1=dmq1,
iqmp=iqmp,
public_numbers=pub)
key_impl = priv.private_key(
cryptography.hazmat.backends.default_backend())
# if the necessary private key values are not specified create the public key
else:
key_impl = pub.public_key(
cryptography.hazmat.backends.default_backend())
rsa_key._rsa_impl = key_impl
return rsa_key
def convert_key(cls, packet, private=False):
if (
isinstance(packet, RSAPrivateKey)
or isinstance(packet, RSAPublicKey)
or isinstance(packet, DSAPublicKey)
or isinstance(packet, DSAPrivateKey)
):
if (not private) and (isinstance(packet, DSAPrivateKey) or isinstance(packet, RSAPrivateKey)):
return packet.public_key()
else:
return packet
packet = cls._parse_packet(packet)
if isinstance(packet, OpenPGP.Message):
packet = packet[0]
if packet.key_algorithm_name() == "DSA":
params = dsa.DSAParameterNumbers(
cls._bytes_to_long(packet.key["p"]),
cls._bytes_to_long(packet.key["q"]),
cls._bytes_to_long(packet.key["g"]),
)
public = dsa.DSAPublicNumbers(cls._bytes_to_long(packet.key["y"]), params)
if private:
return dsa.DSAPrivateNumbers(cls._bytes_to_long(packet.key["x"]), public).private_key(openssl.backend)
else:
return public.public_key(openssl.backend)
else: # RSA
public = rsa.RSAPublicNumbers(cls._bytes_to_long(packet.key["e"]), cls._bytes_to_long(packet.key["n"]))
if private:
d = cls._bytes_to_long(packet.key["d"])
p = cls._bytes_to_long(packet.key["q"])
q = cls._bytes_to_long(packet.key["p"])
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmp1(d, q)
u = cls._bytes_to_long(packet.key["u"])
return rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, u, public).private_key(default_backend())
else:
return public.public_key(default_backend())
def rsa_construct_private(numbers):
args = dict([(k, v) for k, v in numbers.items() if k in ["n", "e", "d"]])
cnum = {"d": numbers["d"]}
if "p" not in numbers and "q" not in numbers:
(p, q) = rsa.rsa_recover_prime_factors(**args)
cnum["p"] = p
cnum["q"] = q
else:
cnum["p"] = numbers["p"]
cnum["q"] = numbers["q"]
try:
cnum["dmp1"] = numbers["dp"]
except KeyError:
cnum["dmp1"] = rsa.rsa_crt_dmp1(cnum["d"], cnum["p"])
else:
if not numbers["dp"]:
cnum["dmp1"] = rsa.rsa_crt_dmp1(cnum["d"], cnum["p"])
try:
cnum["dmq1"] = numbers["dq"]
except KeyError:
cnum["dmq1"] = rsa.rsa_crt_dmq1(cnum["d"], cnum["q"])
else:
if not numbers["dq"]:
cnum["dmq1"] = rsa.rsa_crt_dmq1(cnum["d"], cnum["q"])
try:
cnum["iqmp"] = numbers["di"]
except KeyError:
cnum["iqmp"] = rsa.rsa_crt_iqmp(cnum["p"], cnum["q"])
else:
if not numbers["di"]:
cnum["iqmp"] = rsa.rsa_crt_iqmp(cnum["p"], cnum["q"])
rpubn = rsa.RSAPublicNumbers(e=numbers["e"], n=numbers["n"])
rprivn = rsa.RSAPrivateNumbers(public_numbers=rpubn, **cnum)
return rprivn.private_key(default_backend())
def rsa_construct_private(numbers):
args = dict([(k, v) for k, v in numbers.items() if k in ['n', 'e', 'd']])
cnum = {'d': numbers['d']}
if 'p' not in numbers and 'q' not in numbers:
(p, q) = rsa.rsa_recover_prime_factors(**args)
cnum['p'] = p
cnum['q'] = q
else:
cnum['p'] = numbers['p']
cnum['q'] = numbers['q']
try:
cnum['dmp1'] = numbers['dp']
except KeyError:
cnum['dmp1'] = rsa.rsa_crt_dmp1(cnum['d'], cnum['p'])
else:
if not numbers['dp']:
cnum['dmp1'] = rsa.rsa_crt_dmp1(cnum['d'], cnum['p'])
try:
cnum['dmq1'] = numbers['dq']
except KeyError:
cnum['dmq1'] = rsa.rsa_crt_dmq1(cnum['d'], cnum['q'])
else:
if not numbers['dq']:
cnum['dmq1'] = rsa.rsa_crt_dmq1(cnum['d'], cnum['q'])
try:
cnum['iqmp'] = numbers['di']
except KeyError:
cnum['iqmp'] = rsa.rsa_crt_iqmp(cnum['p'], cnum['p'])
else:
if not numbers['di']:
cnum['iqmp'] = rsa.rsa_crt_iqmp(cnum['p'], cnum['p'])
rpubn = rsa.RSAPublicNumbers(e=numbers['e'], n=numbers['n'])
rprivn = rsa.RSAPrivateNumbers(public_numbers=rpubn, **cnum)
return rprivn.private_key(default_backend())
def __init__(self, n, e, d, p, q):
self.n = n
self.e = e
self.d = d
self.p = p
self.q = q
dmp1 = rsa_crt_dmp1(d, p)
dmq1 = rsa_crt_dmq1(d, q)
iqmp = rsa_crt_iqmp(p, q)
pub = RSAPublicNumbers(e, n)
priv = RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp, pub)
self._key = priv.private_key(default_backend())
def make_rsa_privkey(material, backend):
public_material = material['public']
private_material = material['private']
n = public_material['n'] # Note: all the number are already int
e = public_material['e']
d = private_material['d']
p = private_material['p']
q = private_material['q']
pub = rsa.RSAPublicNumbers(e, n)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
iqmp = rsa.rsa_crt_iqmp(p, q)
return rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp,
pub).private_key(backend)
def rsa_pq(p, q, e=65537):
n = p * q
public_numbers = rsa.RSAPublicNumbers(e=e, n=n)
d = rsa._modinv(e, (p - 1) * (q - 1) // 2)
private_numbers = rsa.RSAPrivateNumbers(
public_numbers=public_numbers,
p=p,
q=q,
d=d,
dmp1=rsa.rsa_crt_dmp1(d, p),
dmq1=rsa.rsa_crt_dmq1(d, q),
iqmp=rsa.rsa_crt_iqmp(p, q),
)
return private_numbers.private_key(backend)
def __init__(self, n, e, d, p, q):
self.n = n
self.e = e
self.d = d
self.p = p
self.q = q
dmp1 = rsa_crt_dmp1(d, p)
dmq1 = rsa_crt_dmq1(d, q)
iqmp = rsa_crt_iqmp(p, q)
pub = RSAPublicNumbers(e, n)
priv = RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp, pub)
self._key = priv.private_key(default_backend())
def make_rsa_key(material):
'''Convert a hex-based dict of values to an RSA key'''
backend = default_backend()
public_material = material['public']
private_material = material['private']
n = int(public_material['n'], 16)
e = int(public_material['e'], 16)
d = int(private_material['d'], 16)
p = int(private_material['p'], 16)
q = int(private_material['q'], 16)
pub = rsa.RSAPublicNumbers(e, n)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
iqmp = rsa.rsa_crt_iqmp(p, q)
return rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp,
pub).private_key(backend), padding.PKCS1v15()
def _check_rsa_private_key(skey):
assert skey
assert skey.modulus
assert skey.public_exponent
assert skey.private_exponent
assert skey.p * skey.q == skey.modulus
assert skey.key_size
assert skey.dmp1 == rsa.rsa_crt_dmp1(skey.d, skey.p)
assert skey.dmq1 == rsa.rsa_crt_dmq1(skey.d, skey.q)
assert skey.iqmp == rsa.rsa_crt_iqmp(skey.p, skey.q)
pkey = skey.public_key()
assert pkey
assert skey.modulus == pkey.modulus
assert skey.public_exponent == pkey.public_exponent
assert skey.key_size == pkey.key_size
def print_sign_test(case, n, e, d, padding_alg):
# Recover the prime factors and CRT numbers.
p, q = rsa.rsa_recover_prime_factors(n, e, d)
# cryptography returns p, q with p < q by default. *ring* requires
# p > q, so swap them here.
p, q = max(p, q), min(p, q)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
iqmp = rsa.rsa_crt_iqmp(p, q)
# Create a private key instance.
pub = rsa.RSAPublicNumbers(e, n)
priv = rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp, pub)
key = priv.private_key(default_backend())
msg = case['Msg'].decode('hex')
# Recalculate and compare the signature to validate our processing.
if padding_alg == 'PKCS#1 1.5':
sig = key.sign(msg, padding.PKCS1v15(),
getattr(hashes, case['SHAAlg'])())
hex_sig = to_hex(sig)
assert hex_sig == case['S']
elif padding_alg == "PSS":
# PSS is randomised, can't recompute this way
pass
else:
print "Invalid padding algorithm"
quit()
# Serialize the private key in DER format.
der = key.private_bytes(serialization.Encoding.DER,
serialization.PrivateFormat.TraditionalOpenSSL,
serialization.NoEncryption())
# Print the test case data in the format used by *ring* test files.
print 'Digest = %s' % case['SHAAlg']
print 'Key = %s' % to_hex(der)
print 'Msg = %s' % reformat_hex(case['Msg'])
if padding_alg == "PSS":
print 'Salt = %s' % reformat_hex(case['SaltVal'])
print 'Sig = %s' % reformat_hex(case['S'])
print 'Result = Pass'
print ''
def from_jwk(cls, jwk):
if jwk.kty != "RSA" and jwk.kty != "RSA-HSM":
raise ValueError(
'The specified jwk must have a key type of "RSA" or "RSA-HSM"')
if not jwk.n or not jwk.e:
raise ValueError(
"Invalid RSA jwk, both n and e must be have values")
rsa_key = cls(kid=jwk.kid)
rsa_key.kty = jwk.kty
rsa_key.key_ops = jwk.key_ops
pub = RSAPublicNumbers(n=_bytes_to_int(jwk.n), e=_bytes_to_int(jwk.e))
# if the private key values are specified construct a private key
# only the secret primes and private exponent are needed as other fields can be calculated
if jwk.p and jwk.q and jwk.d:
# convert the values of p, q, and d from bytes to int
p = _bytes_to_int(jwk.p)
q = _bytes_to_int(jwk.q)
d = _bytes_to_int(jwk.d)
# convert or compute the remaining private key numbers
dmp1 = _bytes_to_int(jwk.dp) if jwk.dp else rsa_crt_dmp1(
private_exponent=d, p=p)
dmq1 = _bytes_to_int(jwk.dq) if jwk.dq else rsa_crt_dmq1(
private_exponent=d, q=q)
iqmp = _bytes_to_int(jwk.qi) if jwk.qi else rsa_crt_iqmp(p=p, q=q)
# create the private key from the jwk key values
priv = RSAPrivateNumbers(p=p,
q=q,
d=d,
dmp1=dmp1,
dmq1=dmq1,
iqmp=iqmp,
public_numbers=pub)
key_impl = priv.private_key(default_backend())
# if the necessary private key values are not specified create the public key
else:
key_impl = pub.public_key(default_backend())
rsa_key._rsa_impl = key_impl # pylint:disable=protected-access
return rsa_key
def from_dict(cls, dct):
if 'oth' in dct:
raise UnsupportedKeyTypeError(
'RSA keys with multiples primes are not supported')
try:
e = uint_b64decode(dct['e'])
n = uint_b64decode(dct['n'])
except KeyError as why:
raise MalformedJWKError('e and n are required')
pub_numbers = RSAPublicNumbers(e, n)
if 'd' not in dct:
return cls(
pub_numbers.public_key(backend=default_backend()), **dct)
d = uint_b64decode(dct['d'])
privparams = {'p', 'q', 'dp', 'dq', 'qi'}
product = set(dct.keys()) & privparams
if len(product) == 0:
p, q = rsa_recover_prime_factors(n, e, d)
priv_numbers = RSAPrivateNumbers(
d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=pub_numbers)
elif product == privparams:
priv_numbers = RSAPrivateNumbers(
d=d,
p=uint_b64decode(dct['p']),
q=uint_b64decode(dct['q']),
dmp1=uint_b64decode(dct['dp']),
dmq1=uint_b64decode(dct['dq']),
iqmp=uint_b64decode(dct['qi']),
public_numbers=pub_numbers)
else:
# If the producer includes any of the other private key parameters,
# then all of the others MUST be present, with the exception of
# "oth", which MUST only be present when more than two prime
# factors were used.
raise MalformedJWKError(
'p, q, dp, dq, qi MUST be present or'
'all of them MUST be absent')
return cls(priv_numbers.private_key(backend=default_backend()), **dct)
def main(fn):
for case in parse(fn):
if case['SHAAlg'] == 'SHA224':
# SHA224 not supported in *ring*.
continue
# Read private key components.
n = int(case['n'], 16)
e = int(case['e'], 16)
d = int(case['d'], 16)
# Recover the prime factors and CRT numbers.
p, q = rsa.rsa_recover_prime_factors(n, e, d)
# cryptography returns p, q with p < q by default. *ring* requires
# p > q, so swap them here.
p, q = max(p, q), min(p, q)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
iqmp = rsa.rsa_crt_iqmp(p, q)
# Create a private key instance.
pub = rsa.RSAPublicNumbers(e, n)
priv = rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp, pub)
key = priv.private_key(default_backend())
# Recalculate and compare the signature to validate our processing.
msg = case['Msg'].decode('hex')
sig = key.sign(msg, padding.PKCS1v15(),
getattr(hashes, case['SHAAlg'])())
hex_sig = ''.join('{:02x}'.format(ord(c)) for c in sig)
assert hex_sig == case['S']
# Serialize the private key in DER format.
der = key.private_bytes(serialization.Encoding.DER,
serialization.PrivateFormat.TraditionalOpenSSL,
serialization.NoEncryption())
hex_der = ''.join('{:02x}'.format(ord(c)) for c in der)
# Print the test case data in the format used by *ring* test files.
print 'Digest = %s' % case['SHAAlg']
print 'Key = %s' % hex_der
print 'Msg = %s' % case['Msg']
print 'Sig = %s' % case['S']
print 'Result = Pass'
print ''
def from_dict(cls, dct):
if 'oth' in dct:
raise UnsupportedKeyTypeError(
'RSA keys with multiples primes are not supported')
try:
e = uint_b64decode(dct['e'])
n = uint_b64decode(dct['n'])
except KeyError as why:
raise MalformedJWKError('e and n are required') from why
pub_numbers = RSAPublicNumbers(e, n)
if 'd' not in dct:
return cls(
pub_numbers.public_key(backend=default_backend()), **dct)
d = uint_b64decode(dct['d'])
privparams = {'p', 'q', 'dp', 'dq', 'qi'}
product = set(dct.keys()) & privparams
if len(product) == 0:
p, q = rsa_recover_prime_factors(n, e, d)
priv_numbers = RSAPrivateNumbers(
d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=pub_numbers)
elif product == privparams:
priv_numbers = RSAPrivateNumbers(
d=d,
p=uint_b64decode(dct['p']),
q=uint_b64decode(dct['q']),
dmp1=uint_b64decode(dct['dp']),
dmq1=uint_b64decode(dct['dq']),
iqmp=uint_b64decode(dct['qi']),
public_numbers=pub_numbers)
else:
# If the producer includes any of the other private key parameters,
# then all of the others MUST be present, with the exception of
# "oth", which MUST only be present when more than two prime
# factors were used.
raise MalformedJWKError(
'p, q, dp, dq, qi MUST be present or'
'all of them MUST be absent')
return cls(priv_numbers.private_key(backend=default_backend()), **dct)
def load_private(self, data, pubfields, backend):
"""Make RSA private key from data."""
n, data = _get_mpint(data)
e, data = _get_mpint(data)
d, data = _get_mpint(data)
iqmp, data = _get_mpint(data)
p, data = _get_mpint(data)
q, data = _get_mpint(data)
if (e, n) != pubfields:
raise ValueError("Corrupt data: rsa field mismatch")
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
public_numbers = rsa.RSAPublicNumbers(e, n)
private_numbers = rsa.RSAPrivateNumbers(p, q, d, dmp1, dmq1, iqmp,
public_numbers)
private_key = private_numbers.private_key(backend)
return private_key, data
def _load_prikey_with_decrypted_data(self, decrypted_prikey_data):
der_pri = der_decoder.decode(decrypted_prikey_data)
der_pri2 = der_decoder.decode(der_pri[0][2])
# (n, e, d, p, q)
(n, e, d, p, q) = (der_pri2[0][1], der_pri2[0][2], der_pri2[0][3], der_pri2[0][4], der_pri2[0][5])
(n, e, d, p, q) = (int(n), int(e), int(d), int(p), int(q))
iqmp = rsa_crt_iqmp(p, q)
dmp1 = rsa_crt_dmp1(e, p)
dmq1 = rsa_crt_dmq1(e, q)
pn = RSAPublicNumbers(n=n, e=e)
self.prikey = RSAPrivateNumbers(p=p, q=q, d=d, dmp1=dmp1, dmq1=dmq1, iqmp=iqmp,
public_numbers=pn).private_key(backend=default_backend())
if len(der_pri[0]) > 3:
# sometimes, r value is not exist - (i don't know why..)
self._rand_num = der_pri[0][3][1][0] # so raw data, can't be eaten
return
def _fromRSAComponents(cls, n, e, d=None, p=None, q=None, u=None):
"""
Build a key from RSA numerical components.
@type n: L{int}
@param n: The 'n' RSA variable.
@type e: L{int}
@param e: The 'e' RSA variable.
@type d: L{int} or C{None}
@param d: The 'd' RSA variable (optional for a public key).
@type p: L{int} or C{None}
@param p: The 'p' RSA variable (optional for a public key).
@type q: L{int} or C{None}
@param q: The 'q' RSA variable (optional for a public key).
@type u: L{int} or C{None}
@param u: The 'u' RSA variable. Ignored, as its value is determined by
p and q.
@rtype: L{Key}
@return: An RSA key constructed from the values as given.
"""
publicNumbers = rsa.RSAPublicNumbers(e=e, n=n)
if d is None:
# We have public components.
keyObject = publicNumbers.public_key(default_backend())
else:
privateNumbers = rsa.RSAPrivateNumbers(
p=p,
q=q,
d=d,
dmp1=rsa.rsa_crt_dmp1(d, p),
dmq1=rsa.rsa_crt_dmq1(d, q),
iqmp=rsa.rsa_crt_iqmp(p, q),
public_numbers=publicNumbers,
)
keyObject = privateNumbers.private_key(default_backend())
return cls(keyObject)
def _process_jwk(self, jwk_dict):
if not jwk_dict.get('kty') == 'RSA':
raise JWKError(
"Incorrect key type. Expected: 'RSA', Received: %s" %
jwk_dict.get('kty'))
e = base64_to_long(jwk_dict.get('e', 256))
n = base64_to_long(jwk_dict.get('n'))
public = rsa.RSAPublicNumbers(e, n)
if 'd' not in jwk_dict:
return public.public_key(self.cryptography_backend())
else:
# This is a private key.
d = base64_to_long(jwk_dict.get('d'))
extra_params = ['p', 'q', 'dp', 'dq', 'qi']
if any(k in jwk_dict for k in extra_params):
# Precomputed private key parameters are available.
if not all(k in jwk_dict for k in extra_params):
# These values must be present when 'p' is according to
# Section 6.3.2 of RFC7518, so if they are not we raise
# an error.
raise JWKError(
'Precomputed private key parameters are incomplete.')
p = base64_to_long(jwk_dict['p'])
q = base64_to_long(jwk_dict['q'])
dp = base64_to_long(jwk_dict['dp'])
dq = base64_to_long(jwk_dict['dq'])
qi = base64_to_long(jwk_dict['qi'])
else:
# The precomputed private key parameters are not available,
# so we use cryptography's API to fill them in.
p, q = rsa.rsa_recover_prime_factors(n, e, d)
dp = rsa.rsa_crt_dmp1(d, p)
dq = rsa.rsa_crt_dmq1(d, q)
qi = rsa.rsa_crt_iqmp(p, q)
private = rsa.RSAPrivateNumbers(p, q, d, dp, dq, qi, public)
return private.private_key(self.cryptography_backend())
def create_privete_key(public_key, q):
n = public_key.public_numbers().n
e = public_key.public_numbers().e
p = n // q
phi = (p - 1) * (q - 1)
d = egcd(e, phi)
d = d % phi
if d < 0:
d += phi
iqmp = rsa.rsa_crt_iqmp(p, q)
dmp1 = rsa.rsa_crt_dmp1(d, p)
dmq1 = rsa.rsa_crt_dmq1(d, q)
private_key = rsa.RSAPrivateNumbers(
p, q, d, dmp1, dmq1, iqmp, public_key.public_numbers()).private_key()
return private_key
def _fromRSAComponents(cls, n, e, d=None, p=None, q=None, u=None):
"""
Build a key from RSA numerical components.
@type n: L{int}
@param n: The 'n' RSA variable.
@type e: L{int}
@param e: The 'e' RSA variable.
@type d: L{int} or L{None}
@param d: The 'd' RSA variable (optional for a public key).
@type p: L{int} or L{None}
@param p: The 'p' RSA variable (optional for a public key).
@type q: L{int} or L{None}
@param q: The 'q' RSA variable (optional for a public key).
@type u: L{int} or L{None}
@param u: The 'u' RSA variable. Ignored, as its value is determined by
p and q.
@rtype: L{Key}
@return: An RSA key constructed from the values as given.
"""
publicNumbers = rsa.RSAPublicNumbers(e=e, n=n)
if d is None:
# We have public components.
keyObject = publicNumbers.public_key(default_backend())
else:
privateNumbers = rsa.RSAPrivateNumbers(
p=p,
q=q,
d=d,
dmp1=rsa.rsa_crt_dmp1(d, p),
dmq1=rsa.rsa_crt_dmq1(d, q),
iqmp=rsa.rsa_crt_iqmp(p, q),
public_numbers=publicNumbers,
)
keyObject = privateNumbers.private_key(default_backend())
return cls(keyObject)
def from_jwk(jwk):
if not isinstance(jwk, JsonWebKey):
raise TypeError('The specified jwk must be a JsonWebKey')
if jwk.kty != 'RSA' and jwk.kty != 'RSA-HSM':
raise ValueError('The specified jwk must have a key type of "RSA" or "RSA-HSM"')
if not jwk.n or not jwk.e:
raise ValueError('Invalid RSA jwk, both n and e must be have values')
rsa_key = _RsaKey()
rsa_key.kid = jwk.kid
rsa_key.kty = jwk.kty
rsa_key.key_ops = jwk.key_ops
pub = RSAPublicNumbers(n=_bytes_to_int(jwk.n), e=_bytes_to_int(jwk.e))
# if the private key values are specified construct a private key
# only the secret primes and private exponent are needed as other fields can be calculated
if jwk.p and jwk.q and jwk.d:
# convert the values of p, q, and d from bytes to int
p = _bytes_to_int(jwk.p)
q = _bytes_to_int(jwk.q)
d = _bytes_to_int(jwk.d)
# convert or compute the remaining private key numbers
dmp1 = _bytes_to_int(jwk.dp) if jwk.dp else rsa_crt_dmp1(private_exponent=d, p=p)
dmq1 = _bytes_to_int(jwk.dq) if jwk.dq else rsa_crt_dmq1(private_exponent=d, q=q)
iqmp = _bytes_to_int(jwk.qi) if jwk.qi else rsa_crt_iqmp(p=p, q=q)
# create the private key from the jwk key values
priv = RSAPrivateNumbers(p=p, q=q, d=d, dmp1=dmp1, dmq1=dmq1, iqmp=iqmp, public_numbers=pub)
key_impl = priv.private_key(cryptography.hazmat.backends.default_backend())
# if the necessary private key values are not specified create the public key
else:
key_impl = pub.public_key(cryptography.hazmat.backends.default_backend())
rsa_key._rsa_impl = key_impl
return rsa_key
def _process_jwk(self, jwk_dict):
if not jwk_dict.get('kty') == 'RSA':
raise JWKError("Incorrect key type. Expected: 'RSA', Received: %s" % jwk_dict.get('kty'))
e = base64_to_long(jwk_dict.get('e', 256))
n = base64_to_long(jwk_dict.get('n'))
public = rsa.RSAPublicNumbers(e, n)
if 'd' not in jwk_dict:
return public.public_key(self.cryptography_backend())
else:
# This is a private key.
d = base64_to_long(jwk_dict.get('d'))
extra_params = ['p', 'q', 'dp', 'dq', 'qi']
if any(k in jwk_dict for k in extra_params):
# Precomputed private key parameters are available.
if not all(k in jwk_dict for k in extra_params):
# These values must be present when 'p' is according to
# Section 6.3.2 of RFC7518, so if they are not we raise
# an error.
raise JWKError('Precomputed private key parameters are incomplete.')
p = base64_to_long(jwk_dict['p'])
q = base64_to_long(jwk_dict['q'])
dp = base64_to_long(jwk_dict['dp'])
dq = base64_to_long(jwk_dict['dq'])
qi = base64_to_long(jwk_dict['qi'])
else:
# The precomputed private key parameters are not available,
# so we use cryptography's API to fill them in.
p, q = rsa.rsa_recover_prime_factors(n, e, d)
dp = rsa.rsa_crt_dmp1(d, p)
dq = rsa.rsa_crt_dmq1(d, q)
qi = rsa.rsa_crt_iqmp(p, q)
private = rsa.RSAPrivateNumbers(p, q, d, dp, dq, qi, public)
return private.private_key(self.cryptography_backend())
def __privkey__(self):
return rsa.RSAPrivateNumbers(self.p, self.q, self.d,
rsa.rsa_crt_dmp1(self.d, self.p),
rsa.rsa_crt_dmq1(self.d, self.q),
rsa.rsa_crt_iqmp(self.p, self.q),
rsa.RSAPublicNumbers(self.e, self.n)).private_key(default_backend())
def from_jwk(jwk):
try:
obj = json.loads(jwk)
except ValueError:
raise InvalidKeyError('Key is not valid JSON')
if obj.get('kty') != 'RSA':
raise InvalidKeyError('Not an RSA key')
if 'd' in obj and 'e' in obj and 'n' in obj:
# Private key
if 'oth' in obj:
raise InvalidKeyError('Unsupported RSA private key: > 2 primes not supported')
other_props = ['p', 'q', 'dp', 'dq', 'qi']
props_found = [prop in obj for prop in other_props]
any_props_found = any(props_found)
if any_props_found and not all(props_found):
raise InvalidKeyError('RSA key must include all parameters if any are present besides d')
public_numbers = RSAPublicNumbers(
from_base64url_uint(obj['e']), from_base64url_uint(obj['n'])
)
if any_props_found:
numbers = RSAPrivateNumbers(
d=from_base64url_uint(obj['d']),
p=from_base64url_uint(obj['p']),
q=from_base64url_uint(obj['q']),
dmp1=from_base64url_uint(obj['dp']),
dmq1=from_base64url_uint(obj['dq']),
iqmp=from_base64url_uint(obj['qi']),
public_numbers=public_numbers
)
else:
d = from_base64url_uint(obj['d'])
p, q = rsa_recover_prime_factors(
public_numbers.n, d, public_numbers.e
)
numbers = RSAPrivateNumbers(
d=d,
p=p,
q=q,
dmp1=rsa_crt_dmp1(d, p),
dmq1=rsa_crt_dmq1(d, q),
iqmp=rsa_crt_iqmp(p, q),
public_numbers=public_numbers
)
return numbers.private_key(default_backend())
elif 'n' in obj and 'e' in obj:
# Public key
numbers = RSAPublicNumbers(
from_base64url_uint(obj['e']), from_base64url_uint(obj['n'])
)
return numbers.public_key(default_backend())
else:
raise InvalidKeyError('Not a public or private key')
