def attack(attack_rsa_obj, publickey, cipher=[]):
"""Use boneh durfee method, should return a d value, else returns 0
only works if the sageworks() function returned True
many of these problems will be solved by the wiener attack module but perhaps some will fall through to here
"""
try:
sageresult = int(
subprocess.check_output(
[
"sage",
"%s/sage/boneh_durfee.sage" % rootpath,
str(publickey.n),
str(publickey.e)
],
timeout=attack_rsa_obj.args.timeout,
))
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
if sageresult > 0:
tmp_priv = RSA.construct(
(int(publickey.n), int(publickey.e), int(sageresult)))
publickey.p = tmp_priv.p
publickey.q = tmp_priv.q
privatekey = PrivateKey(
p=int(publickey.p),
q=int(publickey.q),
e=int(publickey.e),
n=int(publickey.n),
)
return (privatekey, None)
return (None, None)
def attack(attack_rsa_obj, publickeys, cipher=[]):
""" Common factor attack
"""
if not isinstance(publickeys, list):
return (None, None)
# Try to find the gcd between each pair of moduli and resolve the private keys if gcd > 1
priv_keys = []
tmp = 1
for x in publickeys:
tmp *= x.n
for x in publickeys:
g = gcd(x.n, tmp)
if 1 < g < x.n:
logger.info("[*] Found common factor in modulus for " + x.filename)
# update each attackobj with a private_key
x.p = g
x.q = x.n // g
priv_key = PrivateKey(int(x.p), int(x.q), int(x.e), int(x.n))
priv_keys.append(priv_key)
priv_keys = list(set(priv_keys))
if len(priv_keys) == 0:
priv_keys = None
return (priv_keys, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""binary polinomial factoring
"""
try:
sageresult = str(
subprocess.check_output(
[
"sage",
"%s/sage/binary_polinomial_factoring.sage" % rootpath,
str(publickey.n),
],
timeout=attack_rsa_obj.args.timeout,
)).split(" ")
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
try:
p = int(sageresult[0])
except ValueError:
return (None, None)
if p > 0:
q = publickey.n // p
priv_key = PrivateKey(int(p), int(q), int(publickey.e),
int(publickey.n))
return (priv_key, None)
else:
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Try an attack where q < 100,000, from BKPCTF2016 - sourcekris
"""
for prime in primes(100000):
if publickey.n % prime == 0:
publickey.q = prime
publickey.p = publickey.n // publickey.q
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Wiener's attack
"""
wiener = WienerAttack(publickey.n, publickey.e)
if wiener.p is not None and wiener.q is not None:
publickey.p = wiener.p
publickey.q = wiener.q
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""use elliptic curve method, may return a prime or may never return
only works if the sageworks() function returned True
"""
logger.warning(
"[*] ECM Method can run forever and may never succeed, timeout set to %ssec. Hit Ctrl-C to bail out."
% attack_rsa_obj.args.timeout)
try:
try:
ecmdigits = attack_rsa_obj.args.ecmdigits
if ecmdigits:
sageresult = int(
subprocess.check_output(
[
"sage",
"%s/sage/ecm.sage" % rootpath,
str(publickey.n),
str(ecmdigits)
],
timeout=attack_rsa_obj.args.timeout,
))
else:
sageresult = int(
subprocess.check_output(
[
"sage",
"%s/sage/ecm.sage" % rootpath,
str(publickey.n)
],
timeout=attack_rsa_obj.args.timeout,
))
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
if sageresult > 0:
publickey.p = sageresult
publickey.q = publickey.n // publickey.p
try:
priv_key = PrivateKey(
int(publickey.p),
int(publickey.q),
int(publickey.e),
int(publickey.n),
)
return (priv_key, None)
except:
return (None, None)
return (None, None)
except KeyboardInterrupt:
pass
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Do nothing, used for multi-key attacks that succeeded so we just print the
private key without spending any time factoring
"""
londahl_b = 20000000
factors = close_factor(publickey.n, londahl_b)
if factors is not None:
p, q = factors
priv_key = PrivateKey(int(p), int(q), int(publickey.e),
int(publickey.n))
return (priv_key, None)
else:
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Run fermat attack with a timeout
"""
try:
with timeout(seconds=attack_rsa_obj.args.timeout):
publickey.p, publickey.q = fermat(publickey.n)
except FactorizationError:
return (None, None)
if publickey.q is not None:
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Try an attack where the public key has a common factor with the ciphertext - sourcekris
"""
if cipher is not None:
for c in cipher:
commonfactor = gcd(publickey.n, s2n(c))
if commonfactor > 1:
publickey.q = commonfactor
publickey.p = publickey.n // publickey.q
priv_key = PrivateKey(
int(publickey.p),
int(publickey.q),
int(publickey.e),
int(publickey.n),
)
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
""" "primes" of the form 31337 - 313333337 - see ekoparty 2015 "rsa 2070"
not all numbers in this form are prime but some are (25 digit is prime)
"""
maxlen = 25 # max number of digits in the final integer
for i in range(maxlen - 4):
prime = int("3133" + ("3" * i) + "7")
if publickey.n % prime == 0:
publickey.p = prime
publickey.q = publickey.n // publickey.p
priv_key = PrivateKey(
p=int(publickey.p),
q=int(publickey.q),
e=int(publickey.e),
n=int(publickey.n),
)
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
try:
sageresult = subprocess.check_output(
["sage",
"%s/sage/roca_attack.py" % rootpath,
str(publickey.n)],
timeout=attack_rsa_obj.args.timeout,
)
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
if b"FAIL" not in sageresult and b":" in sageresult:
sageresult = sageresult.decode("utf-8").strip()
p, q = map(int, sageresult.split(":"))
priv_key = PrivateKey(int(p), int(q), int(publickey.e),
int(publickey.n))
return (priv_key, None)
else:
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Qi Cheng - A New Class of Unsafe Primes
"""
try:
sageresult = int(
subprocess.check_output(
["sage", "%s/sage/qicheng.sage" % rootpath, str(publickey.n)],
timeout=attack_rsa_obj.args.timeout,
)
)
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
if sageresult > 0:
p = sageresult
q = publickey.n // sageresult
priv_key = PrivateKey(int(p), int(q), int(publickey.e), int(publickey.n))
return (priv_key, None)
else:
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Run attack with Pollard Rho
"""
if not hasattr(publickey, "p"):
publickey.p = None
if not hasattr(publickey, "q"):
publickey.q = None
# pollard Rho attack
try:
poll_res = pollard_rho(publickey.n)
except RecursionError:
print("RecursionError")
return (None, None)
if poll_res and len(poll_res) > 1:
publickey.p, publickey.q = poll_res
if publickey.q is not None:
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Try to factorize using yafu
"""
if publickey.n.bit_length() > 1024:
logger.error("[!] Warning: Modulus too large for SIQS attack module")
return (None, None)
siqsobj = SiqsAttack(attack_rsa_obj, publickey.n)
siqsobj.checkyafu()
siqsobj.testyafu()
if siqsobj.checkyafu() and siqsobj.testyafu():
siqsobj.doattack()
if siqsobj.p and siqsobj.q:
publickey.q = siqsobj.q
publickey.p = siqsobj.p
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Code/idea from Renaud Lifchitz's talk 15 ways to break RSA security @ OPCDE17
only works if the sageworks() function returned True
"""
try:
r = subprocess.check_output(
[
"sage",
"%s/sage/smallfraction.sage" % rootpath,
str(publickey.n)
],
timeout=attack_rsa_obj.args.timeout,
)
sageresult = int(r)
if sageresult > 0:
publickey.p = sageresult
publickey.q = publickey.n // publickey.p
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
except (subprocess.CalledProcessError, subprocess.TimeoutExpired):
return (None, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Factors available online?
"""
try:
url_1 = "http://factordb.com/index.php?query=%i"
url_2 = "http://factordb.com/index.php?id=%s"
s = requests.Session()
r = s.get(url_1 % publickey.n, verify=False)
regex = re.compile(r"index\.php\?id\=([0-9]+)", re.IGNORECASE)
ids = regex.findall(r.text)
# check if only 1 factor is returned
if len(ids) == 2:
# theres a chance that the only factor returned is prime, and so we can derive the priv key from it
regex = re.compile(r"<td>P<\/td>")
prime = regex.findall(r.text)
if len(prime) == 1:
# n is prime, so lets get the key from it
d = invmod(publickey.e, publickey.n - 1)
# construct key using only n and d
priv_key = PrivateKey(e=int(publickey.e), n=int(publickey.n), d=d)
return (priv_key, None)
elif len(ids) == 3:
try:
regex = re.compile(r'value="([0-9\^\-]+)"', re.IGNORECASE)
p_id = ids[1]
r_1 = s.get(url_2 % p_id, verify=False)
key_p = regex.findall(r_1.text)[0]
publickey.p = int(key_p) if key_p.isdigit() else solveforp(key_p)
q_id = ids[2]
r_2 = s.get(url_2 % q_id, verify=False)
key_q = regex.findall(r_2.text)[0]
publickey.q = int(key_q) if key_q.isdigit() else solveforp(key_q)
if publickey.n != int(key_p) * int(key_q):
return (None, None)
except IndexError:
return (None, None)
try:
priv_key = PrivateKey(
p=int(publickey.p),
q=int(publickey.q),
e=int(publickey.e),
n=int(publickey.n),
)
except ValueError:
return (None, None)
return (priv_key, None)
elif len(ids) > 3:
phi = 1
for p in ids[1:]:
phi *= int(p) - 1
d = invmod(publickey.e, phi)
plains = []
for c in cipher:
int_big = int.from_bytes(c, "big")
plain1 = pow(int_big, d, publickey.n)
plains.append(long_to_bytes(plain1))
return (None, plains)
return (None, None)
except NotImplementedError:
return (None, None)
def main():
# Remove insecure warning for factordb.com
urllib3.disable_warnings(InsecureRequestWarning)
# Change recursion limit for... you know, factorizing stuff...
sys.setrecursionlimit(5000)
logger = logging.getLogger("global_logger")
parser = argparse.ArgumentParser(description="RSA CTF Tool")
parser.add_argument(
"--publickey", help="public key file. You can use wildcards for multiple keys."
)
parser.add_argument(
"--output", help="output file for results (privates keys, plaintext data)."
)
parser.add_argument(
"--timeout", help="Timeout for long attacks.", default=30, type=int
)
parser.add_argument(
"--createpub",
help="Take n and e from cli and just print a public key then exit",
action="store_true",
)
parser.add_argument(
"--dumpkey",
help="Just dump the RSA variables from a key - n,e,d,p,q",
action="store_true",
)
parser.add_argument(
"--ext",
help="Extended dump of RSA private variables in --dumpkey mode - dp,dq,pinv,qinv).",
action="store_true",
)
parser.add_argument("--uncipherfile", help="uncipher a file", default=None)
parser.add_argument("--uncipher", help="uncipher a cipher", default=None)
parser.add_argument(
"--verbosity", help="verbose mode", choices=logger_levels.keys(), default="INFO"
)
parser.add_argument(
"--private", help="Display private key if recovered", action="store_true"
)
parser.add_argument(
"--ecmdigits",
type=int,
help="Optionally an estimate as to how long one of the primes is for ECM method",
default=None,
)
parser.add_argument("-n", help="Specify the modulus. format : int or 0xhex")
parser.add_argument(
"-p", help="Specify the first prime number. format : int or 0xhex"
)
parser.add_argument(
"-q", help="Specify the second prime number. format : int or 0xhex"
)
parser.add_argument("-e", help="Specify the public exponent. format : int or 0xhex")
parser.add_argument("--key", help="Specify the private key file.")
parser.add_argument("--password", help="Private key password if needed.")
# Dynamic load all attacks for choices in argparse
attacks = glob(join(dirname(__file__), "attacks", "single_key", "*.py"))
attacks += glob(join(dirname(__file__), "attacks", "multi_keys", "*.py"))
attacks_filtered = [
basename(f)[:-3] for f in attacks if isfile(f) and not f.endswith("__init__.py")
]
attacks_list = [_ for _ in attacks_filtered if _ != "nullattack"] + ["all"]
parser.add_argument(
"--attack", help="Specify the attack mode.", default="all", choices=attacks_list
)
args = parser.parse_args()
unciphers = []
# Set logger level
logging.basicConfig(level=logger_levels[args.verbosity],)
ch = logging.StreamHandler()
ch.setFormatter(CustomFormatter())
logger = logging.getLogger("global_logger")
logger.propagate = False
logger.addHandler(ch)
# If no arguments, diplay help and exit
if len(sys.argv) == 1:
parser.print_help()
sys.exit(1)
# Add information
if not args.private:
logger.warning(
"private argument is not set, the private key will not be displayed, even if recovered."
)
# Parse longs if exists
if args.p is not None:
args.p = get_numeric_value(args.p)
if args.q is not None:
args.q = get_numeric_value(args.q)
if args.e is not None:
args.e = get_numeric_value(args.e)
# get n if we can
if args.n is not None:
args.n = get_numeric_value(args.n)
elif args.p is not None and args.q is not None:
args.n = args.p * args.q
# if we have uncipher but no uncipherfile
if args.uncipher is not None:
uncipher_array = []
for uncipher in args.uncipher.split(","):
uncipher = get_numeric_value(uncipher)
uncipher_array.append(n2s(uncipher))
args.uncipher = uncipher_array
# if we have uncipherfile
if args.uncipherfile is not None:
uncipher_array = []
for uncipher in args.uncipherfile.split(","):
try:
with open(uncipher, "rb") as cipherfile_fd:
uncipher_array.append(cipherfile_fd.read())
except OSError as e:
logger.info("--uncipherfile : file not found or not readable.")
exit(1)
args.uncipher = uncipher_array
# If we have a private key in input and uncipher in args (or uncipherfile)
if args.key and args.uncipher:
priv_key = PrivateKey(filename=args.key, password=args.password)
for u in args.uncipher:
unciphers.append(priv_key.decrypt(args.u))
print_results(args, None, priv_key, unciphers)
exit(0)
# If we have n and one of p and q, calculated the other
if args.n and (args.p or args.q):
args.p, args.q = generate_pq_from_n_and_p_or_q(args.n, args.p, args.q)
# Create pubkey if requested
if args.createpub:
pub_key, priv_key = generate_keys_from_p_q_e_n(args.p, args.q, args.e, args.n)
print(pub_key.decode("utf-8"))
exit(0)
# Load keys
tmpfile = None
if args.publickey is None and args.e is not None and args.n is not None:
tmpfile = tempfile.NamedTemporaryFile()
with open(tmpfile.name, "wb") as tmpfd:
tmpfd.write(RSA.construct((args.n, args.e)).publickey().exportKey())
args.publickey = [tmpfile.name]
elif args.publickey is not None:
if "*" in args.publickey or "?" in args.publickey:
pubkeyfilelist = glob(args.publickey)
args.publickey = pubkeyfilelist
elif "," in args.publickey:
args.publickey = args.publickey.split(",")
else:
args.publickey = [args.publickey]
# If we already have all informations
if (
args.p is not None
and args.q is not None
and args.e is not None
and args.n is not None
):
pub_key, priv_key = generate_keys_from_p_q_e_n(args.p, args.q, args.e, args.n)
if args.createpub:
print(pub_key)
if args.uncipher is not None:
for u in args.uncipher:
unciphers.append(priv_key.decrypt(args.uncipher))
print_results(args, args.publickey[0], priv_key, unciphers)
exit(0)
# Dump public key informations
if (
args.dumpkey
and not args.private
and args.uncipher is None
and args.uncipherfile is None
and args.publickey is not None
):
for publickey in args.publickey:
logger.info("Details for %s:" % publickey)
with open(publickey, "rb") as key_data_fd:
key = RSA.importKey(key_data_fd.read())
print("n: " + str(key.n))
print("e: " + str(key.e))
exit(0)
# if dumpkey mode dump the key components then quit
if args.key is not None and args.dumpkey:
key_data = open(args.key, "rb").read()
key = RSA.importKey(key_data)
print("n: " + str(key.n))
print("e: " + str(key.e))
if key.has_private():
print("d: " + str(key.d))
print("p: " + str(key.p))
print("q: " + str(key.q))
if args.ext:
dp = key.d % (key.p - 1)
dq = key.d % (key.q - 1)
pinv = invmod(key.p, key.q)
qinv = invmod(key.q, key.p)
print("dp: " + str(dp))
print("dq: " + str(dq))
print("pinv: " + str(pinv))
print("qinv: " + str(qinv))
exit(0)
# Run attacks
found = False
attackobj = RSAAttack(args)
if len(args.publickey) > 1:
found = attackobj.attack_multiple_keys(args.publickey, attacks_list)
if not found:
for publickey in args.publickey:
attackobj.implemented_attacks = []
logger.info("\n[*] Testing key %s." % publickey)
attackobj.attack_single_key(publickey, attacks_list)
attackobj.unciphered = []
def attack(attack_rsa_obj, publickey, cipher=[]):
""" Search for previously used primes in CTFs
"""
primes = [
108082147276398906822234149167480016132157014049560913761488880190018027488520386318253742675423286348552334110023434741671427911613197684395221211646299519273129194692306445874938199068586137486874290442314459278649345469626426790676801658394799404284116771456479272808343825651929906737811050557836671896732124546721747709022607151231423494815945385193624295868730390462068156825588342737037490320356361648437686599733,
108082147276398906822234149167480016132157014049560913761488880190018027488520386318253742675423286348552334110023434741671427911613197684395221211646299519273129194692306445874938199068586137486874290442314459278649345469626426790676801658394799404284116771456479272808343825651929906737811050557836671896732124546721747709022607151231423494815945385193624295868730390462068156825588342737037490320356361648437686598461,
108082147276398906822234149167480016132157014049560913761488880190018027488520386318253742675423286348552334110023434741671427911613197684395221211646299519273129194692306445874938199068586137486874290442314459278649345469626426790676801658394799404284116771456479272808343825651929906737811050557836671896732124546721747709022607151231423494815945385193624295868730390462068156825588342737037490320356361648437686597791,
108082147276398906822234149167480016132157014049560913761488880190018027488520386318253742675423286348552334110023434741671427911613197684395221211646299519273129194692306445874938199068586137486874290442314459278649345469626426790676801658394799404284116771456479272808343825651929906737811050557836671896732124546721747709022607151231423494815945385193624295868730390462068156825588342737037490320356361648437686600843,
6703903965361517118576511528025622717463828698514771456694902115718276634989944955753407851598489976727952425488221391817052769267904281935379659980013749,
13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903820008890319855427587165500997237443558735689450602365103,
4101860217206195486319508931988944464741665503169699281154625914180099350459859416508157842908810493659777848990372055112637980426665995893689191266676993,
4101860217206195486319508931988944464741665503169699281154625914180099350459859416508157842908810493659777848990372055112637980426665995893689191266677141,
4101860217206195486319508931988944464741665503169699281154625914180099350459859416508157842908810493659777848990372055112637980426665995893689191266677279,
4165938907260954640804986514555496835723686162893011508104816859692320046868363019435944953520658898678455053432699809898947934756189120526030787871227407,
4165938907260954640804986514555496835723686162893011508104816859692320046868363019435944953520658898678455053432699809898947934756189120526030787871227587,
4165938907260954640804986514555496835723686162893011508104816859692320046868363019435944953520658898678455053432699809898947934756189120526030787871227863,
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]
for prime in primes:
if publickey.n % prime == 0:
publickey.q = prime
publickey.p = publickey.n // publickey.q
priv_key = PrivateKey(int(publickey.p), int(publickey.q),
int(publickey.e), int(publickey.n))
return (priv_key, None)
return (None, None)
def attack(attack_rsa_obj, publickey, cipher=[]):
"""Run tests against mersenne primes
"""
p = q = None
mersenne_tab = [
2,
3,
5,
7,
13,
17,
19,
31,
61,
89,
107,
127,
521,
607,
1279,
2203,
2281,
3217,
4253,
4423,
9689,
9941,
11213,
19937,
21701,
23209,
44497,
86243,
110503,
132049,
216091,
756839,
859433,
1257787,
1398269,
2976221,
3021377,
6972593,
13466917,
20336011,
24036583,
25964951,
30402457,
32582657,
37156667,
42643801,
43112609,
57885161,
74207281,
77232917,
82589933,
]
for mersenne_prime in mersenne_tab:
if publickey.n % ((2**mersenne_prime) - 1) == 0:
p = (2**mersenne_prime) - 1
q = publickey.n // ((2**mersenne_prime) - 1)
break
if p is not None and q is not None:
priv_key = PrivateKey(int(p), int(q), int(publickey.e),
int(publickey.n))
return (priv_key, None)
return (None, None)
