def plot_crypt(max_key_length, trials):
key_lengths = range(8, max_key_length + 1)
encryption_times = []
for key_length in key_lengths:
print('Computing key length', key_length)
key_length_time = 0
for _ in range(trials):
e, _, n = generate_keys(key_length)
time_before = time()
crypt(n - 1, (e, n))
time_after = time()
key_length_time += time_after - time_before
encryption_times.append(key_length_time / trials)
pyplot.plot(key_lengths, encryption_times)
pyplot.title('Encryption Time vs. Key Length')
pyplot.xlabel('Key Length (in bits)')
pyplot.ylabel('Encryption Time (in seconds)')
pyplot.show()
import rsa
# FAKE WORKING EXEMPLE on PYTHON 3
# from https://github.com/Theo6898/Python-RSA-module
# version 1.0 - 15 november 2015
# For security issues, server and user need to know their respective public keys for sure
# You need a trust authoritie to check if the public keys are correct
#Generating key pairs
publicKeyUser, privateKeyUser = rsa.generateKeyPair("RSA-1024")
publicKeyServer, privateKeyServer = rsa.generateKeyPair("RSA-1024")
# user crypt message with server's public key and sign it with its own private key
data = ["Hello this a message", "And another one !"]
data_crypted = rsa.crypt(data, publicKeyServer)
data_signed = rsa.sign(data, privateKeyUser)
# server decrypt the message with its own private key and check if the message has been signed by the user itself
data_decrypted = rsa.decrypt(data_crypted, privateKeyServer)
if rsa.check_signature(data_decrypted, data_signed, publicKeyUser) == True:
print("Message received :\n", data_decrypted)
else:
print("Invalid signature, man in the middle attack")
def parity(ciphertext):
"""Ciphertext is an integer. Depends on privkey."""
decrypt_int = rsa.crypt(ciphertext, privkey)
return int(decrypt_int % 2) # int, not a long.
bounds = [0, n]
start = time.time()
for i in range(2048):
p = parity(multiply(ciphertext, 2**(i + 1), e, n))
half_the_dist = (bounds[1] - bounds[0]) / 2
if p == 0:
bounds = [bounds[0], bounds[1] - half_the_dist]
elif p == 1:
bounds = [bounds[0] + half_the_dist, bounds[1]]
if i % 16 == 0:
print p, i, cleanup(rsa.i2s(bounds[1]),
'_') # get 256 char wide screen
end = time.time()
dur = round(end - start, 1)
print "--------"
for b in bounds:
print rsa.i2s(b)
print "2048 oracularities in", dur, "s =", round(2048 / dur, 1), "per s."
#### tests ####
hi = 'Hi'
c_hi = rsa.encrypt_string(hi, pubkey)
D = multiply(c_hi, 2, pubkey[0], pubkey[1])
assert rsa.s2i(hi) * 2 == rsa.crypt(D, privkey)
warn("Passed assertions:", __file__)
def parity(ciphertext):
"""Ciphertext is an integer. Depends on privkey."""
decrypt_int = rsa.crypt(ciphertext, privkey)
return int(decrypt_int % 2) # int, not a long.
# theory, I think we could just cube-root it, but oh well.
bounds = [0, n]
start = time.time()
for i in range(2048):
p = parity(multiply(ciphertext, 2**(i+1), e, n))
half_the_dist = (bounds[1] - bounds[0]) / 2
if p == 0:
bounds = [bounds[0], bounds[1] - half_the_dist]
elif p == 1:
bounds = [bounds[0] + half_the_dist, bounds[1]]
if i % 16 == 0:
print p, i, cleanup(rsa.i2s(bounds[1]), '_') # get 256 char wide screen
end = time.time()
dur = round(end - start, 1)
print "--------"
for b in bounds:
print rsa.i2s(b)
print "2048 oracularities in", dur, "s =", round(2048 / dur, 1), "per s."
#### tests ####
hi = 'Hi'
c_hi = rsa.encrypt_string(hi, pubkey)
D = multiply(c_hi, 2, pubkey[0], pubkey[1])
assert rsa.s2i(hi) * 2 == rsa.crypt(D, privkey)
warn("Passed assertions:", __file__)
# RSA numbers below RSA-1024 are not secured enough, # use them for better performances during developement # - "RSA-2048" # - "RSA-1536" # - "RSA-1024" # - "RSA-896" # - "RSA-768" # - "RSA-704" # - "RSA-576" #--------------------------------------------------------------------------------- # Crypt a message #--------------------------------------------------------------------------------- data = ["abc", 1, 7] data_crypted = rsa.crypt(data, key) # it takes 2 arguments : # - a LIST of datas to encrypt (it can only contain int and str) # - a key (public or private), the message can be decrypted with the opposite key # exemple : by encrypting a message with a public key you will be able to decrypt # it with the corresponding private key and vice-versa. # the function return a list of the encrypted datas # in this case it could return something like that # [[89, 23, 41], 31, 97] # as you can see every single letter in the 'data' string 'abc' is transformed by a number #--------------------------------------------------------------------------------- # Decrypt a message
parser = argparse.ArgumentParser()
parsers = parser.add_subparsers(dest='command')
generate_keys_parser = parsers.add_parser('generate_keys')
generate_keys_parser.add_argument('seed_length', type=int)
crypt_parser = parsers.add_parser('crypt', aliases=['encrypt', 'decrypt'])
crypt_parser.add_argument('key', type=int, nargs=2)
crypt_parser.add_argument('message', type=int)
crack_parser = parsers.add_parser('crack')
crack_parser.add_argument('key', type=int, nargs=2)
plot_parser = parsers.add_parser('plot')
plot_parser.add_argument('operation', type=str, choices=['crypt', 'crack'])
plot_parser.add_argument('max_key_length', type=int)
plot_parser.add_argument('trials', type=int)
args = parser.parse_args()
if args.command == 'generate_keys':
print(generate_keys(args.seed_length))
elif args.command == 'encrypt' or args.command == 'decrypt':
print(crypt(args.message, args.key))
elif args.command == 'crack':
print(math_attack(*args.key))
elif args.command == 'plot':
if args.operation == 'crypt':
plot_crypt(args.max_key_length, args.trials)
if args.operation == 'crack':
plot_crack(args.max_key_length, args.trials)
else:
raise argparse.ArgumentTypeError('Invalid command')
import rsa
# FAKE WORKING EXEMPLE on PYTHON 3
# from https://github.com/Theo6898/Python-RSA-module
# version 1.0 - 15 november 2015
# For security issues, server and user need to know their respective public keys for sure
# You need a trust authoritie to check if the public keys are correct
#Generating key pairs
publicKeyUser, privateKeyUser = rsa.generateKeyPair("RSA-1024")
publicKeyServer, privateKeyServer = rsa.generateKeyPair("RSA-1024")
# user crypt message with server's public key and sign it with its own private key
data = ["Hello this a message", "And another one !"]
data_crypted = rsa.crypt(data, publicKeyServer)
data_signed = rsa.sign(data, privateKeyUser)
# server decrypt the message with its own private key and check if the message has been signed by the user itself
data_decrypted = rsa.decrypt(data_crypted, privateKeyServer)
if rsa.check_signature(data_decrypted, data_signed, publicKeyUser) == True:
print("Message received :\n", data_decrypted)
else:
print("Invalid signature, man in the middle attack")
