def pow_int(self, a, m):
a = int_check_strict(a, ZN_ERR_MSG_NUM)
m = int_check_strict(m, ZN_ERR_MSG_EXP, ZN_COND_EXP)
n = self.n
a %= n
result = 1
while m > 0:
if m % 2 == 1:
result *= a
if result >= n:
result %= n
m //= 2
a *= a
if a >= n:
a %= n
return result
def input_int(self, msg, err_msg, cond = lambda x: True):
while True:
try:
x = float(input(msg))
x = int_check_strict(x, None, cond)
except ValueError:
print(err_msg)
continue
else:
print('--- Received: {}'.format(x))
return x
def totient(n): # Hàm phi Euler
""" Euler's totient function
"""
n = int_check_strict(n, ZN_ERR_MSG_N, ZN_COND_N)
phi = n
for i in range(2, int(n ** .5) + 1): # +1 after sqrt to ensure it is included in the range
if n % i == 0:
phi -= phi / i
while n % i == 0:
n //= i
if n > 1: # Either n is prime in the first place or n is now the last prime factor > sqrt(n)
phi -= phi / n
return int(phi)
def mul_inv_int(self, num, mode = 'bezout'):
num = int_check_strict(num, ZN_ERR_MSG_NUM)
n = self.n
g = gcd(num, n)
if g > 1:
return ZN_ERR_MSG_INV.format(a = num, n = n, gcd = g)
if mode == 'bezout':
_, inv, _ = bezout(num % n, n)
return inv % n
elif mode == 'euler':
return self.pow_int(num, self.totient() - 1)
else:
raise ValueError
def __pow__(self, m):
m = int_check_strict(m, ZN_ERR_MSG_EXP, ZN_COND_EXP)
n = self.n
a = self.reduced
result = 1
while m > 0:
if m % 2 == 1:
result *= a
if result >= n:
result %= n
m //= 2
a *= a
if a >= n:
a %= n
return ZnNumber(result, n)
def reduce(val, base_n):
n = int_check_strict(base_n, ZN_ERR_MSG_N, ZN_COND_N)
val = int_check_strict(val, ZN_ERR_MSG_NUM)
return val % n
def mul_int(self, a, b):
a = int_check_strict(a, ZN_ERR_MSG_NUM)
b = int_check_strict(b, ZN_ERR_MSG_NUM)
original_product = a * b
return self.reduce(original_product), original_product
def add_int(self, a, b):
a = int_check_strict(a, ZN_ERR_MSG_NUM)
b = int_check_strict(b, ZN_ERR_MSG_NUM)
original_sum = a + b
return self.reduce(original_sum), original_sum
def reduce(self, num):
num = int_check_strict(num, ZN_ERR_MSG_NUM)
return num % self.n
def __init__(self, n):
n = int_check_strict(n, ZN_ERR_MSG_N, ZN_COND_N)
self.n = n