Add classical Shor’s Algorithm implementation with tests (#12318)

Author: khushipy

cryptography/__init__.py

@@ -0,0 +1,102 @@
+"""
+Classical simulation of Shor's Algorithm to factor integers.
+
+Source: https://en.wikipedia.org/wiki/Shor%27s_algorithm
+"""
+
+import random
+import math
+from typing import Tuple, Union
+
+
+def is_prime(n: int) -> bool:
+    """
+    Check if a number is prime.
+
+    >>> is_prime(2)
+    True
+    >>> is_prime(4)
+    False
+    """
+    if n < 2:
+        return False
+    if n in (2, 3):
+        return True
+    if n % 2 == 0:
+        return False
+    r = int(math.isqrt(n))
+    for i in range(3, r + 1, 2):
+        if n % i == 0:
+            return False
+    return True
+
+
+def modexp(a: int, b: int, m: int) -> int:
+    """
+    Modular exponentiation: (a^b) % m
+
+    >>> modexp(2, 5, 13)
+    6
+    """
+    result = 1
+    a = a % m
+    while b > 0:
+        if b & 1:
+            result = (result * a) % m
+        a = (a * a) % m
+        b >>= 1
+    return result
+
+
+def shor_classical(N: int, max_attempts: int = 10) -> Union[str, Tuple[int, int]]:
+    """
+    Classical approximation of Shor's Algorithm to factor a number.
+
+    >>> result = shor_classical(15)
+    >>> isinstance(result, tuple)
+    True
+    >>> sorted(result) == [3, 5]
+    True
+
+    >>> shor_classical(13)  # Prime
+    'No factors: 13 is prime'
+    """
+    if N <= 1:
+        return "Failure: input must be > 1"
+    if N % 2 == 0:
+        return 2, N // 2
+    if is_prime(N):
+        return f"No factors: {N} is prime"
+
+    for _ in range(max_attempts):
+        a = random.randrange(2, N - 1)
+        g = math.gcd(a, N)
+        if g > 1:
+            return g, N // g
+
+        r = 1
+        while r < N:
+            if modexp(a, r, N) == 1:
+                break
+            r += 1
+        else:
+            continue
+
+        if r % 2 != 0:
+            continue
+        x = modexp(a, r // 2, N)
+        if x == N - 1:
+            continue
+
+        factor1 = math.gcd(x - 1, N)
+        factor2 = math.gcd(x + 1, N)
+        if factor1 not in (1, N) and factor2 not in (1, N):
+            return factor1, factor2
+
+    return "Failure: try more attempts"
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

cryptography/shor_algorithm.py

@@ -0,0 +1,36 @@
+import pytest
+from cryptography.shor_algorithm import shor_classical
+
+
+def test_small_composite():
+    factors = shor_classical(15)
+    assert set(factors) == {3, 5}
+
+
+def test_medium_composite():
+    factors = shor_classical(21)
+    assert set(factors) == {3, 7}
+
+
+def test_even_number():
+    factors = shor_classical(18)
+    assert set(factors) == {2, 9}
+
+
+def test_prime_number():
+    result = shor_classical(13)
+    assert isinstance(result, str)
+    assert "prime" in result.lower()
+
+
+def test_invalid_input():
+    result = shor_classical(1)
+    assert isinstance(result, str)
+    assert "failure" in result.lower()
+
+
+def test_larger_composite_number():
+    result = shor_classical(91)
+    assert isinstance(result, (tuple, str))
+    if isinstance(result, tuple):
+        assert all(isinstance(x, int) for x in result)