| Index: tools/telemetry/third_party/gsutilz/third_party/rsa/rsa/_version133.py
|
| diff --git a/tools/telemetry/third_party/gsutilz/third_party/rsa/rsa/_version133.py b/tools/telemetry/third_party/gsutilz/third_party/rsa/rsa/_version133.py
|
| deleted file mode 100644
|
| index 230a03c84b9a0114a421c66d2093884a98352801..0000000000000000000000000000000000000000
|
| --- a/tools/telemetry/third_party/gsutilz/third_party/rsa/rsa/_version133.py
|
| +++ /dev/null
|
| @@ -1,442 +0,0 @@
|
| -"""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
|
| -
|
| -from rsa._compat import byte
|
| -
|
| -# 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]
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| - >>> 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" % (byte(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)
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| - >>> is_prime(p-1)
|
| - 0
|
| - >>> is_prime(p)
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| - 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"]
|
| -
|
|
|