Removed fastrsa.py, way too much duplicate code

1 files changed, 0 insertions, 586 deletions

diff --git a/rsa/fastrsa.py b/rsa/fastrsa.py
deleted file mode 100644
index ce63105..0000000
--- a/rsa/fastrsa.py
+++ /dev/null
@@ -1,586 +0,0 @@
-"""RSA module
-
-Module for calculating large primes, and RSA encryption, decryption,
-signing and verification. Includes generating public and private keys.
-"""
-
-__author__ = "Sybren Stuvel, Marloes de Boer, Ivo Tamboer, and Barry Mead"
-__date__ = "2010-02-08"
-
-import math
-import os
-import random
-import sys
-import types
-
-def bit_size(number):
-    """Returns the number of bits required to hold a specific long number"""
-
-    return int(math.ceil(math.log(number,2)))
-
-def gcd(p, q):
-    """Returns the greatest common divisor of p and q
-    >>> gcd(48, 180)
-    12
-    """
-    # Iterateive Version is faster and uses much less stack space
-    while q != 0:
-        if p < q: (p,q) = (q,p)
-        (p,q) = (q, p % q)
-    return p
-    
-
-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)              #same as bytes2int('\x80@\x0f')
-    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
-    
-    >>>int2bytes(123456789)
-    '\x07[\xcd\x15'
-    >>> 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 to64(number):
-    """Converts a number in the range of 0 to 63 into base 64 digit
-    character in the range of '0'-'9', 'A'-'Z', 'a'-'z','-','_'.
-    
-    >>> to64(10)
-    'A'
-    """
-
-    if not (type(number) is types.LongType or type(number) is types.IntType):
-        raise TypeError("You must pass a long or an int")
-
-    if 0 <= number <= 9:            #00-09 translates to '0' - '9'
-        return chr(number + 48)
-
-    if 10 <= number <= 35:
-        return chr(number + 55)     #10-35 translates to 'A' - 'Z'
-
-    if 36 <= number <= 61:
-        return chr(number + 61)     #36-61 translates to 'a' - 'z'
-
-    if number == 62:                # 62   translates to '-' (minus)
-        return chr(45)
-
-    if number == 63:                # 63   translates to '_' (underscore)
-        return chr(95)
-
-
-def from64(number):
-    """Converts an ordinal character value in the range of
-    0-9,A-Z,a-z,-,_ to a number in the range of 0-63.
-    
-    >>> from64(49)
-    1
-    """
-
-    if not (type(number) is types.LongType or type(number) is types.IntType):
-        raise TypeError("You must pass a long or an int")
-
-    if 48 <= number <= 57:         #ord('0') - ord('9') translates to 0-9
-        return(number - 48)
-
-    if 65 <= number <= 90:         #ord('A') - ord('Z') translates to 10-35
-        return(number - 55)
-
-    if 97 <= number <= 122:        #ord('a') - ord('z') translates to 36-61
-        return(number - 61)
-
-    if number == 45:               #ord('-') translates to 62
-        return(62)
-
-    if number == 95:               #ord('_') translates to 63
-        return(63)
-
-
-
-def int2str64(number):
-    """Converts a number to a string of base64 encoded characters in
-    the range of '0'-'9','A'-'Z,'a'-'z','-','_'.
-    
-    >>> int2str64(123456789)
-    '7MyqL'
-    """
-
-    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" % (to64(number & 0x3F), string)
-        number /= 64
-
-    return string
-
-
-def str642int(string):
-    """Converts a base64 encoded string into an integer.
-    The chars of this string in in the range '0'-'9','A'-'Z','a'-'z','-','_'
-    
-    >>> str642int('7MyqL')
-    123456789
-    """
-
-    if not (type(string) is types.ListType or type(string) is types.StringType):
-        raise TypeError("You must pass a string or a list")
-
-    integer = 0
-    for byte in string:
-        integer *= 64
-        if type(byte) is types.StringType: byte = ord(byte)
-        integer += from64(byte)
-
-    return integer
-
-def read_random_int(nbits):
-    """Reads a random integer of approximately nbits bits rounded up
-    to whole bytes"""
-
-    nbytes = int(math.ceil(nbits/8.))
-    randomdata = os.urandom(nbytes)
-    return bytes2int(randomdata)
-
-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) + 1
-
-    # Which is this number of bytes
-    rangebytes = ((bit_size(range) + 7) / 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 jacobi(a, b):
-    """Calculates the value of the Jacobi symbol (a/b)
-    where both a and b are positive integers, and b is odd
-    """
-
-    if a == 0: return 0
-    result = 1
-    while a > 1:
-        if a & 1:
-            if ((a-1)*(b-1) >> 2) & 1:
-                result = -result
-            a, b = b % a, a
-        else:
-            if (((b * b) - 1) >> 3) & 1:
-                result = -result
-            a >>= 1
-    if a == 0: return 0
-    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 = pow(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 is composite, and True if it's
-    probably prime.
-    """
-
-    # 50% of Jacobi-witnesses can report compositness of non-prime numbers
-
-    for i in range(k):
-        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 randomized_primality_testing(number, 6):
-        # 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
-    """
-
-    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"""
-    pbits = nbits + (nbits/16)  #Make sure that p and q aren't too close
-    qbits = nbits - (nbits/16)  #or the factoring programs can factor n
-    p = getprime(pbits)
-    while True:
-        q = getprime(qbits)
-        #Make sure p and q are different.
-        if not q == p: break
-    return (p, q)
-
-def extended_gcd(a, b):
-    """Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb
-    """
-    # r = gcd(a,b) i = multiplicitive inverse of a mod b
-    #      or      j = multiplicitive inverse of b mod a
-    # Neg return values for i or j are made positive mod b or a respectively
-    # Iterateive Version is faster and uses much less stack space
-    x = 0
-    y = 1
-    lx = 1
-    ly = 0
-    oa = a                             #Remember original a/b to remove
-    ob = b                             #negative values modulo b or a
-    while b != 0:
-        q = long(a/b)
-        (a, b)  = (b, a % b)
-        (x, lx) = ((lx - (q * x)),x)
-        (y, ly) = ((ly - (q * y)),y)
-    if (lx < 0): lx += ob              #If negative wrap modulo original b
-    if (ly < 0): ly += oa              #If negative wrap modulo original a
-    return (a, lx, ly)                 #Return only positive values
-
-# 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, dp, dq, qi)"""
-
-    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 = max(65537,getprime(nbits/4)) #minimum e is 65537 per RSA spec
-        if are_relatively_prime(e, n) and are_relatively_prime(e, phi_n): break
-
-    (r, dp, j) = extended_gcd(e, p-1) #Compute exponent dp
-
-    if not r == 1:
-        raise Exception("e (%d) and p-1 (%d) are not relatively prime" % (e, p-1))
-
-    (r, dq, j) = extended_gcd(e, q-1) #Compute exponent dq
-
-    if not r == 1:
-        raise Exception("e (%d) and q-1 (%d) are not relatively prime" % (e, q-1))
-
-    (r, qi, j) = extended_gcd(q, p)   #Compute q-inverse coefficent qi
-
-    if not r == 1:
-        raise Exception("q (%d) and p (%d) are not relatively prime" % (q, p))
-
-    return (e, dp, dq, qi)
-
-
-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.
-    """
-
-    (p, q) = find_p_q(nbits)
-    (e, dp, dq, qi) = calculate_keys(p, q, nbits)
-
-    return (p, q, e, dp, dq, qi)
-
-def newkeys(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 {p: ..., q: ..., dp: ..., dq: ..., qi: ...}.
-    """
-    nbits = max(9,nbits)         #Minimum key size is 9 bits for p and q 
-    (p, q, e, dp, dq, qi) = gen_keys(nbits)
-
-    return ( {'e':e,'n':p*q}, {'p':p,'q':q,'dp':dp,'dq':dq,'qi':qi} )
-
-def encrypt_int(message, key):
-    """Encrypts a message using public key 'key', working modulo n"""
-
-    if type(message) is types.IntType:
-        message = long(message)
-
-    if not type(message) is types.LongType:
-        raise TypeError("You must pass a long or int")
-    n = key['n']                                #reduce dictionary lookups
-    if message < 0 or message > n:
-        raise OverflowError("The message is too long")
-
-    #Note: Bit exponents start at zero (bit counts start at 1) this is correct
-    safebit = bit_size(n) - 2                   #safe bit is (MSB - 1)
-    message += (1 << safebit)                   #add safebit to ensure folding
-
-    return pow(message, key['e'], n)
-
-def verify_int(cyphertext, key):
-    """Decrypts cyphertext using public key 'key', working modulo n"""
-
-    if type(cyphertext) is types.IntType:
-        cyphertext = long(cyphertext)
-
-    if not type(cyphertext) is types.LongType:
-        raise TypeError("You must pass a long or int")
-    n = key['n']                                #reduce dictionary lookups
-    message = pow(cyphertext, key['e'], n)
-
-    #Note: Bit exponents start at zero (bit counts start at 1) this is correct
-    safebit = bit_size(n) - 2                   #safe bit is (MSB - 1)
-    message -= (1 << safebit)                   #remove safe bit before decode
-
-    return message
-
-def decrypt_int(cyphertext, key):
-    """Decrypts a cypher text using the private key 'key', working
-    modulo n"""
-    p = key['p']                #Reduce dictionary lookups
-    q = key['q']
-    n = p * q
-    #Decrypt in 2 parts, using faster Chinese Remainder Theorem method
-    m1 = pow(cyphertext, key['dp'], p)
-    m2 = pow(cyphertext, key['dq'], q)
-    dif = m1 - m2
-    if dif < 0: dif += p
-    h = (key['qi'] * dif) % p
-    message = m2 + (h * q)
-
-    safebit = bit_size(n) - 2                   #safe bit is (MSB - 1)
-    message -= (1 << safebit)                   #remove safebit before decode
-
-    return message
-
-def sign_int(message, key):
-    """Encrypts a message with the private key 'key', working
-    modulo n"""
-
-    if type(message) is types.IntType:
-        message = long(message)
-
-    if not type(message) is types.LongType:
-        raise TypeError("You must pass a long or int")
-
-    p = key['p']                                #Reduce dictionary lookups
-    q = key['q']
-    n = p * q
-
-    if message < 0 or message > n:
-        raise OverflowError("The message is too long")
-
-    safebit = bit_size(n) - 2                   #safe bit is (MSB - 1)
-    message += (1 << safebit)                   #add safebit before encrypt
-
-    #Encrypt in 2 parts, using faster Chinese Remainder Theorem method
-    c1 = pow(message, key['dp'], p)
-    c2 = pow(message, key['dq'], q)
-    dif = c1 - c2
-    if dif < 0: dif += p
-    h = (key['qi'] * dif) % p
-    cyphertext = c2 + (h * q)
-
-    return cyphertext
-
-def encode64chops(chops):
-    """base64encodes chops and combines them into a ',' delimited string"""
-
-    chips = []                              #chips are character chops
-
-    for value in chops:
-        chips.append(int2str64(value))
-
-    encoded = ""
-
-    for string in chips:
-        encoded = encoded + string + ','    #delimit chops with comma
-
-    return encoded
-
-def decode64chops(string):
-    """base64decodes and makes a ',' delimited string into chops"""
-
-    chips = string.split(',')               #split chops at commas
-
-    chops = []
-
-    for string in chips:                    #make char chops (chips) into chops
-        chops.append(str642int(string))
-
-    return chops
-
-def chopstring(message, key, funcref):
-    """Chops the 'message' into integers that fit into n,
-    leaving room for a safebit to be added to ensure that all
-    messages fold during exponentiation.  The MSB of the number n
-    is not independant modulo n (setting it could cause overflow), so
-    use the next lower bit for the safebit.  Therefore reserve 2-bits
-    in the number n for non-data bits.  Calls specified encryption
-    function for each chop.
-
-    Used by 'encrypt' and 'sign'.
-    """
-
-    if 'n' in key:
-        n = key['n']                        #Public key has n already
-    else:
-        n = key['p'] * key['q']             #Private key has p & q
-    
-    msglen = len(message)
-    mbits = msglen * 8
-    #Set aside 2-bits so setting of safebit won't overflow modulo n
-    nbits = bit_size(n) - 2                 # leave room for safebit
-    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))
-
-    return encode64chops(cypher)   #Encode encrypted ints to base64 strings
-
-def gluechops(string, key, funcref):
-    """Glues chops back together into a string.  calls
-    funcref(integer, key) for each chop.
-
-    Used by 'decrypt' and 'verify'.
-    """
-    message = ""
-
-    chops = decode64chops(string)  #Decode base64 strings into integer chops
-    
-    for cpart in chops:
-        mpart = funcref(cpart, key)    #Decrypt each chop
-        message += int2bytes(mpart)    #Combine decrypted strings into a msg
-    
-    return message
-
-def encrypt(message, key):
-    """Encrypts a string 'message' with the public key 'key'"""
-    if 'n' not in key:
-        raise Exception("You must use the public key with encrypt")
-
-    return chopstring(message, key, encrypt_int)
-
-def sign(message, key):
-    """Signs a string 'message' with the private key 'key'"""
-    if 'p' not in key:
-        raise Exception("You must use the private key with sign")
-
-    return chopstring(message, key, sign_int)
-
-def decrypt(cypher, key):
-    """Decrypts a string 'cypher' with the private key 'key'"""
-    if 'p' not in key:
-        raise Exception("You must use the private key with decrypt")
-
-    return gluechops(cypher, key, decrypt_int)
-
-def verify(cypher, key):
-    """Verifies a string 'cypher' with the public key 'key'"""
-    if 'n' not in key:
-        raise Exception("You must use the public key with verify")
-
-    return gluechops(cypher, key, verify_int)
-
-# Do doctest if we're not imported
-if __name__ == "__main__":
-    import doctest
-    doctest.testmod()
-
-__all__ = ["newkeys", "encrypt", "decrypt", "sign", "verify"]
-