--- /dev/null
+"""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<q: return gcd(q, p)
+ if q == 0: return p
+ return gcd(q, abs(p%q))
+
+def bytes2int(bytes):
+ """Converts a list of bytes or a string to an integer
+
+ >>> (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"]
+
projects / NK2015_Client_Python_Alpha.git / blobdiff