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| -rw-r--r-- | rsa/_version200.py | 532 |
1 files changed, 532 insertions, 0 deletions
diff --git a/rsa/_version200.py b/rsa/_version200.py new file mode 100644 index 0000000..c297aee --- /dev/null +++ b/rsa/_version200.py @@ -0,0 +1,532 @@ +"""RSA module + +Module for calculating large primes, and RSA encryption, decryption, +signing and verification. Includes generating public and private keys. + +WARNING: this implementation does not use random padding, compression of the +cleartext input to prevent repetitions, or other common security improvements. +Use with care. + +""" + +__author__ = "Sybren Stuvel, Marloes de Boer, Ivo Tamboer, and Barry Mead" +__date__ = "2010-02-08" +__version__ = '2.0' + +import math +import os +import random +import sys +import types + +# Display a warning that this insecure version is imported. +import warnings +warnings.warn('Insecure version of the RSA module is imported as %s' % __name__) + + +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) + + raise ValueError(u'Invalid Base64 value: %i' % number) + + +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) + + raise ValueError(u'Invalid Base64 value: %i' % number) + + +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 from return results + 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 neg wrap modulo orignal b + if (ly < 0): ly += oa #If neg wrap modulo orignal 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, 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 = max(65537,getprime(nbits/4)) + if are_relatively_prime(e, n) and are_relatively_prime(e, phi_n): break + + (d, i, j) = extended_gcd(e, phi_n) + + if not d == 1: + raise Exception("e (%d) and phi_n (%d) are not relatively prime" % (e, phi_n)) + if (i < 0): + raise Exception("New extended_gcd shouldn't return negative values") + 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. + """ + + (p, q) = find_p_q(nbits) + (e, d) = calculate_keys(p, q, nbits) + + return (p, q, e, d) + +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 {d: ...., p: ...., q: ....). + """ + nbits = max(9,nbits) # Don't let nbits go below 9 bits + (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: + message = long(message) + + if not type(message) is types.LongType: + raise TypeError("You must pass a long or int") + + 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 #compute safe bit (MSB - 1) + message += (1 << safebit) #add safebit to ensure folding + + return pow(message, ekey, n) + +def decrypt_int(cyphertext, dkey, n): + """Decrypts a cypher text using the decryption key 'dkey', working + modulo n""" + + message = pow(cyphertext, dkey, n) + + safebit = bit_size(n) - 2 #compute safe bit (MSB - 1) + message -= (1 << safebit) #remove safebit before decode + + return message + +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)) + + #delimit chops with comma + encoded = ','.join(chips) + + 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, n, 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'. + """ + + 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, n)) + + return encode64chops(cypher) #Encode encrypted ints to base64 strings + +def gluechops(string, 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 = decode64chops(string) #Decode base64 strings into integer chops + + for cpart in chops: + mpart = funcref(cpart, key, n) #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['e'], key['n'], 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['d'], key['p']*key['q'], encrypt_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['d'], key['p']*key['q'], 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['e'], key['n'], decrypt_int) + +# Do doctest if we're not imported +if __name__ == "__main__": + import doctest + doctest.testmod() + +__all__ = ["newkeys", "encrypt", "decrypt", "sign", "verify"] + |