From 0e50709c23d37434f3199130873a847df9fc48b8 Mon Sep 17 00:00:00 2001
From: Johannes <j.rosvik@gmail.com>
Date: Sun, 24 May 2020 15:15:42 +0200
Subject: [PATCH] Remove the bug

---
 TTM4135.ipynb | 27 +++++++--------------------
 1 file changed, 7 insertions(+), 20 deletions(-)

diff --git a/TTM4135.ipynb b/TTM4135.ipynb
index fa460e6..e58ff68 100644
--- a/TTM4135.ipynb
+++ b/TTM4135.ipynb
@@ -1,12 +1,5 @@
 {
  "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -713,7 +706,7 @@
     "3. Select $e$ randomly with $gcd(e, \\varphi(n)) = 1$.\n",
     "4. Compute $d = e−1 \\mod \\varphi(n)$.\n",
     "5. The public key is the pair $n$ and $e$.\n",
-    "6. The private key consists of the values $p$, $q$ and $d$.\n",
+    "6. The private key consists of the values $p$, $q$ (or $n = pq$) and $d$.\n",
     "\n",
     "### Encryption\n",
     "\n",
@@ -723,13 +716,13 @@
     "\n",
     "### Decryption\n",
     "\n",
-    "The private key for decryption is KD = d (values p and q are not used here).\n",
-    "1. Compute D(C,KD) = Cd mod n = M."
+    "The private key for decryption is $KD = d$ (values $p$ and $q$ are not used here).\n",
+    "1. Compute $D(C,KD) = Cd \\mod n = M$."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -785,15 +778,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "C = M^e (mod n) = 50^102900819 (mod 604604729) = 2488\n",
-      "\n",
       "Ciphertext: 2488\n"
      ]
     }
@@ -809,28 +800,25 @@
     "\n",
     "M = 50\n",
     "C = rsa_encrypt(M, rsa_keys)\n",
-    "print(f\"C = M^e (mod n) = {M}^{e} (mod {n}) = {C}\\n\")\n",
     "print(f\"Ciphertext: {C}\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "M = C^d (mod n) = 2488^1 (mod 604604729) = 50\n",
-      "\n",
       "Message: 50\n"
      ]
     }
    ],
    "source": [
     "def rsa_decrypt(C, rsa_keys):\n",
-    "    # private key\n",
+    "    # Private key\n",
     "    p = rsa_keys['p']\n",
     "    q = rsa_keys['q']\n",
     "    d = rsa_keys['d']\n",
@@ -840,7 +828,6 @@
     "    return square_and_multiply(C,d,n)\n",
     "\n",
     "M = rsa_decrypt(C, rsa_keys)\n",
-    "print(f\"M = C^d (mod n) = {C}^{d} (mod {n}) = {M}\\n\")\n",
     "print(f\"Message: {M}\")"
    ]
   }