X-Git-Url: http://gitweb.pimeys.fr/?p=NK2015_Client_Python_Alpha.git;a=blobdiff_plain;f=rsa_source%2Frsa%2F_version133.py;fp=rsa_source%2Frsa%2F_version133.py;h=1adae42bdcdc92718045d0164ce3570e9b15e9f9;hp=0000000000000000000000000000000000000000;hb=76e06d82c94bcb814b95419c7faaeacf4beb0155;hpb=d621c5224a44dc20bc2aaf661954fd1df65dd147 diff --git a/rsa_source/rsa/_version133.py b/rsa_source/rsa/_version133.py new file mode 100644 index 0000000..1adae42 --- /dev/null +++ b/rsa_source/rsa/_version133.py @@ -0,0 +1,440 @@ +"""RSA module +pri = k[1] //Private part of keys d,p,q + +Module for calculating large primes, and RSA encryption, decryption, +signing and verification. Includes generating public and private keys. + +WARNING: this code implements the mathematics of RSA. It is not suitable for +real-world secure cryptography purposes. It has not been reviewed by a security +expert. It does not include padding of data. There are many ways in which the +output of this module, when used without any modification, can be sucessfully +attacked. +""" + +__author__ = "Sybren Stuvel, Marloes de Boer and Ivo Tamboer" +__date__ = "2010-02-05" +__version__ = '1.3.3' + +# NOTE: Python's modulo can return negative numbers. We compensate for +# this behaviour using the abs() function + +from cPickle import dumps, loads +import base64 +import math +import os +import random +import sys +import types +import zlib + +# Display a warning that this insecure version is imported. +import warnings +warnings.warn('Insecure version of the RSA module is imported as %s, be careful' + % __name__) + +def gcd(p, q): + """Returns the greatest common divisor of p and q + + + >>> gcd(42, 6) + 6 + """ + if p>> (128*256 + 64)*256 + + 15 + 8405007 + >>> l = [128, 64, 15] + >>> bytes2int(l) + 8405007 + """ + + if not (type(bytes) is types.ListType or type(bytes) is types.StringType): + raise TypeError("You must pass a string or a list") + + # Convert byte stream to integer + integer = 0 + for byte in bytes: + integer *= 256 + if type(byte) is types.StringType: byte = ord(byte) + integer += byte + + return integer + +def int2bytes(number): + """Converts a number to a string of bytes + + >>> bytes2int(int2bytes(123456789)) + 123456789 + """ + + if not (type(number) is types.LongType or type(number) is types.IntType): + raise TypeError("You must pass a long or an int") + + string = "" + + while number > 0: + string = "%s%s" % (chr(number & 0xFF), string) + number /= 256 + + return string + +def fast_exponentiation(a, p, n): + """Calculates r = a^p mod n + """ + result = a % n + remainders = [] + while p != 1: + remainders.append(p & 1) + p = p >> 1 + while remainders: + rem = remainders.pop() + result = ((a ** rem) * result ** 2) % n + return result + +def read_random_int(nbits): + """Reads a random integer of approximately nbits bits rounded up + to whole bytes""" + + nbytes = ceil(nbits/8.) + randomdata = os.urandom(nbytes) + return bytes2int(randomdata) + +def ceil(x): + """ceil(x) -> int(math.ceil(x))""" + + return int(math.ceil(x)) + +def randint(minvalue, maxvalue): + """Returns a random integer x with minvalue <= x <= maxvalue""" + + # Safety - get a lot of random data even if the range is fairly + # small + min_nbits = 32 + + # The range of the random numbers we need to generate + range = maxvalue - minvalue + + # Which is this number of bytes + rangebytes = ceil(math.log(range, 2) / 8.) + + # Convert to bits, but make sure it's always at least min_nbits*2 + rangebits = max(rangebytes * 8, min_nbits * 2) + + # Take a random number of bits between min_nbits and rangebits + nbits = random.randint(min_nbits, rangebits) + + return (read_random_int(nbits) % range) + minvalue + +def fermat_little_theorem(p): + """Returns 1 if p may be prime, and something else if p definitely + is not prime""" + + a = randint(1, p-1) + return fast_exponentiation(a, p-1, p) + +def jacobi(a, b): + """Calculates the value of the Jacobi symbol (a/b) + """ + + if a % b == 0: + return 0 + result = 1 + while a > 1: + if a & 1: + if ((a-1)*(b-1) >> 2) & 1: + result = -result + b, a = a, b % a + else: + if ((b ** 2 - 1) >> 3) & 1: + result = -result + a = a >> 1 + return result + +def jacobi_witness(x, n): + """Returns False if n is an Euler pseudo-prime with base x, and + True otherwise. + """ + + j = jacobi(x, n) % n + f = fast_exponentiation(x, (n-1)/2, n) + + if j == f: return False + return True + +def randomized_primality_testing(n, k): + """Calculates whether n is composite (which is always correct) or + prime (which is incorrect with error probability 2**-k) + + Returns False if the number if composite, and True if it's + probably prime. + """ + + q = 0.5 # Property of the jacobi_witness function + + # t = int(math.ceil(k / math.log(1/q, 2))) + t = ceil(k / math.log(1/q, 2)) + for i in range(t+1): + x = randint(1, n-1) + if jacobi_witness(x, n): return False + + return True + +def is_prime(number): + """Returns True if the number is prime, and False otherwise. + + >>> is_prime(42) + 0 + >>> is_prime(41) + 1 + """ + + """ + if not fermat_little_theorem(number) == 1: + # Not prime, according to Fermat's little theorem + return False + """ + + if randomized_primality_testing(number, 5): + # Prime, according to Jacobi + return True + + # Not prime + return False + + +def getprime(nbits): + """Returns a prime number of max. 'math.ceil(nbits/8)*8' bits. In + other words: nbits is rounded up to whole bytes. + + >>> p = getprime(8) + >>> is_prime(p-1) + 0 + >>> is_prime(p) + 1 + >>> is_prime(p+1) + 0 + """ + + nbytes = int(math.ceil(nbits/8.)) + + while True: + integer = read_random_int(nbits) + + # Make sure it's odd + integer |= 1 + + # Test for primeness + if is_prime(integer): break + + # Retry if not prime + + return integer + +def are_relatively_prime(a, b): + """Returns True if a and b are relatively prime, and False if they + are not. + + >>> are_relatively_prime(2, 3) + 1 + >>> are_relatively_prime(2, 4) + 0 + """ + + d = gcd(a, b) + return (d == 1) + +def find_p_q(nbits): + """Returns a tuple of two different primes of nbits bits""" + + p = getprime(nbits) + while True: + q = getprime(nbits) + if not q == p: break + + return (p, q) + +def extended_euclid_gcd(a, b): + """Returns a tuple (d, i, j) such that d = gcd(a, b) = ia + jb + """ + + if b == 0: + return (a, 1, 0) + + q = abs(a % b) + r = long(a / b) + (d, k, l) = extended_euclid_gcd(b, q) + + return (d, l, k - l*r) + +# Main function: calculate encryption and decryption keys +def calculate_keys(p, q, nbits): + """Calculates an encryption and a decryption key for p and q, and + returns them as a tuple (e, d)""" + + n = p * q + phi_n = (p-1) * (q-1) + + while True: + # Make sure e has enough bits so we ensure "wrapping" through + # modulo n + e = getprime(max(8, nbits/2)) + if are_relatively_prime(e, n) and are_relatively_prime(e, phi_n): break + + (d, i, j) = extended_euclid_gcd(e, phi_n) + + if not d == 1: + raise Exception("e (%d) and phi_n (%d) are not relatively prime" % (e, phi_n)) + + if not (e * i) % phi_n == 1: + raise Exception("e (%d) and i (%d) are not mult. inv. modulo phi_n (%d)" % (e, i, phi_n)) + + return (e, i) + + +def gen_keys(nbits): + """Generate RSA keys of nbits bits. Returns (p, q, e, d). + + Note: this can take a long time, depending on the key size. + """ + + while True: + (p, q) = find_p_q(nbits) + (e, d) = calculate_keys(p, q, nbits) + + # For some reason, d is sometimes negative. We don't know how + # to fix it (yet), so we keep trying until everything is shiny + if d > 0: break + + return (p, q, e, d) + +def gen_pubpriv_keys(nbits): + """Generates public and private keys, and returns them as (pub, + priv). + + The public key consists of a dict {e: ..., , n: ....). The private + key consists of a dict {d: ...., p: ...., q: ....). + """ + + (p, q, e, d) = gen_keys(nbits) + + return ( {'e': e, 'n': p*q}, {'d': d, 'p': p, 'q': q} ) + +def encrypt_int(message, ekey, n): + """Encrypts a message using encryption key 'ekey', working modulo + n""" + + if type(message) is types.IntType: + return encrypt_int(long(message), ekey, n) + + if not type(message) is types.LongType: + raise TypeError("You must pass a long or an int") + + if message > 0 and \ + math.floor(math.log(message, 2)) > math.floor(math.log(n, 2)): + raise OverflowError("The message is too long") + + return fast_exponentiation(message, ekey, n) + +def decrypt_int(cyphertext, dkey, n): + """Decrypts a cypher text using the decryption key 'dkey', working + modulo n""" + + return encrypt_int(cyphertext, dkey, n) + +def sign_int(message, dkey, n): + """Signs 'message' using key 'dkey', working modulo n""" + + return decrypt_int(message, dkey, n) + +def verify_int(signed, ekey, n): + """verifies 'signed' using key 'ekey', working modulo n""" + + return encrypt_int(signed, ekey, n) + +def picklechops(chops): + """Pickles and base64encodes it's argument chops""" + + value = zlib.compress(dumps(chops)) + encoded = base64.encodestring(value) + return encoded.strip() + +def unpicklechops(string): + """base64decodes and unpickes it's argument string into chops""" + + return loads(zlib.decompress(base64.decodestring(string))) + +def chopstring(message, key, n, funcref): + """Splits 'message' into chops that are at most as long as n, + converts these into integers, and calls funcref(integer, key, n) + for each chop. + + Used by 'encrypt' and 'sign'. + """ + + msglen = len(message) + mbits = msglen * 8 + nbits = int(math.floor(math.log(n, 2))) + nbytes = nbits / 8 + blocks = msglen / nbytes + + if msglen % nbytes > 0: + blocks += 1 + + cypher = [] + + for bindex in range(blocks): + offset = bindex * nbytes + block = message[offset:offset+nbytes] + value = bytes2int(block) + cypher.append(funcref(value, key, n)) + + return picklechops(cypher) + +def gluechops(chops, key, n, funcref): + """Glues chops back together into a string. calls + funcref(integer, key, n) for each chop. + + Used by 'decrypt' and 'verify'. + """ + message = "" + + chops = unpicklechops(chops) + + for cpart in chops: + mpart = funcref(cpart, key, n) + message += int2bytes(mpart) + + return message + +def encrypt(message, key): + """Encrypts a string 'message' with the public key 'key'""" + + return chopstring(message, key['e'], key['n'], encrypt_int) + +def sign(message, key): + """Signs a string 'message' with the private key 'key'""" + + return chopstring(message, key['d'], key['p']*key['q'], decrypt_int) + +def decrypt(cypher, key): + """Decrypts a cypher with the private key 'key'""" + + return gluechops(cypher, key['d'], key['p']*key['q'], decrypt_int) + +def verify(cypher, key): + """Verifies a cypher with the public key 'key'""" + + return gluechops(cypher, key['e'], key['n'], encrypt_int) + +# Do doctest if we're not imported +if __name__ == "__main__": + import doctest + doctest.testmod() + +__all__ = ["gen_pubpriv_keys", "encrypt", "decrypt", "sign", "verify"] +