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@MarkLavrynenko
Created May 3, 2015 07:54
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Easy Crypt
#from os import urandom
from random import randint
from time import *
__author__ = 'mlavrynenko'
smal_rsa_primes = [
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19,
23 , 29 , 31 , 37 , 41 , 43 , 47 , 53,
59 , 61 , 67 , 71 , 73 , 79 , 83 , 89,
]
test_primes = [
6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563,
6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637,
6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779,
6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907]
def gcd(a, b, logging = False):
while a > 0 and b > 0:
if logging:
print("GCD: %s %s" % (a, b))
if a > b:
a %= b
else:
b %= a
return a + b
def gcd_extended(a, b):
if a == 0:
#print ("%s %s | %s %s" % (a, b, 0, 1))
return b, 0, 1
res, x, y = gcd_extended(b % a, a)
#print ("%s %s | %s %s" % (a, b, x, y))
tmp = x
x = y - (b / a) * x
y = tmp
return res, x, y
def f1(x):
return sum([1 for i in range(1, x+1) if gcd(x, i) == 1])
def fact(x):
limit = pow(x, 0.5)
divs = []
d = 2
while x > 1 and d <= limit:
if x % d == 0:
x /= d
divs.append(d)
else:
d += 1
if x > 1:
divs.append(x)
return divs
assert fact(30) == [2, 3, 5]
assert fact(49) == [7, 7]
assert fact(50) == [2, 5, 5]
def find_root(m):
def pass_test(g, f, m):
if pow(g, f) % m != 1:
return False
for i in range(1, f):
if pow(g, i) % m == 1:
return False
return True
f = f1(m)
for t in range(1, m):
if pass_test(t, f, m):
return t
def find_root_fast(m):
phi = f1(m)
print("Phi is %s" % phi)
divs = fact(phi)
print("Divisors is %s" % divs)
for to_test in range(2, m+1): # test all number from 2 to m
flag = True
for divisor in divs:
flag &= pow(to_test, phi / divisor, m) != 1
if flag:
return to_test
def find_roots(m):
def pass_test(g, f, m):
if pow(g, f) % m != 1:
return False
for i in range(1, f):
if pow(g, i) % m == 1:
return False
return True
res = []
f = f1(m)
for t in range(1, m):
if pass_test(t, f, m):
res.append(t)
return res
def test_find_root(number, expected):
root = find_root(number)
if root != expected:
raise Exception('Invalid find_root function. Got %s expected %s on number %s' % (root, expected, number))
test_find_root(2, 1)
test_find_root(3, 2)
test_find_root(4, 3)
test_find_root(5, 2)
test_find_root(6, 5)
test_find_root(7, 3)
test_find_root(8, None)
test_find_root(9, 2)
test_find_root(10, 3)
test_find_root(11, 2)
test_find_root(12, None)
test_find_root(13, 2)
test_find_root(14, 3)
def one_party_step(g, p, a):
return pow(g, a) % p
def do_algo():
p = 16921 # should be prime number
g = find_root_fast(p)
print("P is %d" % p)
print("g is %d" % g)
a_power, b_power = 6, 15
a_response = one_party_step(g, p, a_power)
b_response = one_party_step(g, p, b_power)
print("A public is %s" % a_response)
print("B public is %s" % b_response)
a_secret = one_party_step(b_response, p, a_power)
b_secret = one_party_step(a_response, p, b_power)
print("Common secret is %s for A, and %s for B" % (a_secret, b_secret))
def test_primitive_root_existence():
print(find_roots(94))
for i in range(1, 100):
if find_root(i) is None:
print i
def test_slow_and_fast_PRM(number):
print("Test number %s" % number)
start = time()
root1 = find_root_fast(number)
end = time()
print("Fast result is %s in %s" % (root1, end - start))
start = time()
root2 = find_root(number)
end = time()
print("Slow result is %s in %s" % (root2, end - start))
assert root1 == root2
def test_slow_and_fast_PRM_multiple():
for prime in test_primes:
test_slow_and_fast_PRM(prime)
def rsa():
def get_open_exponent(n):
flag = False
while not flag:
d = randint(2, n-1)
flag = gcd(d, n) == 1
return d
def get_private_exponent(e, phi):
gcd, x, y = gcd_extended(e, phi)
assert gcd == 1
return ((x + phi) % phi)
primes = smal_rsa_primes
limit = len(primes) - 1
p = primes[randint(0, limit)]
q = primes[randint(0, limit)]
phi = (q - 1) * (p - 1)
n = p * q # module
e = get_open_exponent(phi)
d = get_private_exponent(e, phi)
print("p and q for RSA is %s %s" % (p, q))
print("Exponents is %s %s" % (e, d))
def encrypt(message):
assert message >= 0 and message < n
return pow(message, e) % n
def decrypt(cypher):
assert cypher >= 0 and cypher < n
return pow(cypher, d) % n
return {
"encrypt": encrypt,
"decrypt": decrypt,
"open_key": (e, n),
"private_key": (d, n)
}
def gcd_tutorial(a,b):
res = gcd_extended(a, b)
print("%s*%s + %s*%s=%s" % (res[1], a, res[2], b, res[0]))
#do_algo()
alg = rsa()
encryted = alg["encrypt"](344 % alg["open_key"][1]) # n can be less then input message
print("Encrypted is %s" % encryted)
decrypted = alg["decrypt"](encryted)
print("Initial is %s" % decrypted)
#test_slow_and_fast_PRM_multiple()
#test_primitive_root_existence()
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