From 5cdffffaec6b791d8b7583e1a4b85650df0dc6c0 Mon Sep 17 00:00:00 2001
From: Khushi Pal <khushipaltwt@gmail.com>
Date: Wed, 18 Jun 2025 21:40:17 +0530
Subject: [PATCH 1/3] Add classical implementation of Shor's Algorithm (#12318)

---
 cryptography/shor_algorithm.py | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 cryptography/shor_algorithm.py

diff --git a/cryptography/shor_algorithm.py b/cryptography/shor_algorithm.py
new file mode 100644
index 000000000000..e69de29bb2d1

From d37302382265732e2da77bab07a67124e3465226 Mon Sep 17 00:00:00 2001
From: Khushi Pal <khushipaltwt@gmail.com>
Date: Wed, 18 Jun 2025 22:13:58 +0530
Subject: [PATCH 2/3] =?UTF-8?q?Add=20classical=20Shor=E2=80=99s=20Algorith?=
 =?UTF-8?q?m=20implementation=20with=20tests=20(#12318)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 cryptography/__init__.py                  |   0
 cryptography/shor_algorithm.py            | 102 ++++++++++++++++++++++
 cryptography/tests/__init__.py            |   0
 cryptography/tests/test_shor_algorithm.py |  36 ++++++++
 4 files changed, 138 insertions(+)
 create mode 100644 cryptography/__init__.py
 create mode 100644 cryptography/tests/__init__.py
 create mode 100644 cryptography/tests/test_shor_algorithm.py

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
index e69de29bb2d1..4f070fe67ca1 100644
--- a/cryptography/shor_algorithm.py
+++ b/cryptography/shor_algorithm.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()
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)

From c568a092f3532cb341fabac9197a3dc47966a084 Mon Sep 17 00:00:00 2001
From: Khushi Pal <114483555+khushipy@users.noreply.github.com>
Date: Fri, 20 Jun 2025 09:57:50 +0530
Subject: [PATCH 3/3] Update shor_algorithm.py

---
 cryptography/shor_algorithm.py | 43 ++++++++++++++++------------------
 1 file changed, 20 insertions(+), 23 deletions(-)

diff --git a/cryptography/shor_algorithm.py b/cryptography/shor_algorithm.py
index 4f070fe67ca1..110d3278b40d 100644
--- a/cryptography/shor_algorithm.py
+++ b/cryptography/shor_algorithm.py
@@ -4,9 +4,9 @@
 Source: https://en.wikipedia.org/wiki/Shor%27s_algorithm
 """
 
-import random
 import math
-from typing import Tuple, Union
+import random
+from typing import Any
 
 
 def is_prime(n: int) -> bool:
@@ -24,11 +24,8 @@ def is_prime(n: int) -> bool:
         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
+    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:
@@ -48,7 +45,7 @@ def modexp(a: int, b: int, m: int) -> int:
     return result
 
 
-def shor_classical(N: int, max_attempts: int = 10) -> Union[str, Tuple[int, int]]:
+def shor_classical(n: int, max_attempts: int = 10) -> str | tuple[int, int]:
     """
     Classical approximation of Shor's Algorithm to factor a number.
 
@@ -61,22 +58,22 @@ def shor_classical(N: int, max_attempts: int = 10) -> Union[str, Tuple[int, int]
     >>> shor_classical(13)  # Prime
     'No factors: 13 is prime'
     """
-    if N <= 1:
+    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"
+    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)
+        a = random.randrange(2, n - 1)
+        g = math.gcd(a, n)
         if g > 1:
-            return g, N // g
+            return g, n // g
 
         r = 1
-        while r < N:
-            if modexp(a, r, N) == 1:
+        while r < n:
+            if modexp(a, r, n) == 1:
                 break
             r += 1
         else:
@@ -84,13 +81,13 @@ def shor_classical(N: int, max_attempts: int = 10) -> Union[str, Tuple[int, int]
 
         if r % 2 != 0:
             continue
-        x = modexp(a, r // 2, N)
-        if x == N - 1:
+        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):
+        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"