From f610031f9e0411395c062ba387c295f6e563b960 Mon Sep 17 00:00:00 2001
From: Aditya Kumar Mishra <154746713+adityakrmishra@users.noreply.github.com>
Date: Wed, 29 Jan 2025 19:47:41 +0530
Subject: [PATCH 1/2] =?UTF-8?q?Added=20classical=20implementation=20of=20S?=
 =?UTF-8?q?hor=E2=80=99s=20Algorithm?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

- Implemented a classical simulation of Shor’s Algorithm in `algorithms/cryptography/shor_algorithm.py`
- The algorithm factors a composite number N without using quantum computing libraries
- Uses modular exponentiation and order-finding to determine factors
- Includes an example usage for testing
---
 algorithms/cryptography/shor_algorithm.py | 56 +++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 algorithms/cryptography/shor_algorithm.py

diff --git a/algorithms/cryptography/shor_algorithm.py b/algorithms/cryptography/shor_algorithm.py
new file mode 100644
index 000000000000..b5ac08f59549
--- /dev/null
+++ b/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}")

From b0833eb96b223522993eafe98b6b0ec8f40b84c9 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 29 Jan 2025 14:19:42 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 algorithms/cryptography/shor_algorithm.py | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/algorithms/cryptography/shor_algorithm.py b/algorithms/cryptography/shor_algorithm.py
index b5ac08f59549..1cdefaa3c0fb 100644
--- a/algorithms/cryptography/shor_algorithm.py
+++ b/algorithms/cryptography/shor_algorithm.py
@@ -1,12 +1,14 @@
 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
@@ -17,6 +19,7 @@ def modular_exponentiation(base, exp, mod):
         exp //= 2
     return result
 
+
 def find_order(a, N):
     """Finds the smallest r such that a^r ≡ 1 (mod N)"""
     r = 1
@@ -26,6 +29,7 @@ def find_order(a, N):
             return None
     return r
 
+
 def shor_algorithm(N):
     """Simulates Shor’s Algorithm classically to factorize N."""
     if N % 2 == 0:
@@ -49,6 +53,7 @@ def shor_algorithm(N):
         if 1 < factor2 < N:
             return factor2, N // factor2
 
+
 # Example usage
 if __name__ == "__main__":
     N = 15  # You can test with 21, 35, 55, etc.