From 611a6c45ea285a9a2a889037a6a7069680e261e0 Mon Sep 17 00:00:00 2001
From: HeshamTB <hishaminv@gmail.com>
Date: Sat, 18 Apr 2020 18:34:36 +0300
Subject: [PATCH] Added Miller Rabin's algorithm: 	- Now can generate a
 4096-bit key in seconds. 	However, a longer key makes the cipher way too
 	long. Should make a padding or an encoding to 	reduce the cipher size
 with big keys.

Signed-off-by: HeshamTB <hishaminv@gmail.com>
---
 MillerRabin.py | 30 ++++++++++++++++++++++++++++++
 TODO           |  1 +
 rsa.py         |  3 ++-
 3 files changed, 33 insertions(+), 1 deletion(-)
 create mode 100644 MillerRabin.py

diff --git a/MillerRabin.py b/MillerRabin.py
new file mode 100644
index 0000000..8f89609
--- /dev/null
+++ b/MillerRabin.py
@@ -0,0 +1,30 @@
+#From: https://stackoverflow.com/questions/17298130/working-with-large-primes-in-python
+from random import randrange
+def is_prime(n, k=10):
+    if n == 2:
+        return True
+    if not n & 1:
+        return False
+
+    def check(a, s, d, n):
+        x = pow(a, d, n)
+        if x == 1:
+            return True
+        for i in range(s - 1):
+            if x == n - 1:
+                return True
+            x = pow(x, 2, n)
+        return x == n - 1
+
+    s = 0
+    d = n - 1
+
+    while d % 2 == 0:
+        d >>= 1
+        s += 1
+
+    for i in range(k):
+        a = randrange(2, n - 1)
+        if not check(a, s, d, n):
+            return False
+    return True
\ No newline at end of file
diff --git a/TODO b/TODO
index 3c5fe29..90e8be2 100644
--- a/TODO
+++ b/TODO
@@ -10,3 +10,4 @@ resources:
 	https://crypto.stackexchange.com/questions/1448/definition-of-textbook-rsa
 	https://crypto.stackexchange.com/questions/3608/why-is-padding-used-for-rsa-encryption-given-that-it-is-not-a-block-cipher
 	https://www.inf.pucrs.br/~calazans/graduate/TPVLSI_I/RSA-oaep_spec.pdf
+	https://stackoverflow.com/questions/17298130/working-with-large-primes-in-python
diff --git a/rsa.py b/rsa.py
index 02ea1e2..4df10b3 100755
--- a/rsa.py
+++ b/rsa.py
@@ -13,6 +13,7 @@ https://crypto.stackexchange.com/questions/13113/how-can-i-find-the-prime-number
 import math
 import os
 import sys
+import MillerRabin as mr
 
 keysFolder = "keys/"
 byteOrder = "little"
@@ -135,7 +136,7 @@ def getPrime(bits):
         #Byte order "little" or "big" does not matter here since we want a random number from os.urandom()
         x = int.from_bytes(os.urandom(int(bits/8)), byteOrder)
         print("trying: ", x, end="")
-        if isPrime(x):
+        if mr.is_prime(x):
             print("\nprime: ", x)
             return x
         print("\r",end="")