51 lines
1022 B
Python
51 lines
1022 B
Python
import random, copy
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#sprawdza czy liczby są pierwsze
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def fermat(dokladnosc, liczba):
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i = 0
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while i < dokladnosc:
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a = random.randint(1, liczba - 1)
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if pow(a, (liczba - 1), liczba) == 1:
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i = i + 1
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else:
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return False
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return True
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#x * u + N * v = d
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#Jeśli d == 1 to liczby są względnie pierwsze
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#d to NWD
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def euklides(x, N):
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A,B,U,V = N, x, 0, 1
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while True:
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q = A // B
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A_new = copy.deepcopy(B)
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B = A - B * q
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A = A_new
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U_new = copy.deepcopy(V)
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V = U - V * q
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U = U_new
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if B == 0:
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break
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d, u = A, U
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v = (d - x * u)/N
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return u, v, d
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#liczba odwrotna do b w modulo n
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def odwrotnosc(b, n):
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u, _, d = euklides(b, n)
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if d == 1:
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return u % n
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else:
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return False
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#potegowanie x do k w mod n
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def potegowanieimod(x, k, n):
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y = 1
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while k > 0:
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if k & 1:
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y = y*x % n
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x = x**2 % n
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k = k >> 1
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return y |