First commit

lib/miller_rabin.py

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+# Python Miller-Rabin implementation
+
+import random
+import lib.arithmetics as arithm
+
+def get_d_and_s(n: int) -> (int, int):
+    d = n - 1
+    s = 0
+    while d % 2 == 0:
+        d //= 2
+        s += 1
+    return (d, s)
+
+def rabin_witness(n: int, a: int) -> bool:
+    d, s = get_d_and_s(n)
+    x = arithm.modpow(a, d, n)
+    if x == 1 or x == n - 1:
+        return False
+    for _ in range(s - 1):
+        x = arithm.modpow(x, 2, n)
+        if x == n - 1:
+            return False
+    return True
+
+def miller_rabin(n: int, k: int) -> bool:
+    if n < 3: return False
+    for _ in range(k):
+        a = random.randint(2, n - 1)
+        if rabin_witness(n, a): return False
+    return True
+
+def is_prime(n: int) -> bool:
+    return miller_rabin(n, 25)
+
+def get_random_prime(n: int) -> int:
+    a = random.randint(2**(n-1), 2**(n) - 1)
+    while not is_prime(a):
+        a = random.randint(2**(n-1), 2**(n) - 1)
+    return a 
+