From 1993551a593322b7dd561c2fac57bbd99237554c Mon Sep 17 00:00:00 2001
From: HeshamTB <hishaminv@gmail.com>
Date: Thu, 16 Apr 2020 09:48:31 +0300
Subject: [PATCH] Working key pair generation, encryption and decryption   
 TODO:    - Clean up    - Split into methods    - Save a key pair in a file
 (interactivly)?

---
 rsa.py | 38 ++++++++++++++++++++++++++++++++++++--
 1 file changed, 36 insertions(+), 2 deletions(-)

diff --git a/rsa.py b/rsa.py
index 1c4e32b..eeee00c 100755
--- a/rsa.py
+++ b/rsa.py
@@ -5,14 +5,48 @@
 
 import math
 import os
+import decimal
 
 def main():
 
-    #Prime of size 32 bit random
-    print(getPrime(32))
+    #Primes of size 32 bit random
+    #resulting in a 64-bit key mod
+    p = getPrime(32)
+    print("p: ", p)
+    q = getPrime(32)
+    print("q: ", q)
+    n = p*q
+    print("n: ", n)
+    print("%d bit key" % n.bit_length())
+
+    #lamda(n) = LCM(p-1, q-1)
+    #Since LCM(a,b) = ab/GCD(a,b)
+    #gcd = math.gcd(p-1, q-1)
+    #print("GCD: ", gcd)
+    #lcm = abs((p-1) * (q-1)) / gcd
+    #print("LCM: ", lcm)
+    phi = (p-1)*(q-1)
+    print("phi: ", phi)
+    #e exponant should be 1 < e < lamda(n) and GCD(e, lamda(n)) = 1 (coprime)
+    # recommended value is 65,537
+    e = 65537
+    d = pow(e,-1,phi)
+    print("d: ", d)
+    print("--------------")
+    print("public key (%d, %d)" % (n,e) )
+
+    msg_text = "Hello"
+    msg_number_form = int.from_bytes(msg_text.encode(),"little")
+    print("Message: %s or %d" % (msg_text, msg_number_form))
+
+    msg_encrypted_number_form = pow(msg_number_form, e, n)
+    print("Encrypted msg: ", msg_encrypted_number_form)
+    msg_decrypted_number_form = pow(msg_encrypted_number_form, d, n)
+    print("Decrypted msg: ", msg_decrypted_number_form)
 
 def getPrime(bits):
     while True:
+        #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)),"little")
         if isPrime(x):
             return x