rsa_math.py

## rsa_math.py

#librería para funciones matematicas en el algoritmo rsa.
#código obtenido de la URL: http://pastebin.com/ziaUdaw8
import random
import sys

#Exponenciacion modular
def modex(base, exponente, modulo):
    r = 1
    while exponente > 0:
        if exponente & 1:
            r = (r * base) % modulo
        exponente >>= 1
        base = (base * base) % modulo
    return r

# Generacion/Comprobacion de numeros primos
# Genera una lista de primos
def genprimelist(t):
    l = [2]
    i = 3

    while i < t :
        prime = True

        for c in l:
            if i % c == 0 :
                prime = False
                break

        if prime:
            l.append(i)

        i += 2
    return l

# Lista de primos precomputada con genprimelist(5000)
primelist=[
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093,
 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327,
 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481,
 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721,
 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867,
 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113,
 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381,
 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531,
 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671,
 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777,
 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217,
 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347,
 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499,
 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617,
 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761,
 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027,
 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481,
 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637,
 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783,
 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933,
 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999]

# Comprobacion preliminar contra la lista precomputada
def firstcheck(n):
    for p in primelist:

        if n%p==0:
            if n==p:
                return True
            else:
                return False

    return True

# Comprobacion con un test de primalidad de Fermat
# http://en.wikipedia.org/wiki/Fermat_primality_test
def fermattest(n,k=100):

    for i in range (0,k):
        a=random.randint(1,n-1)

        if modex(a,n-1,n) != 1:
            return False
    return True

# Divide el numero en digitos binarios
def toBin(n):
  l = []
  while (n > 0):
    l.append(n % 2)
    n /= 2
  return l

# Comprobacion con el algoritmo de Miller-Rabin
# http://snippets.dzone.com/posts/show/4200
def miller_rabin(a, n):
  b = toBin(n - 1)
  d = 1

  for i in xrange(len(b) - 1, -1, -1):
    x = d
    d = (d * d) % n

    if d == 1 and x != 1 and x != n - 1:
      return True # Complex

    if b[i] == 1:
      d = (d * a) % n

  if d != 1:
    return True # Complex

  return False # Prime


#Comprueba si es primo con una lista de primos hasta 5000, un test de Fermat
# y un test de Miller-Rabin
def checkprime(n,k=100):
    if (not firstcheck(n)):
        return False

    if (not fermattest(n,k)):
        return False

    for iteration in range(0,k):
        i=random.randint(1,n-1)
        if miller_rabin(i,n):
            return False
    return True


# Multiplicacion modular inversa
# [ http://en.wikipedia.org/wiki/Modular_multiplicative_inverse ]
def extended_gcd(a, b):
    x, last_x = 0, 1
    y, last_y = 1, 0

    while b:
        quotient = a // b
        a, b = b, a % b
        x, last_x = last_x - quotient*x, x
        y, last_y = last_y - quotient*y, y

    return (last_x, last_y, a)

# Multiplicacion modular inversa
# [ http://en.wikipedia.org/wiki/Modular_multiplicative_inverse ]
def inverse_mod(a, m):
    x, q, gcd = extended_gcd(a, m)

    if gcd == 1:
        # x is the inverse, but we want to be sure a positive number is returned.
        return (x + m) % m
    else:
        # if gcd != 1 then a and m are not coprime and the inverse does not exist.
        return None

# Generacion de numeros primos
#Generar un numero primo de "bitn" bits y con una precision de "prec"
def genprime(bitn,k=100):

    #Esto se puede sustituir por una lectura a /dev/random, por ejemplo
    prime = random.randint(2**(bitn-1),2**bitn)
    prime |= 1 # Hacemos que sea impar
    while not checkprime(prime,k):
        prime += 2
    return prime

# Con psyco puede ir mas rapido
try:
    import psyco
    psyco.full()
except ImportError:
    pass

#fin del codigo