Added classical implementation of Shor’s Algorithm

algorithms/cryptography/shor_algorithm.py

@@ -0,0 +1,56 @@
+import math
+import random
+
+def gcd(a, b):
+    """Computes the greatest common divisor using Euclidean algorithm."""
+    while b:
+        a, b = b, a % b
+    return a
+
+def modular_exponentiation(base, exp, mod):
+    """Computes (base^exp) % mod using fast modular exponentiation."""
+    result = 1
+    while exp > 0:
+        if exp % 2 == 1:
+            result = (result * base) % mod
+        base = (base * base) % mod
+        exp //= 2
+    return result
+
+def find_order(a, N):
+    """Finds the smallest r such that a^r ≡ 1 (mod N)"""
+    r = 1
+    while modular_exponentiation(a, r, N) != 1:
+        r += 1
+        if r > N:  # Prevent infinite loops
+            return None
+    return r
+
+def shor_algorithm(N):
+    """Simulates Shor’s Algorithm classically to factorize N."""
+    if N % 2 == 0:
+        return 2, N // 2  # Trivial case if N is even
+
+    while True:
+        a = random.randint(2, N - 1)
+        factor = gcd(a, N)
+        if factor > 1:
+            return factor, N // factor  # Lucky case: a and N are not coprime
+
+        r = find_order(a, N)
+        if r is None or r % 2 == 1:
+            continue  # Retry if order is not even
+
+        factor1 = gcd(modular_exponentiation(a, r // 2, N) - 1, N)
+        factor2 = gcd(modular_exponentiation(a, r // 2, N) + 1, N)
+
+        if 1 < factor1 < N:
+            return factor1, N // factor1
+        if 1 < factor2 < N:
+            return factor2, N // factor2
+
+# Example usage
+if __name__ == "__main__":
+    N = 15  # You can test with 21, 35, 55, etc.
+    factors = shor_algorithm(N)
+    print(f"Factors of {N}: {factors}")