def test_smoothness_and_smoothness_p():
assert smoothness(1) == (1, 1)
assert smoothness(2 ** 4 * 3 ** 2) == (3, 16)
assert smoothness_p(10431, m=1) == (1, [(3, (2, 2, 4)), (19, (1, 5, 5)), (61, (1, 31, 31))])
assert smoothness_p(10431) == (-1, [(3, (2, 2, 2)), (19, (1, 3, 9)), (61, (1, 5, 5))])
assert smoothness_p(10431, power=1) == (-1, [(3, (2, 2, 2)), (61, (1, 5, 5)), (19, (1, 3, 9))])
assert (
smoothness_p(21477639576571, visual=1)
== "p**i=4410317**1 has p-1 B=1787, B-pow=1787\n" + "p**i=4869863**1 has p-1 B=2434931, B-pow=2434931"
)
def test_smoothness_and_smoothness_p():
assert smoothness(1) == (1, 1)
assert smoothness(2**4*3**2) == (3, 16)
assert smoothness_p(10431, m=1) == \
(1, [(3, (2, 2, 4)), (19, (1, 5, 5)), (61, (1, 31, 31))])
assert smoothness_p(10431) == \
(-1, [(3, (2, 2, 2)), (19, (1, 3, 9)), (61, (1, 5, 5))])
assert smoothness_p(10431, power=1) == \
(-1, [(3, (2, 2, 2)), (61, (1, 5, 5)), (19, (1, 3, 9))])
assert smoothness_p(21477639576571, visual=1) == \
'p**i=4410317**1 has p-1 B=1787, B-pow=1787\n' + \
'p**i=4869863**1 has p-1 B=2434931, B-pow=2434931'
def generate_key(self):
"""
Генерация ключа для схемы Шнорра
:return: открытый и закрытый ключ
"""
p = get_random_prime()
q = smoothness(p - 1)[0] # максимальный простой делитель
x = randint(1, min(MAX_POWER, q))
g = find_root(p, q)
y = find_open_key(p, pow(g, x))
public_key = (y, p, q, g)
private_key = x
self.steps = locals()
return public_key, private_key
def generate_key(self):
"""
Генерация ключа для ГОСТ 30.10-94
:return: открытый и закрытый ключ
"""
p = get_random_prime()
q = smoothness(p - 1)[0] # максимальный простой делитель
a = find_root(p, q)
x = randint(1, q-1) # закрытый ключ
y = pow(a, x, p) # открытый ключ
public_key = (p, q, a, y)
private_key = x
self.steps = locals()
return public_key, private_key
def largest_prime_factor(n):
p, g = smoothness(n)
return p
from itertools import permutations
from sympy.ntheory.factor_ import smoothness
from math import sqrt
smooth = 0;
for i in range(1,10**10 + 1,1):
if(i%10**6 == 0):
print(i//10**6)
if(smoothness(i)[0] < sqrt(i)):
smooth+=1
print(smooth + 1)