def check_integrity(self, msg=12345678987654321):
# Assert gcd(e, phi(n)) == 1
phi_n = (self.p - 1) * (self.q - 1)
gcd = NumberTheory.gcd(phi_n, self.e)
if gcd != 1:
raise KeyCorruptException(
"Expected gcd(phi(n), e) to be 1, but was %d." % (gcd))
# Truncate msg if too large for exponent
msg = msg % self.n
# Calculate normale signature and verify
sig = pow(msg, self.d, self.n)
verify = pow(sig, self.e, self.n)
if verify != msg:
raise KeyCorruptException("Expected verify value %d, but got %d." %
(msg, verify))
# Test that RSA-CRT constants work
m1 = pow(msg, self.dmp1, self.p)
m2 = pow(msg, self.dmq1, self.q)
sig_crt = (((self.iqmp * (m1 - m2)) % self.p) * self.q) + m2
if sig != sig_crt:
raise KeyCorruptException(
"Expected same signature for naive signature as RSA-CRT signature, but former was 0x%x and latter 0x%x."
% (sig, sig_crt))
def test_gcd_n_phi_n(self):
with tempfile.TemporaryDirectory() as tempdir, WorkDir(tempdir):
PrimeDB().add(0x1fd22b50d1e28365855635,
0x3af25062dcf148b85084f5).write()
output = self._run_x509sak(
["genbrokenrsa", "--bitlen", "257", "--gcd-n-phi-n",
"-v"]).stdout
key = RSAPrivateKey.read_pemfile("broken_rsa.key")[0]
self.assertEqual(key.n.bit_length(), 257)
self.assertEqual(key.p, 0x1fd22b50d1e28365855635)
self.assertEqual(key.q,
0xea778f672d05715314fd556a2667dca7743e33da973)
self.assertEqual((key.q - 1) % (2 * key.p), 0)
self.assertNotEqual(NumberTheory.gcd(key.n, key.phi_n), 1)
self.assertEqual(key.e, 0x10001)
self.assertIn(b"gcd(n, phi(n)) = p", output)
key.check_integrity()
def create(cls,
p,
q,
e=0x10001,
swap_e_d=False,
valid_only=True,
carmichael_totient=False):
n = p * q
if not carmichael_totient:
totient = (p - 1) * (q - 1)
else:
totient = NumberTheory.lcm(p - 1, q - 1)
gcd = NumberTheory.gcd(e, totient)
if (gcd != 1) and valid_only:
raise KeyCorruptException(
"e = 0x%x isnt't relative prime to totient, gcd = 0x%x. Either accept broken keys or fix e."
% (e, gcd))
d = NumberTheory.modinv(e, totient)
if swap_e_d:
(e, d) = (d, e)
dmp1 = d % (p - 1)
dmq1 = d % (q - 1)
iqmp = NumberTheory.modinv(q, p)
asn1 = cls._ASN1_MODEL()
asn1["version"] = 0
asn1["modulus"] = n
asn1["publicExponent"] = e
asn1["privateExponent"] = d
asn1["prime1"] = p
asn1["prime2"] = q
asn1["exponent1"] = dmp1
asn1["exponent2"] = dmq1
asn1["coefficient"] = iqmp
der = pyasn1.codec.der.encoder.encode(asn1)
return cls(der)
def __init__(self, cmdname, args):
BaseAction.__init__(self, cmdname, args)
if (not self._args.force) and os.path.exists(self._args.outfile):
raise UnfulfilledPrerequisitesException(
"File/directory %s already exists. Remove it first or use --force."
% (self._args.outfile))
if not self._args.gcd_n_phi_n:
self._primetype = "2msb"
self._p_bitlen = self._args.bitlen // 2
self._q_bitlen = self._args.bitlen - self._p_bitlen
else:
self._primetype = "3msb"
self._p_bitlen = self._args.bitlen // 3
self._q_bitlen = self._args.bitlen - (2 * self._p_bitlen) - 1
if (self._args.close_q) and (self._p_bitlen != self._q_bitlen):
raise UnfulfilledPrerequisitesException(
"Generating a close-q keypair with a %d modulus does't work, because p would have to be %d bit and q %d bit. Choose an even modulus bitlength."
% (self._args.bitlen, self._p_bitlen, self._q_bitlen))
if self._args.q_stepping < 1:
raise InvalidInputException(
"q-stepping value must be greater or equal to 1, was %d." %
(self._args.q_stepping))
self._log.debug("Selecting %s primes with p = %d bit and q = %d bit.",
self._primetype, self._p_bitlen, self._q_bitlen)
self._prime_db = PrimeDB(self._args.prime_db,
generator_program=self._args.generator)
p = None
q = None
while True:
if p is None:
p = self._prime_db.get(bitlen=self._p_bitlen,
primetype=self._primetype)
q_generator = self._select_q(p)
if q is None:
q = next(q_generator)
if self._args.gcd_n_phi_n:
# q = (2 * r * p) + 1
r = q
q = 2 * r * p + 1
if not NumberTheory.is_probable_prime(q):
q = None
continue
# Always make p the smaller factor
if p > q:
(p, q) = (q, p)
n = p * q
if self._args.public_exponent == -1:
e = random.randint(2, n - 1)
else:
e = self._args.public_exponent
if self._args.carmichael_totient:
totient = NumberTheory.lcm(p - 1, q - 1)
else:
totient = (p - 1) * (q - 1)
gcd = NumberTheory.gcd(totient, e)
if self._args.accept_unusable_key or (gcd == 1):
break
else:
# Pair (phi(n), e) wasn't acceptable.
self._log.debug("gcd(totient, e) was %d, retrying.", gcd)
if self._args.public_exponent != -1:
# Public exponent e is fixed, need to choose another q.
if p.bit_length() == q.bit_length():
# Can re-use q as next p
(p, q) = (q, None)
q_generator = self._select_q(p)
else:
# When they differ in length, need to re-choose both values
(p, q) = (None, None)
rsa_keypair = RSAPrivateKey.create(
p=p,
q=q,
e=e,
swap_e_d=self._args.switch_e_d,
valid_only=not self._args.accept_unusable_key,
carmichael_totient=self._args.carmichael_totient)
rsa_keypair.write_pemfile(self._args.outfile)
if self._args.verbose >= 1:
diff = q - p
print("Generated %d bit RSA key:" % (rsa_keypair.n.bit_length()))
print("p = 0x%x" % (rsa_keypair.p))
if not self._args.gcd_n_phi_n:
print("q = 0x%x" % (rsa_keypair.q))
else:
print("q = 2 * r * p + 1 = 0x%x" % (rsa_keypair.q))
print("r = 0x%x" % (r))
print("phi(n) = 0x%x" % (rsa_keypair.phi_n))
print("lambda(n) = 0x%x" % (rsa_keypair.lambda_n))
print("phi(n) / lambda(n) = gcd(p - 1, q - 1) = %d" %
(rsa_keypair.phi_n // rsa_keypair.lambda_n))
gcd_n_phin = NumberTheory.gcd(rsa_keypair.n, rsa_keypair.phi_n)
if gcd_n_phin == rsa_keypair.p:
print("gcd(n, phi(n)) = p")
else:
print("gcd(n, phi(n)) = 0x%x" % (gcd_n_phin))
if self._args.close_q:
print("q - p = %d (%d bit)" % (diff, diff.bit_length()))
print("n = 0x%x" % (rsa_keypair.n))
print("d = 0x%x" % (rsa_keypair.d))
print("e = 0x%x" % (rsa_keypair.e))