diff --git a/cryptography/__init__.py b/cryptography/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/cryptography/shor_algorithm.py b/cryptography/shor_algorithm.py
new file mode 100644
index 000000000000..110d3278b40d
--- /dev/null
+++ b/cryptography/shor_algorithm.py
@@ -0,0 +1,99 @@
+"""
+Classical simulation of Shor's Algorithm to factor integers.
+
+Source: https://en.wikipedia.org/wiki/Shor%27s_algorithm
+"""
+
+import math
+import random
+from typing import Any
+
+
+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 = math.isqrt(n)
+ return all(n % i != 0 for i in range(3, r + 1, 2))
+
+
+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) -> 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()
diff --git a/cryptography/tests/__init__.py b/cryptography/tests/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/cryptography/tests/test_shor_algorithm.py b/cryptography/tests/test_shor_algorithm.py
new file mode 100644
index 000000000000..6c12e748a2a2
--- /dev/null
+++ b/cryptography/tests/test_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)
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