From 18a4cf0e411b760ffc867551bcf24e59a287cc75 Mon Sep 17 00:00:00 2001
From: Zizhou Zhang <z1335447535@gmail.com>
Date: Sat, 9 Nov 2019 14:08:47 +1100
Subject: [PATCH 1/3] added RSA_factorization.py

This algorithm can effectively factor RSA large prime N given public key e and private key d.
---
 ciphers/RSA_factorization.py | 45 ++++++++++++++++++++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100644 ciphers/RSA_factorization.py

diff --git a/ciphers/RSA_factorization.py b/ciphers/RSA_factorization.py
new file mode 100644
index 000000000000..75c289ab5c0d
--- /dev/null
+++ b/ciphers/RSA_factorization.py
@@ -0,0 +1,45 @@
+"""
+An RSA prime factor algorithm.
+
+The program can efficiently factor RSA prime number given the private key d and
+public key e.
+Source: on page 3 of https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf
+large number can take minutes to factor, therefore are not included in doctest.
+"""
+import math
+import random
+from typing import List
+
+
+def rsafactor(d: int, e: int, N: int) -> List[int]:
+    """
+    This function returns the factors of N, where p*q=N
+      Return: [p, q]
+
+    >>> rsafactor(3,16971,25777)
+    [149, 173]
+    >>> rsafactor(7331,11,27233)
+    [113, 241]
+    >>> rsafactor(4021,13,17711)
+    [89, 199]
+    """
+    k = d * e - 1
+    p = 0
+    q = 0
+    while p == 0:
+        g = random.randint(2, N - 1)
+        t = k
+        if t % 2 == 0:
+            t = t // 2
+            x = (g ** t) % N
+            y = math.gcd(x - 1, N)
+            if x > 1 and y > 1:
+                p = y
+                q = N // y
+    return sorted([p, q])
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From 40f88ff42295ca49f5a39aaf3b68dd6af5d9331b Mon Sep 17 00:00:00 2001
From: Zizhou Zhang <z1335447535@gmail.com>
Date: Sat, 9 Nov 2019 23:40:12 +1100
Subject: [PATCH 2/3] Rename RSA_factorization.py to rsa_factorization.py

---
 ciphers/{RSA_factorization.py => rsa_factorization.py} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename ciphers/{RSA_factorization.py => rsa_factorization.py} (100%)

diff --git a/ciphers/RSA_factorization.py b/ciphers/rsa_factorization.py
similarity index 100%
rename from ciphers/RSA_factorization.py
rename to ciphers/rsa_factorization.py

From 6f7959cd3aff3975012bcf8352555b551d5c8080 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Sat, 9 Nov 2019 15:02:11 +0100
Subject: [PATCH 3/3] Add definitions for d, e, and N

---
 ciphers/rsa_factorization.py | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/ciphers/rsa_factorization.py b/ciphers/rsa_factorization.py
index 75c289ab5c0d..58bdc554a861 100644
--- a/ciphers/rsa_factorization.py
+++ b/ciphers/rsa_factorization.py
@@ -15,12 +15,18 @@ def rsafactor(d: int, e: int, N: int) -> List[int]:
     """
     This function returns the factors of N, where p*q=N
       Return: [p, q]
+    
+    We call N the RSA modulus, e the encryption exponent, and d the decryption exponent.
+    The pair (N, e) is the public key. As its name suggests, it is public and is used to
+        encrypt messages.
+    The pair (N, d) is the secret key or private key and is known only to the recipient
+        of encrypted messages.
 
-    >>> rsafactor(3,16971,25777)
+    >>> rsafactor(3, 16971, 25777)
     [149, 173]
-    >>> rsafactor(7331,11,27233)
+    >>> rsafactor(7331, 11, 27233)
     [113, 241]
-    >>> rsafactor(4021,13,17711)
+    >>> rsafactor(4021, 13, 17711)
     [89, 199]
     """
     k = d * e - 1