Anul 3 Semestrul 1

Anul 3/Semestrul 1/Public Key Cryptography/Crypto3.py

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+#1. Miller-Rabin algorithm. It will work for numbers of arbitrary size.
+
+import random
+
+def miller_rabin(n, k=5) -> bool:
+    if n % 2 == 0 or n <= 2:
+        return False
+    s, t = step1(n)
+    for _ in range(k):
+        a: int = random.randint(2, n - 2) 
+        x: int = pow(a, t, n)
+        if x == 1:
+            continue
+        for _ in range(s):
+            y: int = pow(x, 2, n)
+            if y == 1 and x != 1 and x != n - 1:
+                return False
+            x = y
+        if y != 1:
+            return False
+    return True
+
+
+
+def step1(n) -> tuple[int, int]:
+    t: int = n - 1
+    s = 0
+    while t % 2 == 0:
+        t //= 2
+        s += 1
+    return s, t
+
+def main():
+    print(miller_rabin(13))
+    print(miller_rabin(15))
+    print(miller_rabin(2**1279 - 1))
+        
+if __name__ == '__main__':
+    main()