Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "inclusive-arizona",
   "metadata": {},
   "source": [
    "# FMSI Project Notebook\n",
    "\n",
    "Authors:\n",
    "- Alexandre Dias\n",
    "- Bastien Coutadeur\n",
    "- Benjamin Peter\n",
    "- Mathieu Guérin"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "typical-steam",
   "metadata": {},
   "source": [
    "Importing our work:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "balanced-telephone",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating prime numbers\n",
    "from genPrime import erathosthene, is_prime\n",
    "from miller_rabin import MillerRabin, generate_prime\n",
    "\n",
    "# RSA Implementation\n",
    "from rsa import RSA\n",
    "\n",
    "# Cracking RSA\n",
    "import p_1_pollard\n",
    "import rho_pollard\n",
    "import fermat as ferm\n",
    "\n",
    "# Timer\n",
    "import time_cracking as tm\n",
    "\n",
    "# Plot\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Helper functions\n",
    "from helper import tuple_val_eq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "equipped-madonna",
   "metadata": {},
   "source": [
    "## Prime numbers generation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "discrete-caribbean",
   "metadata": {},
   "source": [
    "### Sieve of Eratosthenes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "italian-power",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating prime numbers between 2 and 1024...\n",
      "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021]\n",
      "\n",
      "Success: All the numbers are prime numbers!\n"
     ]
    }
   ],
   "source": [
    "print(\"Generating prime numbers between 2 and 1024...\")\n",
    "L = erathosthene(1024)\n",
    "print(L)\n",
    "\n",
    "print()  # Newline\n",
    "not_primes = []\n",
    "for p in L:\n",
    "    if not is_prime(p):\n",
    "        not_primes.append(p)\n",
    "if not not_primes:\n",
    "    print(\"Success: All the numbers are prime numbers!\")\n",
    "else:\n",
    "    print(\"Error: Found non-prime numbers:\", not_primes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "consistent-cookie",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating prime numbers between 2 and 1048576...\n",
      "Success: All the numbers are prime numbers!\n"
     ]
    }
   ],
   "source": [
    "print(\"Generating prime numbers between 2 and 1048576...\")\n",
    "L = erathosthene(1048576)\n",
    "\n",
    "not_primes = []\n",
    "for p in L:\n",
    "    if not is_prime(p):\n",
    "        not_primes.append(p)\n",
    "if not not_primes:\n",
    "    print(\"Success: All the numbers are prime numbers!\")\n",
    "else:\n",
    "    print(\"Error: Found non-prime numbers:\", not_primes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advised-survivor",
   "metadata": {},
   "source": [
    "### Basic primality test\n",
    "\n",
    "We've implemented a basic primality test (`is_prime`), used above for checking that the sieve of eratosthenes works properly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continued-lottery",
   "metadata": {},
   "source": [
    "### Miller-Rabin primality test\n",
    "\n",
    "We've implemented the Miller-Rabin primality test, faster than `is_prime`, for generating large prime numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "military-louis",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generate random prime numbers between 2^127 and 2^128...\n",
      "1: 275171808720465096917259472861937439847\n",
      "2: 293707757098952331225737381341972786951\n",
      "3: 312674183610567132791838316902226700651\n"
     ]
    }
   ],
   "source": [
    "print(\"Generate random prime numbers between 2^127 and 2^128...\")\n",
    "print(\"1:\", generate_prime(128))\n",
    "print(\"2:\", generate_prime(128))\n",
    "print(\"3:\", generate_prime(128))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "handy-station",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generate random prime numbers between 2^1023 and 2^1024...\n",
      "111573650573299075204902698785700831105759642629485558877624325162612398554032348928405692003770154549506312142934181574243995237006644865572190548814787190368187342899903456210948035773151077971961604047258529955281663970352105365168806984171582756294950618385877401285353709724118214686665090635047946112459\n"
     ]
    }
   ],
   "source": [
    "# Works for generating large prime numbers:\n",
    "print(\"Generate random prime numbers between 2^1023 and 2^1024...\")\n",
    "print(generate_prime(1024))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stock-savage",
   "metadata": {},
   "source": [
    "## RSA Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "checked-contamination",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3233, 7), (3233, 1783))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate RSA public and private keys from given prime numbers\n",
    "RSA.generate_keys(61, 53)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "enabling-mineral",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a RSA object from given prime numbers\n",
    "r = RSA.generate(61, 53)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "martial-kingston",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3233"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The RSA ciphering modulus\n",
    "r.n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "related-trademark",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The RSA public exponent\n",
    "r.e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "whole-sullivan",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3233, 7)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The RSA public key\n",
    "r.pub_key()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "charming-dairy",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1783"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The RSA private exponent\n",
    "r.d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "exposed-patrick",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3233, 1783)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The RSA private key\n",
    "r.priv_key()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "excessive-release",
   "metadata": {},
   "source": [
    "### Encryption"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "allied-joining",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our message: Hello, world!\n"
     ]
    }
   ],
   "source": [
    "# Our clear message\n",
    "msg = \"Hello, world!\"\n",
    "print(\"Our message:\", msg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "blocked-belize",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Encrypted message: [1087, 3071, 1877, 1877, 3183, 1129, 2774, 863, 3183, 1797, 1877, 2872, 2417]\n"
     ]
    }
   ],
   "source": [
    "# Encrypt a message\n",
    "encrypted_msg = r.encrypt(\"Hello, world!\")\n",
    "print(\"Encrypted message:\", encrypted_msg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "buried-relative",
   "metadata": {},
   "source": [
    "Encryption is done character per character."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "excessive-hepatitis",
   "metadata": {},
   "source": [
    "### Decryption"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "stainless-problem",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Decrypted message: Hello, world!\n",
      "This matches our original message!\n"
     ]
    }
   ],
   "source": [
    "decrypted_msg = r.decrypt(encrypted_msg)\n",
    "print(\"Decrypted message:\", decrypted_msg)\n",
    "\n",
    "if decrypted_msg == msg:\n",
    "    print(\"This matches our original message!\")\n",
    "else:\n",
    "    print(\"This does not match our original message..\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "preliminary-chemistry",
   "metadata": {},
   "source": [
    "## Cracking RSA\n",
    "\n",
    "We've implemented three cracking algorithms:\n",
    "- Pollard's p-1 Algorithm\n",
    "- Pollard's rho Algorithm\n",
    "- Fermat's factorization Algorithm\n",
    "\n",
    "_Note:  \n",
    "In the examples below, we're using `tuple_val_eq` to check if the cracked primes match what is expected.  \n",
    "This checks if `(a, b)` is equal to `(c, d)` or `(d, c)`._ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "several-national",
   "metadata": {},
   "source": [
    "### Pollard's p-1 Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cathedral-loading",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our message: Hello, world! This is my very secret message.\n",
      "Encrypting using RSA, from prime numbers (661, 673)\n",
      "\n",
      "********** Cracking with Fermat factorisation **********\n",
      "\n",
      "Cracked primes: (673, 661)\n",
      "Success!\n",
      "\n",
      "Cracked message: Hello, world! This is my very secret message.\n",
      "Success!\n"
     ]
    }
   ],
   "source": [
    "msg = \"Hello, world! This is my very secret message.\"\n",
    "print(\"Our message:\", msg)\n",
    "\n",
    "primes = (661, 673)\n",
    "print(\"Encrypting using RSA, from prime numbers\", primes)\n",
    "r = RSA.generate(*primes)\n",
    "encrypted_msg = r.encrypt(msg)\n",
    "# print(\"Encrypted data:\", encrypted_msg)\n",
    "\n",
    "print()  # Newline\n",
    "print(10 * '*', \"Cracking with Fermat factorisation\", 10 * '*')\n",
    "\n",
    "print()  # Newline\n",
    "cracked_primes = p_1_pollard.crack_primes(r.n)\n",
    "print(\"Cracked primes:\", cracked_primes)\n",
    "print(\"Success!\" if tuple_val_eq(cracked_primes, primes) else \"Failure.\")\n",
    "\n",
    "print()  # Newline\n",
    "cracked_msg = p_1_pollard.crack_msg(encrypted_msg, r.n)\n",
    "print(\"Cracked message:\", cracked_msg)\n",
    "print(\"Success!\" if cracked_msg == msg else \"Failure.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "framed-success",
   "metadata": {},
   "source": [
    "### Pollard's rho Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "infectious-industry",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our message: Hello, world! This is my very secret message.\n",
      "Encrypting using RSA, from prime numbers (661, 673)\n",
      "\n",
      "********** Cracking with Fermat factorisation **********\n",
      "\n",
      "Cracked primes: (673, 661)\n",
      "Success!\n",
      "\n",
      "Cracked message: Hello, world! This is my very secret message.\n",
      "Success!\n"
     ]
    }
   ],
   "source": [
    "msg = \"Hello, world! This is my very secret message.\"\n",
    "print(\"Our message:\", msg)\n",
    "\n",
    "primes = (661, 673)\n",
    "print(\"Encrypting using RSA, from prime numbers\", primes)\n",
    "r = RSA.generate(*primes)\n",
    "encrypted_msg = r.encrypt(msg)\n",
    "# print(\"Encrypted data:\", encrypted_msg)\n",
    "\n",
    "print()  # Newline\n",
    "print(10 * '*', \"Cracking with Fermat factorisation\", 10 * '*')\n",
    "\n",
    "print()  # Newline\n",
    "cracked_primes = rho_pollard.crack_primes(r.n)\n",
    "print(\"Cracked primes:\", cracked_primes)\n",
    "print(\"Success!\" if tuple_val_eq(cracked_primes, primes) else \"Failure.\")\n",
    "\n",
    "print()  # Newline\n",
    "cracked_msg = rho_pollard.crack_msg(encrypted_msg, r.n)\n",
    "print(\"Cracked message:\", cracked_msg)\n",
    "print(\"Success!\" if cracked_msg == msg else \"Failure.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "interested-constant",
   "metadata": {},
   "source": [
    "### Fermat's factorization Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "selected-creek",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our message: Hello, world! This is my very secret message.\n",
      "Encrypting using RSA, from prime numbers (661, 673)\n",
      "\n",
      "********** Cracking with Fermat factorisation **********\n",
      "\n",
      "Cracked primes: (661, 673)\n",
      "Success!\n",
      "\n",
      "Cracked message: Hello, world! This is my very secret message.\n",
      "Success!\n"
     ]
    }
   ],
   "source": [
    "msg = \"Hello, world! This is my very secret message.\"\n",
    "print(\"Our message:\", msg)\n",
    "\n",
    "primes = (661, 673)\n",
    "print(\"Encrypting using RSA, from prime numbers\", primes)\n",
    "r = RSA.generate(*primes)\n",
    "encrypted_msg = r.encrypt(msg)\n",
    "# print(\"Encrypted data:\", encrypted_msg)\n",
    "\n",
    "print()  # Newline\n",
    "print(10 * '*', \"Cracking with Fermat factorisation\", 10 * '*')\n",
    "\n",
    "print()  # Newline\n",
    "cracked_primes = ferm.crack_primes(r.n)\n",
    "print(\"Cracked primes:\", cracked_primes)\n",
    "print(\"Success!\" if tuple_val_eq(cracked_primes, primes) else \"Failure.\")\n",
    "\n",
    "print()  # Newline\n",
    "cracked_msg = ferm.crack_msg(encrypted_msg, r.n)\n",
    "print(\"Cracked message:\", cracked_msg)\n",
    "print(\"Success!\" if cracked_msg == msg else \"Failure.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "violent-trust",
   "metadata": {},
   "source": [
    "### Time comparaison for different algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ecf6a82f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save time by not regenerating benchmarks\n",
    "skip_live_benchmarking = True"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "architectural-astronomy",
   "metadata": {},
   "source": [
    "#### Pollard's rho Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "special-hands",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Couldn't crack p = 2 q = 3\n",
      "p = 19 q = 17 --- 0.0 seconds ---\n",
      "p = 43 q = 41 --- 0.0001 seconds ---\n",
      "p = 67 q = 71 --- 0.0003 seconds ---\n",
      "p = 97 q = 101 --- 0.0004 seconds ---\n",
      "p = 131 q = 127 --- 0.0025 seconds ---\n",
      "p = 163 q = 157 --- 0.0013 seconds ---\n",
      "p = 191 q = 193 --- 0.0014 seconds ---\n",
      "p = 227 q = 229 --- 0.004 seconds ---\n",
      "p = 257 q = 263 --- 0.0058 seconds ---\n",
      "p = 283 q = 293 --- 0.0022 seconds ---\n",
      "p = 337 q = 331 --- 0.0045 seconds ---\n",
      "p = 367 q = 373 --- 0.007 seconds ---\n",
      "p = 409 q = 401 --- 0.0091 seconds ---\n",
      "p = 443 q = 439 --- 0.0198 seconds ---\n",
      "Couldn't crack p = 467 q = 479\n",
      "p = 509 q = 521 --- 0.0234 seconds ---\n",
      "p = 563 q = 569 --- 0.0283 seconds ---\n",
      "p = 599 q = 601 --- 0.0398 seconds ---\n",
      "p = 641 q = 631 --- 0.0421 seconds ---\n",
      "p = 673 q = 661 --- 0.0043 seconds ---\n",
      "p = 709 q = 719 --- 0.0132 seconds ---\n",
      "p = 757 q = 751 --- 0.0137 seconds ---\n",
      "p = 809 q = 797 --- 0.0548 seconds ---\n",
      "p = 839 q = 829 --- 0.0192 seconds ---\n",
      "p = 881 q = 877 --- 0.0581 seconds ---\n",
      "p = 919 q = 929 --- 0.0217 seconds ---\n",
      "p = 967 q = 971 --- 0.0321 seconds ---\n",
      "p = 1013 q = 1009 --- 0.1037 seconds ---\n",
      "p = 1039 q = 1049 --- 0.0275 seconds ---\n",
      "p = 1091 q = 1087 --- 0.0873 seconds ---\n",
      "p = 1123 q = 1117 --- 0.0638 seconds ---\n",
      "p = 1181 q = 1171 --- 0.1265 seconds ---\n",
      "p = 1217 q = 1223 --- 0.1263 seconds ---\n",
      "p = 1277 q = 1259 --- 0.139 seconds ---\n",
      "p = 1297 q = 1301 --- 0.1232 seconds ---\n",
      "p = 1361 q = 1327 --- 0.0328 seconds ---\n",
      "p = 1423 q = 1409 --- 0.2064 seconds ---\n",
      "p = 1451 q = 1447 --- 0.1925 seconds ---\n",
      "p = 1487 q = 1483 --- 0.1132 seconds ---\n",
      "p = 1531 q = 1523 --- 0.1706 seconds ---\n",
      "p = 1567 q = 1571 --- 0.0883 seconds ---\n",
      "p = 1609 q = 1607 --- 0.1971 seconds ---\n",
      "p = 1637 q = 1657 --- 0.2767 seconds ---\n",
      "p = 1697 q = 1699 --- 0.2255 seconds ---\n",
      "p = 1741 q = 1747 --- 0.2255 seconds ---\n",
      "p = 1789 q = 1787 --- 0.2719 seconds ---\n",
      "p = 1861 q = 1847 --- 0.3221 seconds ---\n",
      "p = 1879 q = 1889 --- 0.0964 seconds ---\n",
      "p = 1933 q = 1949 --- 0.4277 seconds ---\n",
      "p = 1997 q = 1993 --- 0.2287 seconds ---\n",
      "p = 2029 q = 2027 --- 0.351 seconds ---\n",
      "p = 2081 q = 2083 --- 0.1652 seconds ---\n",
      "p = 2113 q = 2129 --- 0.4595 seconds ---\n",
      "p = 2153 q = 2161 --- 0.3783 seconds ---\n",
      "p = 2237 q = 2221 --- 0.1816 seconds ---\n",
      "p = 2273 q = 2269 --- 0.5448 seconds ---\n",
      "p = 2309 q = 2311 --- 0.3684 seconds ---\n",
      "p = 2357 q = 2351 --- 0.4714 seconds ---\n",
      "p = 2389 q = 2393 --- 0.5946 seconds ---\n",
      "p = 2441 q = 2437 --- 0.682 seconds ---\n",
      "p = 2503 q = 2477 --- 0.3166 seconds ---\n",
      "p = 2551 q = 2549 --- 0.3013 seconds ---\n",
      "p = 2617 q = 2609 --- 0.5223 seconds ---\n",
      "p = 2663 q = 2659 --- 0.7123 seconds ---\n",
      "p = 2689 q = 2693 --- 0.7292 seconds ---\n",
      "p = 2719 q = 2729 --- 0.1886 seconds ---\n",
      "p = 2777 q = 2767 --- 0.7757 seconds ---\n",
      "p = 2803 q = 2819 --- 0.7929 seconds ---\n",
      "p = 2861 q = 2857 --- 0.3293 seconds ---\n",
      "p = 2917 q = 2909 --- 0.6456 seconds ---\n",
      "Couldn't crack p = 2963 q = 2969\n",
      "p = 3023 q = 3019 --- 0.9148 seconds ---\n",
      "p = 3067 q = 3079 --- 0.7176 seconds ---\n",
      "p = 3137 q = 3121 --- 0.3389 seconds ---\n",
      "p = 3187 q = 3191 --- 0.7267 seconds ---\n",
      "p = 3229 q = 3251 --- 0.5666 seconds ---\n",
      "p = 3301 q = 3299 --- 0.3936 seconds ---\n",
      "p = 3331 q = 3329 --- 1.1958 seconds ---\n",
      "p = 3373 q = 3371 --- 1.2492 seconds ---\n",
      "p = 3433 q = 3449 --- 1.1888 seconds ---\n",
      "p = 3491 q = 3469 --- 0.8685 seconds ---\n",
      "p = 3529 q = 3533 --- 1.2501 seconds ---\n",
      "p = 3571 q = 3559 --- 0.5805 seconds ---\n",
      "p = 3617 q = 3613 --- 0.6564 seconds ---\n",
      "p = 3659 q = 3671 --- 1.1225 seconds ---\n",
      "p = 3709 q = 3701 --- 0.246 seconds ---\n",
      "p = 3767 q = 3761 --- 1.1868 seconds ---\n",
      "p = 3821 q = 3803 --- 1.22 seconds ---\n",
      "p = 3863 q = 3853 --- 0.3864 seconds ---\n",
      "p = 3917 q = 3911 --- 1.3383 seconds ---\n",
      "p = 3947 q = 3943 --- 0.8727 seconds ---\n",
      "p = 4013 q = 4007 --- 1.5118 seconds ---\n",
      "p = 4051 q = 4057 --- 1.1913 seconds ---\n",
      "p = 4099 q = 4111 --- 0.6075 seconds ---\n",
      "p = 4153 q = 4157 --- 0.8658 seconds ---\n",
      "p = 4217 q = 4219 --- 1.341 seconds ---\n",
      "p = 4253 q = 4259 --- 1.5212 seconds ---\n",
      "p = 4289 q = 4297 --- 1.386 seconds ---\n",
      "p = 4363 q = 4357 --- 0.9538 seconds ---\n",
      "p = 4423 q = 4421 --- 2.0971 seconds ---\n",
      "p = 4481 q = 4463 --- 1.6789 seconds ---\n",
      "p = 4517 q = 4519 --- 1.5432 seconds ---\n",
      "p = 4583 q = 4567 --- 1.0492 seconds ---\n",
      "p = 4639 q = 4637 --- 1.6174 seconds ---\n",
      "p = 4663 q = 4673 --- 0.5515 seconds ---\n",
      "p = 4729 q = 4723 --- 2.2335 seconds ---\n",
      "p = 4787 q = 4789 --- 1.7272 seconds ---\n",
      "p = 4817 q = 4831 --- 1.5921 seconds ---\n",
      "p = 4909 q = 4903 --- 2.4305 seconds ---\n",
      "p = 4951 q = 4943 --- 2.6021 seconds ---\n",
      "p = 4987 q = 4993 --- 1.2633 seconds ---\n",
      "p = 5023 q = 5021 --- 0.9143 seconds ---\n",
      "p = 5087 q = 5081 --- 2.1613 seconds ---\n",
      "p = 5119 q = 5147 --- 1.9893 seconds ---\n",
      "p = 5189 q = 5197 --- 2.0442 seconds ---\n",
      "p = 5237 q = 5261 --- 2.3109 seconds ---\n",
      "p = 5303 q = 5309 --- 2.3606 seconds ---\n",
      "p = 5387 q = 5381 --- 2.4246 seconds ---\n",
      "p = 5419 q = 5417 --- 2.2102 seconds ---\n",
      "p = 5449 q = 5471 --- 0.5361 seconds ---\n",
      "p = 5503 q = 5507 --- 1.5281 seconds ---\n",
      "p = 5557 q = 5563 --- 1.5516 seconds ---\n",
      "p = 5639 q = 5623 --- 3.1935 seconds ---\n",
      "p = 5659 q = 5657 --- 2.4323 seconds ---\n",
      "p = 5711 q = 5701 --- 1.1772 seconds ---\n",
      "p = 5749 q = 5779 --- 0.8498 seconds ---\n",
      "p = 5821 q = 5813 --- 0.6532 seconds ---\n",
      "p = 5857 q = 5851 --- 0.6381 seconds ---\n",
      "p = 5897 q = 5881 --- 2.0749 seconds ---\n",
      "p = 5981 q = 5953 --- 3.2191 seconds ---\n",
      "p = 6043 q = 6037 --- 1.8711 seconds ---\n",
      "p = 6079 q = 6089 --- 0.9618 seconds ---\n",
      "p = 6131 q = 6133 --- 3.5436 seconds ---\n",
      "p = 6197 q = 6199 --- 2.9531 seconds ---\n",
      "p = 6229 q = 6247 --- 2.983 seconds ---\n",
      "p = 6277 q = 6287 --- 4.1482 seconds ---\n",
      "p = 6329 q = 6323 --- 3.4198 seconds ---\n",
      "p = 6367 q = 6361 --- 2.991 seconds ---\n",
      "p = 6421 q = 6427 --- 3.3491 seconds ---\n",
      "p = 6481 q = 6491 --- 3.0202 seconds ---\n",
      "p = 6553 q = 6563 --- 1.0812 seconds ---\n",
      "p = 6607 q = 6599 --- 3.2926 seconds ---\n",
      "p = 6661 q = 6673 --- 1.5996 seconds ---\n",
      "p = 6703 q = 6709 --- 4.5192 seconds ---\n",
      "p = 6763 q = 6779 --- 4.6699 seconds ---\n",
      "p = 6827 q = 6823 --- 2.4558 seconds ---\n",
      "p = 6869 q = 6863 --- 4.1463 seconds ---\n",
      "p = 6917 q = 6911 --- 4.085 seconds ---\n",
      "p = 6971 q = 6967 --- 3.5319 seconds ---\n",
      "p = 7013 q = 7001 --- 4.6676 seconds ---\n",
      "p = 7057 q = 7069 --- 3.7605 seconds ---\n",
      "p = 7127 q = 7129 --- 3.8279 seconds ---\n",
      "p = 7207 q = 7193 --- 2.6038 seconds ---\n",
      "p = 7237 q = 7243 --- 2.6353 seconds ---\n",
      "p = 7309 q = 7307 --- 4.0227 seconds ---\n",
      "p = 7369 q = 7351 --- 1.8659 seconds ---\n",
      "p = 7451 q = 7457 --- 4.6498 seconds ---\n",
      "p = 7489 q = 7499 --- 1.4129 seconds ---\n",
      "p = 7537 q = 7541 --- 5.1168 seconds ---\n",
      "Couldn't crack p = 7573 q = 7577\n",
      "p = 7621 q = 7607 --- 3.1638 seconds ---\n",
      "p = 7681 q = 7673 --- 0.6904 seconds ---\n",
      "p = 7717 q = 7723 --- 3.0663 seconds ---\n",
      "p = 7759 q = 7789 --- 1.5379 seconds ---\n",
      "p = 7853 q = 7841 --- 5.1875 seconds ---\n",
      "p = 7883 q = 7901 --- 5.287 seconds ---\n",
      "p = 7949 q = 7937 --- 5.3096 seconds ---\n",
      "p = 8011 q = 8017 --- 3.4572 seconds ---\n",
      "p = 8081 q = 8087 --- 5.4846 seconds ---\n",
      "p = 8123 q = 8117 --- 5.5202 seconds ---\n",
      "p = 8179 q = 8191 --- 3.0649 seconds ---\n",
      "p = 8233 q = 8237 --- 3.4064 seconds ---\n",
      "p = 8287 q = 8291 --- 2.4784 seconds ---\n",
      "p = 8353 q = 8329 --- 6.9934 seconds ---\n",
      "p = 8419 q = 8389 --- 1.7824 seconds ---\n",
      "p = 8461 q = 8447 --- 3.8431 seconds ---\n",
      "p = 8527 q = 8537 --- 7.3354 seconds ---\n",
      "p = 8597 q = 8581 --- 7.0977 seconds ---\n",
      "p = 8641 q = 8629 --- 8.0418 seconds ---\n",
      "p = 8689 q = 8681 --- 5.204 seconds ---\n",
      "p = 8731 q = 8719 --- 2.7653 seconds ---\n",
      "p = 8761 q = 8779 --- 8.19 seconds ---\n",
      "p = 8831 q = 8821 --- 7.9825 seconds ---\n",
      "p = 8863 q = 8867 --- 3.9322 seconds ---\n",
      "p = 8941 q = 8933 --- 7.7024 seconds ---\n",
      "p = 8999 q = 9001 --- 8.7324 seconds ---\n",
      "p = 9043 q = 9041 --- 8.7742 seconds ---\n",
      "p = 9103 q = 9109 --- 8.3125 seconds ---\n",
      "p = 9161 q = 9157 --- 0.9581 seconds ---\n",
      "p = 9203 q = 9209 --- 7.068 seconds ---\n",
      "p = 9277 q = 9257 --- 8.5934 seconds ---\n",
      "p = 9319 q = 9323 --- 8.715 seconds ---\n",
      "p = 9371 q = 9377 --- 7.3685 seconds ---\n",
      "p = 9419 q = 9421 --- 9.5438 seconds ---\n",
      "p = 9461 q = 9463 --- 9.6385 seconds ---\n",
      "p = 9497 q = 9511 --- 4.8799 seconds ---\n",
      "p = 9551 q = 9587 --- 7.6761 seconds ---\n",
      "p = 9631 q = 9629 --- 9.9879 seconds ---\n",
      "p = 9689 q = 9679 --- 2.346 seconds ---\n",
      "p = 9743 q = 9739 --- 9.5592 seconds ---\n",
      "p = 9791 q = 9787 --- 8.3492 seconds ---\n",
      "p = 9833 q = 9839 --- 8.2101 seconds ---\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p = 9883 q = 9887 --- 4.98 seconds ---\n",
      "p = 9931 q = 9941 --- 11.3826 seconds ---\n",
      "Sucess rate: 201/4\n",
      "[0.0, 0.0001, 0.0003, 0.0004, 0.0025, 0.0013, 0.0014, 0.004, 0.0058, 0.0022, 0.0045, 0.007, 0.0091, 0.0198, 0.0234, 0.0283, 0.0398, 0.0421, 0.0043, 0.0132, 0.0137, 0.0548, 0.0192, 0.0581, 0.0217, 0.0321, 0.1037, 0.0275, 0.0873, 0.0638, 0.1265, 0.1263, 0.139, 0.1232, 0.0328, 0.2064, 0.1925, 0.1132, 0.1706, 0.0883, 0.1971, 0.2767, 0.2255, 0.2255, 0.2719, 0.3221, 0.0964, 0.4277, 0.2287, 0.351, 0.1652, 0.4595, 0.3783, 0.1816, 0.5448, 0.3684, 0.4714, 0.5946, 0.682, 0.3166, 0.3013, 0.5223, 0.7123, 0.7292, 0.1886, 0.7757, 0.7929, 0.3293, 0.6456, 0.9148, 0.7176, 0.3389, 0.7267, 0.5666, 0.3936, 1.1958, 1.2492, 1.1888, 0.8685, 1.2501, 0.5805, 0.6564, 1.1225, 0.246, 1.1868, 1.22, 0.3864, 1.3383, 0.8727, 1.5118, 1.1913, 0.6075, 0.8658, 1.341, 1.5212, 1.386, 0.9538, 2.0971, 1.6789, 1.5432, 1.0492, 1.6174, 0.5515, 2.2335, 1.7272, 1.5921, 2.4305, 2.6021, 1.2633, 0.9143, 2.1613, 1.9893, 2.0442, 2.3109, 2.3606, 2.4246, 2.2102, 0.5361, 1.5281, 1.5516, 3.1935, 2.4323, 1.1772, 0.8498, 0.6532, 0.6381, 2.0749, 3.2191, 1.8711, 0.9618, 3.5436, 2.9531, 2.983, 4.1482, 3.4198, 2.991, 3.3491, 3.0202, 1.0812, 3.2926, 1.5996, 4.5192, 4.6699, 2.4558, 4.1463, 4.085, 3.5319, 4.6676, 3.7605, 3.8279, 2.6038, 2.6353, 4.0227, 1.8659, 4.6498, 1.4129, 5.1168, 3.1638, 0.6904, 3.0663, 1.5379, 5.1875, 5.287, 5.3096, 3.4572, 5.4846, 5.5202, 3.0649, 3.4064, 2.4784, 6.9934, 1.7824, 3.8431, 7.3354, 7.0977, 8.0418, 5.204, 2.7653, 8.19, 7.9825, 3.9322, 7.7024, 8.7324, 8.7742, 8.3125, 0.9581, 7.068, 8.5934, 8.715, 7.3685, 9.5438, 9.6385, 4.8799, 7.6761, 9.9879, 2.346, 9.5592, 8.3492, 8.2101, 4.98, 11.3826]\n",
      "[323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 1806047, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]\n"
     ]
    }
   ],
   "source": [
    "# 10000 represent the maximum prime that will be generated\n",
    "if not skip_live_benchmarking:\n",
    "    time_array_rho, prime_array_rho = tm.time_crack(rho_pollard.crack_primes, 10000)\n",
    "else:\n",
    "    print(\"Skipping live benchmarking.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cathedral-practice",
   "metadata": {},
   "source": [
    "Expected success rate: 202/3  \n",
    "Pre-calculated values for up to 10000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "private-murray",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_array_rho = [0.0, 0.0001, 0.0001, 0.0003, 0.0004, 0.0022, 0.0015, 0.0032, 0.0106, 0.0088, 0.0026, 0.0051, 0.0079, 0.014, 0.0219, 0.0226, 0.025, 0.0342, 0.0408, 0.0039, 0.0172, 0.0128, 0.053, 0.0163, 0.052, 0.0178, 0.0293, 0.1042, 0.0294, 0.0785, 0.0554, 0.1254, 0.1069, 0.1372, 0.1134, 0.0288, 0.1956, 0.1984, 0.2006, 0.2098, 0.101, 0.2158, 0.2566, 0.2086, 0.2128, 0.315, 0.3169, 0.1056, 0.3757, 0.1993, 0.3135, 0.1443, 0.4537, 0.3519, 0.1723, 0.4914, 0.4245, 0.514, 0.6494, 0.7109, 0.3256, 0.2695, 0.4898, 0.7988, 0.6877, 0.1666, 0.7458, 0.8711, 0.3322, 0.6827, 0.9639, 0.7635, 0.417, 0.8226, 0.5387, 0.422, 1.1741, 1.2285, 1.3259, 1.2349, 1.328, 0.525, 0.6761, 1.0239, 0.2203, 1.4379, 1.4836, 0.3903, 1.2986, 1.0889, 1.432, 1.1458, 0.6131, 0.947, 1.3, 1.4991, 1.3208, 0.9602, 2.1076, 1.6503, 1.5014, 0.9936, 1.5101, 0.5198, 2.2232, 1.8269, 1.5873, 2.4936, 2.4993, 1.2519, 0.979, 2.387, 2.3598, 2.0883, 2.344, 2.4012, 2.3089, 2.1327, 0.5363, 1.541, 1.7619, 3.0871, 2.656, 1.2783, 1.0338, 0.5991, 0.5948, 2.009, 3.6872, 1.9164, 0.9372, 3.4094, 2.7169, 2.8892, 4.0216, 3.3282, 3.1572, 3.8634, 2.9925, 1.0143, 3.098, 1.5456, 4.5204, 4.5304, 2.3364, 4.5141, 4.1206, 4.0091, 4.4849, 4.2813, 4.0907, 2.5899, 2.612, 3.9125, 1.8955, 4.8265, 1.5092, 5.7389, 3.2041, 0.7273, 3.0639, 1.5517, 5.0352, 5.2943, 5.2711, 3.7822, 5.6818, 5.694, 2.9565, 3.3363, 2.5784, 6.7062, 1.7, 3.6832, 7.6507, 6.877, 7.6216, 4.8301, 2.6478, 7.7124, 7.4552, 3.6331, 7.7717, 9.0953, 9.2279, 8.4999, 1.0656, 7.6717, 9.0685, 9.3504, 8.2633, 9.6673, 10.6646, 5.1518, 8.1452, 10.4738, 2.6179, 10.4077, 8.5293, 8.2327, 5.1565, 12.4187]\n",
    "prime_array_rho = [6, 323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 1806047, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "urban-cloud",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, rho = plt.subplots()\n",
    "\n",
    "rho.plot(prime_array_rho, time_array_rho, 'o')\n",
    "rho.set(xlabel = \"n (module de chiffrement)\",\n",
    "        ylabel = \"time (s)\",\n",
    "        title = \"Pollard's rho Algorithm\")\n",
    "rho.grid()\n",
    "\n",
    "plt.xscale(\"log\")\n",
    "# fig.savefig(\"rho_big.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "neither-bottle",
   "metadata": {},
   "outputs": [],
   "source": [
    "bits_rho = [6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62] \n",
    "time_rho = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0001, 0.0005, 0.0002, 0.0008, 0.0009, 0.001, 0.0023, 0.0043, 0.0023, 0.0008, 0.0002, 0.0069, 0.0199, 0.0183, 0.0079, 0.029, 0.023]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "miniature-boulder",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, rho = plt.subplots()\n",
    "\n",
    "rho.plot(bits_rho, time_rho, 'o')\n",
    "rho.set(xlabel = \"bits\",\n",
    "        ylabel = \"time (s)\",\n",
    "        title = \"Pollard's rho Algorithm\")\n",
    "rho.grid()\n",
    "\n",
    "# fig.savefig(\"rho_small.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "handed-discharge",
   "metadata": {},
   "source": [
    "#### Fermat's factorization Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "stupid-skirt",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Couldn't crack p = 2 q = 3\n",
      "p = 17 q = 19 --- 0.0 seconds ---\n",
      "p = 41 q = 43 --- 0.0001 seconds ---\n",
      "p = 67 q = 71 --- 0.0003 seconds ---\n",
      "p = 97 q = 101 --- 0.0004 seconds ---\n",
      "p = 127 q = 131 --- 0.0019 seconds ---\n",
      "p = 157 q = 163 --- 0.0014 seconds ---\n",
      "p = 191 q = 193 --- 0.0014 seconds ---\n",
      "p = 227 q = 229 --- 0.0038 seconds ---\n",
      "p = 257 q = 263 --- 0.006 seconds ---\n",
      "p = 283 q = 293 --- 0.0022 seconds ---\n",
      "p = 331 q = 337 --- 0.0043 seconds ---\n",
      "p = 367 q = 373 --- 0.0067 seconds ---\n",
      "p = 401 q = 409 --- 0.0091 seconds ---\n",
      "p = 439 q = 443 --- 0.02 seconds ---\n",
      "p = 467 q = 479 --- 0.0188 seconds ---\n",
      "p = 509 q = 521 --- 0.0229 seconds ---\n",
      "p = 563 q = 569 --- 0.0296 seconds ---\n",
      "p = 599 q = 601 --- 0.0415 seconds ---\n",
      "p = 631 q = 641 --- 0.0441 seconds ---\n",
      "p = 661 q = 673 --- 0.0047 seconds ---\n",
      "p = 709 q = 719 --- 0.0151 seconds ---\n",
      "p = 751 q = 757 --- 0.0148 seconds ---\n",
      "p = 797 q = 809 --- 0.056 seconds ---\n",
      "p = 829 q = 839 --- 0.0192 seconds ---\n",
      "p = 877 q = 881 --- 0.0578 seconds ---\n",
      "p = 919 q = 929 --- 0.0221 seconds ---\n",
      "p = 967 q = 971 --- 0.033 seconds ---\n",
      "p = 1009 q = 1013 --- 0.1046 seconds ---\n",
      "p = 1039 q = 1049 --- 0.0278 seconds ---\n",
      "p = 1087 q = 1091 --- 0.0876 seconds ---\n",
      "p = 1117 q = 1123 --- 0.0647 seconds ---\n",
      "p = 1171 q = 1181 --- 0.1265 seconds ---\n",
      "p = 1217 q = 1223 --- 0.1286 seconds ---\n",
      "p = 1259 q = 1277 --- 0.1425 seconds ---\n",
      "p = 1297 q = 1301 --- 0.1244 seconds ---\n",
      "p = 1327 q = 1361 --- 0.0337 seconds ---\n",
      "p = 1409 q = 1423 --- 0.2032 seconds ---\n",
      "p = 1447 q = 1451 --- 0.1933 seconds ---\n",
      "p = 1483 q = 1487 --- 0.1132 seconds ---\n",
      "p = 1523 q = 1531 --- 0.1695 seconds ---\n",
      "p = 1567 q = 1571 --- 0.089 seconds ---\n",
      "p = 1607 q = 1609 --- 0.1971 seconds ---\n",
      "p = 1637 q = 1657 --- 0.2806 seconds ---\n",
      "p = 1697 q = 1699 --- 0.2343 seconds ---\n",
      "p = 1741 q = 1747 --- 0.2252 seconds ---\n",
      "p = 1787 q = 1789 --- 0.2473 seconds ---\n",
      "p = 1847 q = 1861 --- 0.3287 seconds ---\n",
      "p = 1879 q = 1889 --- 0.0916 seconds ---\n",
      "p = 1933 q = 1949 --- 0.3876 seconds ---\n",
      "p = 1993 q = 1997 --- 0.202 seconds ---\n",
      "p = 2027 q = 2029 --- 0.3142 seconds ---\n",
      "p = 2081 q = 2083 --- 0.1581 seconds ---\n",
      "p = 2113 q = 2129 --- 0.455 seconds ---\n",
      "p = 2153 q = 2161 --- 0.3401 seconds ---\n",
      "p = 2221 q = 2237 --- 0.1835 seconds ---\n",
      "p = 2269 q = 2273 --- 0.5231 seconds ---\n",
      "p = 2309 q = 2311 --- 0.37 seconds ---\n",
      "p = 2351 q = 2357 --- 0.4691 seconds ---\n",
      "p = 2389 q = 2393 --- 0.5777 seconds ---\n",
      "p = 2437 q = 2441 --- 0.686 seconds ---\n",
      "p = 2477 q = 2503 --- 0.3167 seconds ---\n",
      "p = 2549 q = 2551 --- 0.3033 seconds ---\n",
      "p = 2609 q = 2617 --- 0.5235 seconds ---\n",
      "p = 2659 q = 2663 --- 0.7168 seconds ---\n",
      "p = 2689 q = 2693 --- 0.7367 seconds ---\n",
      "p = 2719 q = 2729 --- 0.1891 seconds ---\n",
      "p = 2767 q = 2777 --- 0.7783 seconds ---\n",
      "p = 2803 q = 2819 --- 0.7971 seconds ---\n",
      "p = 2857 q = 2861 --- 0.3281 seconds ---\n",
      "p = 2909 q = 2917 --- 0.6511 seconds ---\n",
      "p = 2963 q = 2969 --- 0.7432 seconds ---\n",
      "p = 3019 q = 3023 --- 0.9185 seconds ---\n",
      "p = 3067 q = 3079 --- 0.7205 seconds ---\n",
      "p = 3121 q = 3137 --- 0.3412 seconds ---\n",
      "p = 3187 q = 3191 --- 0.7379 seconds ---\n",
      "p = 3229 q = 3251 --- 0.5725 seconds ---\n",
      "p = 3299 q = 3301 --- 0.3954 seconds ---\n",
      "p = 3329 q = 3331 --- 1.2071 seconds ---\n",
      "p = 3371 q = 3373 --- 1.237 seconds ---\n",
      "p = 3433 q = 3449 --- 1.2239 seconds ---\n",
      "p = 3469 q = 3491 --- 0.921 seconds ---\n",
      "p = 3529 q = 3533 --- 1.3071 seconds ---\n",
      "p = 3559 q = 3571 --- 0.6474 seconds ---\n",
      "p = 3613 q = 3617 --- 0.7553 seconds ---\n",
      "p = 3659 q = 3671 --- 1.1315 seconds ---\n",
      "p = 3701 q = 3709 --- 0.2506 seconds ---\n",
      "p = 3761 q = 3767 --- 1.1927 seconds ---\n",
      "p = 3803 q = 3821 --- 1.2252 seconds ---\n",
      "p = 3853 q = 3863 --- 0.383 seconds ---\n",
      "p = 3911 q = 3917 --- 1.2819 seconds ---\n",
      "p = 3943 q = 3947 --- 0.7878 seconds ---\n",
      "p = 4007 q = 4013 --- 1.3434 seconds ---\n",
      "p = 4051 q = 4057 --- 1.1797 seconds ---\n",
      "p = 4099 q = 4111 --- 0.6103 seconds ---\n",
      "p = 4153 q = 4157 --- 0.8766 seconds ---\n",
      "p = 4217 q = 4219 --- 1.3463 seconds ---\n",
      "p = 4253 q = 4259 --- 1.5199 seconds ---\n",
      "p = 4289 q = 4297 --- 1.3934 seconds ---\n",
      "p = 4357 q = 4363 --- 0.9591 seconds ---\n",
      "p = 4421 q = 4423 --- 2.1161 seconds ---\n",
      "p = 4463 q = 4481 --- 1.6765 seconds ---\n",
      "p = 4517 q = 4519 --- 1.5467 seconds ---\n",
      "p = 4567 q = 4583 --- 1.059 seconds ---\n",
      "p = 4637 q = 4639 --- 1.6332 seconds ---\n",
      "p = 4663 q = 4673 --- 0.5528 seconds ---\n",
      "p = 4723 q = 4729 --- 2.2368 seconds ---\n",
      "p = 4787 q = 4789 --- 1.7276 seconds ---\n",
      "p = 4817 q = 4831 --- 1.6068 seconds ---\n",
      "p = 4903 q = 4909 --- 2.4211 seconds ---\n",
      "p = 4943 q = 4951 --- 2.6245 seconds ---\n",
      "p = 4987 q = 4993 --- 1.27 seconds ---\n",
      "p = 5021 q = 5023 --- 0.9119 seconds ---\n",
      "p = 5081 q = 5087 --- 2.1698 seconds ---\n",
      "p = 5119 q = 5147 --- 1.9861 seconds ---\n",
      "p = 5189 q = 5197 --- 2.0508 seconds ---\n",
      "p = 5237 q = 5261 --- 2.3302 seconds ---\n",
      "p = 5303 q = 5309 --- 2.3748 seconds ---\n",
      "p = 5381 q = 5387 --- 2.4347 seconds ---\n",
      "p = 5417 q = 5419 --- 2.3543 seconds ---\n",
      "p = 5449 q = 5471 --- 0.5695 seconds ---\n",
      "p = 5503 q = 5507 --- 1.7204 seconds ---\n",
      "p = 5557 q = 5563 --- 1.7514 seconds ---\n",
      "p = 5623 q = 5639 --- 3.1883 seconds ---\n",
      "p = 5657 q = 5659 --- 2.4179 seconds ---\n",
      "p = 5701 q = 5711 --- 1.1793 seconds ---\n",
      "p = 5749 q = 5779 --- 0.8423 seconds ---\n",
      "p = 5813 q = 5821 --- 0.6181 seconds ---\n",
      "p = 5851 q = 5857 --- 0.6234 seconds ---\n",
      "p = 5881 q = 5897 --- 2.0048 seconds ---\n",
      "p = 5953 q = 5981 --- 3.1901 seconds ---\n",
      "p = 6037 q = 6043 --- 1.8357 seconds ---\n",
      "p = 6079 q = 6089 --- 0.9353 seconds ---\n",
      "p = 6131 q = 6133 --- 3.4383 seconds ---\n",
      "p = 6197 q = 6199 --- 2.8976 seconds ---\n",
      "p = 6229 q = 6247 --- 2.9363 seconds ---\n",
      "p = 6277 q = 6287 --- 3.9647 seconds ---\n",
      "p = 6323 q = 6329 --- 3.3501 seconds ---\n",
      "p = 6361 q = 6367 --- 2.8988 seconds ---\n",
      "p = 6421 q = 6427 --- 3.3222 seconds ---\n",
      "p = 6481 q = 6491 --- 3.0288 seconds ---\n",
      "p = 6553 q = 6563 --- 1.0863 seconds ---\n",
      "p = 6599 q = 6607 --- 3.2933 seconds ---\n",
      "p = 6661 q = 6673 --- 1.605 seconds ---\n",
      "p = 6703 q = 6709 --- 4.5127 seconds ---\n",
      "p = 6763 q = 6779 --- 4.6095 seconds ---\n",
      "p = 6823 q = 6827 --- 2.3658 seconds ---\n",
      "p = 6863 q = 6869 --- 3.9592 seconds ---\n",
      "p = 6911 q = 6917 --- 4.0245 seconds ---\n",
      "p = 6967 q = 6971 --- 3.5465 seconds ---\n",
      "p = 7001 q = 7013 --- 4.2367 seconds ---\n",
      "p = 7057 q = 7069 --- 3.7836 seconds ---\n",
      "p = 7127 q = 7129 --- 3.8555 seconds ---\n",
      "p = 7193 q = 7207 --- 2.6197 seconds ---\n",
      "p = 7237 q = 7243 --- 2.6418 seconds ---\n",
      "p = 7307 q = 7309 --- 4.0263 seconds ---\n",
      "p = 7351 q = 7369 --- 1.8764 seconds ---\n",
      "p = 7451 q = 7457 --- 4.659 seconds ---\n",
      "p = 7489 q = 7499 --- 1.4166 seconds ---\n",
      "p = 7537 q = 7541 --- 5.1043 seconds ---\n",
      "p = 7573 q = 7577 --- 2.8913 seconds ---\n",
      "p = 7607 q = 7621 --- 3.1359 seconds ---\n",
      "p = 7673 q = 7681 --- 0.6793 seconds ---\n",
      "p = 7717 q = 7723 --- 2.9858 seconds ---\n",
      "p = 7759 q = 7789 --- 1.5186 seconds ---\n",
      "p = 7841 q = 7853 --- 5.1518 seconds ---\n",
      "p = 7883 q = 7901 --- 5.2206 seconds ---\n",
      "p = 7937 q = 7949 --- 5.3095 seconds ---\n",
      "p = 8011 q = 8017 --- 3.4809 seconds ---\n",
      "p = 8081 q = 8087 --- 5.4746 seconds ---\n",
      "p = 8117 q = 8123 --- 5.5205 seconds ---\n",
      "p = 8179 q = 8191 --- 3.0746 seconds ---\n",
      "p = 8233 q = 8237 --- 3.4184 seconds ---\n",
      "p = 8287 q = 8291 --- 2.4814 seconds ---\n",
      "p = 8329 q = 8353 --- 6.9784 seconds ---\n",
      "p = 8389 q = 8419 --- 1.7872 seconds ---\n",
      "p = 8447 q = 8461 --- 3.864 seconds ---\n",
      "p = 8527 q = 8537 --- 7.3246 seconds ---\n",
      "p = 8581 q = 8597 --- 7.1049 seconds ---\n",
      "p = 8629 q = 8641 --- 8.0244 seconds ---\n",
      "p = 8681 q = 8689 --- 5.1835 seconds ---\n",
      "p = 8719 q = 8731 --- 2.7706 seconds ---\n",
      "p = 8761 q = 8779 --- 8.5432 seconds ---\n",
      "p = 8821 q = 8831 --- 8.3159 seconds ---\n",
      "p = 8863 q = 8867 --- 4.4636 seconds ---\n",
      "p = 8933 q = 8941 --- 8.6833 seconds ---\n",
      "p = 8999 q = 9001 --- 8.744 seconds ---\n",
      "p = 9041 q = 9043 --- 8.7955 seconds ---\n",
      "p = 9103 q = 9109 --- 8.3519 seconds ---\n",
      "p = 9157 q = 9161 --- 0.9712 seconds ---\n",
      "p = 9203 q = 9209 --- 7.1391 seconds ---\n",
      "p = 9257 q = 9277 --- 8.6284 seconds ---\n",
      "p = 9319 q = 9323 --- 8.7526 seconds ---\n",
      "p = 9371 q = 9377 --- 7.3677 seconds ---\n",
      "p = 9419 q = 9421 --- 9.5349 seconds ---\n",
      "p = 9461 q = 9463 --- 9.6383 seconds ---\n",
      "p = 9497 q = 9511 --- 4.8785 seconds ---\n",
      "p = 9551 q = 9587 --- 7.6409 seconds ---\n",
      "p = 9629 q = 9631 --- 9.9615 seconds ---\n",
      "p = 9679 q = 9689 --- 2.3606 seconds ---\n",
      "p = 9739 q = 9743 --- 9.5681 seconds ---\n",
      "p = 9787 q = 9791 --- 8.3345 seconds ---\n",
      "p = 9833 q = 9839 --- 8.0879 seconds ---\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p = 9883 q = 9887 --- 4.9158 seconds ---\n",
      "p = 9931 q = 9941 --- 11.264 seconds ---\n",
      "Sucess rate: 204/1\n",
      "[0.0, 0.0001, 0.0003, 0.0004, 0.0019, 0.0014, 0.0014, 0.0038, 0.006, 0.0022, 0.0043, 0.0067, 0.0091, 0.02, 0.0188, 0.0229, 0.0296, 0.0415, 0.0441, 0.0047, 0.0151, 0.0148, 0.056, 0.0192, 0.0578, 0.0221, 0.033, 0.1046, 0.0278, 0.0876, 0.0647, 0.1265, 0.1286, 0.1425, 0.1244, 0.0337, 0.2032, 0.1933, 0.1132, 0.1695, 0.089, 0.1971, 0.2806, 0.2343, 0.2252, 0.2473, 0.3287, 0.0916, 0.3876, 0.202, 0.3142, 0.1581, 0.455, 0.3401, 0.1835, 0.5231, 0.37, 0.4691, 0.5777, 0.686, 0.3167, 0.3033, 0.5235, 0.7168, 0.7367, 0.1891, 0.7783, 0.7971, 0.3281, 0.6511, 0.7432, 0.9185, 0.7205, 0.3412, 0.7379, 0.5725, 0.3954, 1.2071, 1.237, 1.2239, 0.921, 1.3071, 0.6474, 0.7553, 1.1315, 0.2506, 1.1927, 1.2252, 0.383, 1.2819, 0.7878, 1.3434, 1.1797, 0.6103, 0.8766, 1.3463, 1.5199, 1.3934, 0.9591, 2.1161, 1.6765, 1.5467, 1.059, 1.6332, 0.5528, 2.2368, 1.7276, 1.6068, 2.4211, 2.6245, 1.27, 0.9119, 2.1698, 1.9861, 2.0508, 2.3302, 2.3748, 2.4347, 2.3543, 0.5695, 1.7204, 1.7514, 3.1883, 2.4179, 1.1793, 0.8423, 0.6181, 0.6234, 2.0048, 3.1901, 1.8357, 0.9353, 3.4383, 2.8976, 2.9363, 3.9647, 3.3501, 2.8988, 3.3222, 3.0288, 1.0863, 3.2933, 1.605, 4.5127, 4.6095, 2.3658, 3.9592, 4.0245, 3.5465, 4.2367, 3.7836, 3.8555, 2.6197, 2.6418, 4.0263, 1.8764, 4.659, 1.4166, 5.1043, 2.8913, 3.1359, 0.6793, 2.9858, 1.5186, 5.1518, 5.2206, 5.3095, 3.4809, 5.4746, 5.5205, 3.0746, 3.4184, 2.4814, 6.9784, 1.7872, 3.864, 7.3246, 7.1049, 8.0244, 5.1835, 2.7706, 8.5432, 8.3159, 4.4636, 8.6833, 8.744, 8.7955, 8.3519, 0.9712, 7.1391, 8.6284, 8.7526, 7.3677, 9.5349, 9.6383, 4.8785, 7.6409, 9.9615, 2.3606, 9.5681, 8.3345, 8.0879, 4.9158, 11.264]\n",
      "[323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 223693, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 1806047, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 8797147, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57380621, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]\n"
     ]
    }
   ],
   "source": [
    "if not skip_live_benchmarking:\n",
    "    time_array_fermat, prime_array_fermat = tm.time_crack(ferm.crack_primes, 10000)\n",
    "else:\n",
    "    print(\"Skipping live benchmarking.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "inside-copying",
   "metadata": {},
   "source": [
    "Expected success rate: 204/1  \n",
    "Pre-calculated values for up to 10000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "expressed-uruguay",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_array_fermat = [0.0001, 0.0001, 0.0003, 0.0005, 0.0026, 0.0016, 0.0014, 0.0044, 0.0064, 0.0023, 0.0049, 0.0153, 0.0087, 0.0235, 0.0206, 0.0197, 0.026, 0.0361, 0.0443, 0.0041, 0.0186, 0.0142, 0.0569, 0.0176, 0.0494, 0.0195, 0.0307, 0.1008, 0.0241, 0.0829, 0.0675, 0.1231, 0.1243, 0.1326, 0.1222, 0.0289, 0.1948, 0.2103, 0.1403, 0.1533, 0.0766, 0.195, 0.2622, 0.2925, 0.246, 0.2267, 0.3901, 0.0922, 0.4052, 0.2021, 0.3081, 0.1738, 0.4913, 0.2843, 0.1514, 0.4397, 0.3021, 0.4026, 0.5863, 0.5812, 0.272, 0.2602, 0.4796, 0.7493, 0.6525, 0.1558, 0.7809, 0.7451, 0.3755, 0.5593, 0.6638, 0.9685, 0.6602, 0.3152, 0.6755, 0.5496, 0.3689, 1.3034, 1.2079, 1.1335, 0.8055, 1.4236, 0.6119, 0.6249, 1.2016, 0.2651, 1.1034, 1.1959, 0.3852, 1.3006, 0.7028, 1.2101, 1.092, 0.6161, 0.8442, 1.2944, 1.5889, 1.3933, 1.0849, 1.9544, 1.5792, 1.5, 0.9875, 1.512, 0.532, 2.103, 1.6648, 1.5475, 2.1935, 2.4966, 1.1803, 0.8501, 2.2316, 1.8999, 1.891, 2.3179, 2.299, 2.3072, 2.3217, 0.5385, 1.4273, 1.4879, 3.3262, 2.344, 1.093, 0.7986, 0.5988, 0.6375, 1.9435, 3.0267, 1.8067, 0.9051, 3.4219, 2.9328, 2.9134, 3.9913, 3.55, 3.4075, 3.4015, 3.0534, 1.257, 3.5046, 1.8387, 4.4902, 4.716, 2.3644, 3.7381, 4.0524, 3.5921, 4.2716, 3.9497, 3.9007, 2.5626, 2.4736, 3.8604, 1.8125, 4.7324, 1.5268, 5.6682, 2.9581, 3.2966, 0.6926, 3.0761, 1.4874, 5.0568, 5.1483, 5.208, 3.5258, 5.5522, 5.6685, 2.9445, 3.552, 2.3554, 6.8711, 1.6889, 3.7798, 8.75, 7.2993, 7.5098, 5.1172, 2.7103, 8.134, 7.6038, 3.7508, 7.2771, 8.5252, 8.5519, 8.1985, 0.9747, 6.9, 8.3217, 8.8035, 7.2466, 9.8034, 10.3513, 5.3129, 7.7111, 9.4676, 2.3101, 9.4102, 8.4091, 8.2935, 4.9216, 12.2592]\n",
    "prime_array_fermat = [323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 223693, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 1806047, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 8797147, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57380621, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "unique-novelty",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, fermat = plt.subplots()\n",
    "\n",
    "fermat.plot(prime_array_fermat, time_array_fermat, 'o')\n",
    "fermat.set(xlabel = \"n (module de chiffrement)\",\n",
    "           ylabel = \"time (s)\",\n",
    "           title = \"Fermat's factorization Algorithm\")\n",
    "fermat.grid()\n",
    "\n",
    "plt.xscale(\"log\")\n",
    "# fig.savefig(\"fermat_big.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "narrow-medline",
   "metadata": {},
   "source": [
    "Pre calulcated values for big numbers not done in the notebook (because it's too slow)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "center-notice",
   "metadata": {},
   "outputs": [],
   "source": [
    "bits_fermat = [6, 8, 10, 12,14, 16,18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62]\n",
    "time_fermat = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0001, 0.0, 0.0012, 0.0086, 0.0012, 0.0005, 0.0089, 0.0018, 0.0515, 0.366, 0.0613, 1.6567, 0.0003, 1.9363, 14.548, 24.9772]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "recreational-support",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, fermat = plt.subplots()\n",
    "\n",
    "fermat.plot(bits_fermat, time_fermat, 'o')\n",
    "fermat.set(xlabel = \"bits\",\n",
    "           ylabel = \"time (s)\",\n",
    "           title = \"Fermat's factorization Algorithm\")\n",
    "fermat.grid()\n",
    "\n",
    "# fig.savefig(\"fermat_small.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ignored-twenty",
   "metadata": {},
   "source": [
    "#### Pollard's p-1 Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "adjacent-roads",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p = 3 q = 2 --- 0.0 seconds ---\n",
      "p = 17 q = 19 --- 0.0001 seconds ---\n",
      "p = 41 q = 43 --- 0.0001 seconds ---\n",
      "p = 71 q = 67 --- 0.0003 seconds ---\n",
      "p = 97 q = 101 --- 0.0004 seconds ---\n",
      "p = 127 q = 131 --- 0.002 seconds ---\n",
      "p = 163 q = 157 --- 0.0014 seconds ---\n",
      "p = 193 q = 191 --- 0.0014 seconds ---\n",
      "p = 229 q = 227 --- 0.0041 seconds ---\n",
      "p = 257 q = 263 --- 0.006 seconds ---\n",
      "p = 283 q = 293 --- 0.0036 seconds ---\n",
      "p = 331 q = 337 --- 0.0046 seconds ---\n",
      "p = 373 q = 367 --- 0.008 seconds ---\n",
      "p = 401 q = 409 --- 0.0094 seconds ---\n",
      "p = 443 q = 439 --- 0.033 seconds ---\n",
      "p = 467 q = 479 --- 0.0632 seconds ---\n",
      "p = 521 q = 509 --- 0.0231 seconds ---\n",
      "p = 569 q = 563 --- 0.031 seconds ---\n",
      "p = 601 q = 599 --- 0.0397 seconds ---\n",
      "p = 631 q = 641 --- 0.0437 seconds ---\n",
      "p = 673 q = 661 --- 0.0044 seconds ---\n",
      "p = 709 q = 719 --- 0.0156 seconds ---\n",
      "p = 757 q = 751 --- 0.0134 seconds ---\n",
      "p = 809 q = 797 --- 0.0617 seconds ---\n",
      "p = 829 q = 839 --- 0.0184 seconds ---\n",
      "p = 881 q = 877 --- 0.0563 seconds ---\n",
      "p = 919 q = 929 --- 0.023 seconds ---\n",
      "p = 967 q = 971 --- 0.0354 seconds ---\n",
      "p = 1009 q = 1013 --- 0.1056 seconds ---\n",
      "p = 1049 q = 1039 --- 0.0385 seconds ---\n",
      "p = 1091 q = 1087 --- 0.096 seconds ---\n",
      "p = 1123 q = 1117 --- 0.0651 seconds ---\n",
      "p = 1171 q = 1181 --- 0.1273 seconds ---\n",
      "p = 1217 q = 1223 --- 0.1291 seconds ---\n",
      "p = 1277 q = 1259 --- 0.1366 seconds ---\n",
      "p = 1297 q = 1301 --- 0.1263 seconds ---\n",
      "Couldn't crack p = 1327 q = 1361\n",
      "p = 1409 q = 1423 --- 0.2031 seconds ---\n",
      "p = 1451 q = 1447 --- 0.1926 seconds ---\n",
      "p = 1483 q = 1487 --- 0.1158 seconds ---\n",
      "p = 1531 q = 1523 --- 0.1707 seconds ---\n",
      "p = 1567 q = 1571 --- 0.0909 seconds ---\n",
      "p = 1609 q = 1607 --- 0.204 seconds ---\n",
      "p = 1657 q = 1637 --- 0.2791 seconds ---\n",
      "p = 1697 q = 1699 --- 0.2203 seconds ---\n",
      "p = 1741 q = 1747 --- 0.2238 seconds ---\n",
      "p = 1787 q = 1789 --- 0.2472 seconds ---\n",
      "p = 1861 q = 1847 --- 0.3098 seconds ---\n",
      "p = 1889 q = 1879 --- 0.0928 seconds ---\n",
      "p = 1933 q = 1949 --- 0.3845 seconds ---\n",
      "p = 1993 q = 1997 --- 0.2068 seconds ---\n",
      "p = 2029 q = 2027 --- 0.3155 seconds ---\n",
      "p = 2081 q = 2083 --- 0.1581 seconds ---\n",
      "p = 2113 q = 2129 --- 0.4563 seconds ---\n",
      "p = 2161 q = 2153 --- 0.3377 seconds ---\n",
      "p = 2221 q = 2237 --- 0.1804 seconds ---\n",
      "p = 2269 q = 2273 --- 0.519 seconds ---\n",
      "p = 2311 q = 2309 --- 0.3667 seconds ---\n",
      "p = 2357 q = 2351 --- 0.4719 seconds ---\n",
      "p = 2393 q = 2389 --- 0.5813 seconds ---\n",
      "p = 2437 q = 2441 --- 0.6932 seconds ---\n",
      "p = 2503 q = 2477 --- 0.3275 seconds ---\n",
      "p = 2549 q = 2551 --- 0.3046 seconds ---\n",
      "p = 2617 q = 2609 --- 0.536 seconds ---\n",
      "p = 2663 q = 2659 --- 0.7167 seconds ---\n",
      "p = 2689 q = 2693 --- 0.7343 seconds ---\n",
      "p = 2729 q = 2719 --- 0.1892 seconds ---\n",
      "p = 2777 q = 2767 --- 0.8748 seconds ---\n",
      "p = 2803 q = 2819 --- 1.0008 seconds ---\n",
      "p = 2861 q = 2857 --- 0.3681 seconds ---\n",
      "p = 2917 q = 2909 --- 0.6453 seconds ---\n",
      "p = 2969 q = 2963 --- 0.8349 seconds ---\n",
      "p = 3019 q = 3023 --- 1.1105 seconds ---\n",
      "p = 3079 q = 3067 --- 0.7153 seconds ---\n",
      "p = 3121 q = 3137 --- 0.3381 seconds ---\n",
      "p = 3191 q = 3187 --- 0.7408 seconds ---\n",
      "p = 3251 q = 3229 --- 0.568 seconds ---\n",
      "p = 3301 q = 3299 --- 0.3978 seconds ---\n",
      "p = 3329 q = 3331 --- 1.1865 seconds ---\n",
      "p = 3373 q = 3371 --- 1.2833 seconds ---\n",
      "p = 3433 q = 3449 --- 1.1893 seconds ---\n",
      "p = 3469 q = 3491 --- 0.8729 seconds ---\n",
      "p = 3529 q = 3533 --- 1.2592 seconds ---\n",
      "p = 3571 q = 3559 --- 0.5885 seconds ---\n",
      "p = 3613 q = 3617 --- 0.666 seconds ---\n",
      "p = 3659 q = 3671 --- 1.1524 seconds ---\n",
      "p = 3701 q = 3709 --- 0.2501 seconds ---\n",
      "p = 3761 q = 3767 --- 1.1979 seconds ---\n",
      "p = 3821 q = 3803 --- 1.2562 seconds ---\n",
      "p = 3853 q = 3863 --- 0.3884 seconds ---\n",
      "p = 3911 q = 3917 --- 1.2955 seconds ---\n",
      "p = 3943 q = 3947 --- 0.7928 seconds ---\n",
      "p = 4013 q = 4007 --- 1.3546 seconds ---\n",
      "p = 4051 q = 4057 --- 1.1817 seconds ---\n",
      "p = 4111 q = 4099 --- 0.6251 seconds ---\n",
      "p = 4153 q = 4157 --- 0.895 seconds ---\n",
      "p = 4217 q = 4219 --- 1.3439 seconds ---\n",
      "p = 4253 q = 4259 --- 2.3946 seconds ---\n",
      "p = 4289 q = 4297 --- 1.3941 seconds ---\n",
      "p = 4357 q = 4363 --- 0.9617 seconds ---\n",
      "p = 4421 q = 4423 --- 2.111 seconds ---\n",
      "p = 4481 q = 4463 --- 1.6716 seconds ---\n",
      "p = 4519 q = 4517 --- 1.5865 seconds ---\n",
      "p = 4583 q = 4567 --- 1.0624 seconds ---\n",
      "p = 4637 q = 4639 --- 1.6358 seconds ---\n",
      "p = 4663 q = 4673 --- 0.5568 seconds ---\n",
      "p = 4729 q = 4723 --- 2.2821 seconds ---\n",
      "p = 4789 q = 4787 --- 1.7256 seconds ---\n",
      "p = 4831 q = 4817 --- 1.6052 seconds ---\n",
      "p = 4903 q = 4909 --- 2.4228 seconds ---\n",
      "p = 4951 q = 4943 --- 2.61 seconds ---\n",
      "p = 4993 q = 4987 --- 1.2661 seconds ---\n",
      "p = 5023 q = 5021 --- 0.9145 seconds ---\n",
      "p = 5081 q = 5087 --- 2.1749 seconds ---\n",
      "p = 5147 q = 5119 --- 2.0014 seconds ---\n",
      "p = 5197 q = 5189 --- 2.1727 seconds ---\n",
      "p = 5237 q = 5261 --- 2.3122 seconds ---\n",
      "p = 5303 q = 5309 --- 2.4056 seconds ---\n",
      "p = 5381 q = 5387 --- 2.4887 seconds ---\n",
      "p = 5419 q = 5417 --- 2.2141 seconds ---\n",
      "p = 5449 q = 5471 --- 0.575 seconds ---\n",
      "p = 5503 q = 5507 --- 1.5444 seconds ---\n",
      "p = 5563 q = 5557 --- 1.5692 seconds ---\n",
      "p = 5623 q = 5639 --- 3.8608 seconds ---\n",
      "p = 5659 q = 5657 --- 2.4163 seconds ---\n",
      "p = 5701 q = 5711 --- 1.179 seconds ---\n",
      "p = 5779 q = 5749 --- 0.8513 seconds ---\n",
      "p = 5821 q = 5813 --- 0.6209 seconds ---\n",
      "p = 5851 q = 5857 --- 0.6184 seconds ---\n",
      "p = 5881 q = 5897 --- 2.0154 seconds ---\n",
      "p = 5981 q = 5953 --- 3.1882 seconds ---\n",
      "p = 6043 q = 6037 --- 1.8549 seconds ---\n",
      "p = 6089 q = 6079 --- 1.377 seconds ---\n",
      "p = 6133 q = 6131 --- 3.4297 seconds ---\n",
      "p = 6199 q = 6197 --- 3.7233 seconds ---\n",
      "p = 6229 q = 6247 --- 3.0797 seconds ---\n",
      "p = 6287 q = 6277 --- 4.143 seconds ---\n",
      "p = 6323 q = 6329 --- 3.3847 seconds ---\n",
      "p = 6361 q = 6367 --- 2.9502 seconds ---\n",
      "p = 6427 q = 6421 --- 3.4369 seconds ---\n",
      "p = 6481 q = 6491 --- 3.1508 seconds ---\n",
      "p = 6553 q = 6563 --- 1.2056 seconds ---\n",
      "p = 6607 q = 6599 --- 3.8109 seconds ---\n",
      "p = 6661 q = 6673 --- 1.6167 seconds ---\n",
      "p = 6709 q = 6703 --- 4.5226 seconds ---\n",
      "p = 6763 q = 6779 --- 4.6041 seconds ---\n",
      "p = 6823 q = 6827 --- 2.4568 seconds ---\n",
      "p = 6863 q = 6869 --- 3.9863 seconds ---\n",
      "p = 6917 q = 6911 --- 4.0207 seconds ---\n",
      "p = 6971 q = 6967 --- 3.5522 seconds ---\n",
      "p = 7001 q = 7013 --- 4.1298 seconds ---\n",
      "p = 7057 q = 7069 --- 3.7884 seconds ---\n",
      "p = 7129 q = 7127 --- 3.8576 seconds ---\n",
      "p = 7193 q = 7207 --- 2.6149 seconds ---\n",
      "p = 7237 q = 7243 --- 2.6349 seconds ---\n",
      "p = 7309 q = 7307 --- 4.0403 seconds ---\n",
      "p = 7351 q = 7369 --- 1.8681 seconds ---\n",
      "p = 7451 q = 7457 --- 4.6666 seconds ---\n",
      "p = 7489 q = 7499 --- 1.4185 seconds ---\n",
      "p = 7541 q = 7537 --- 5.1119 seconds ---\n",
      "p = 7573 q = 7577 --- 3.1749 seconds ---\n",
      "p = 7621 q = 7607 --- 3.1424 seconds ---\n",
      "p = 7681 q = 7673 --- 0.6872 seconds ---\n",
      "p = 7723 q = 7717 --- 3.0022 seconds ---\n",
      "p = 7789 q = 7759 --- 1.52 seconds ---\n",
      "p = 7841 q = 7853 --- 5.171 seconds ---\n",
      "p = 7901 q = 7883 --- 5.2182 seconds ---\n",
      "p = 7937 q = 7949 --- 5.2881 seconds ---\n",
      "p = 8011 q = 8017 --- 3.4815 seconds ---\n",
      "p = 8081 q = 8087 --- 5.5457 seconds ---\n",
      "p = 8123 q = 8117 --- 5.5328 seconds ---\n",
      "p = 8191 q = 8179 --- 3.0669 seconds ---\n",
      "p = 8233 q = 8237 --- 3.4166 seconds ---\n",
      "p = 8291 q = 8287 --- 2.9992 seconds ---\n",
      "p = 8353 q = 8329 --- 7.0471 seconds ---\n",
      "p = 8419 q = 8389 --- 1.796 seconds ---\n",
      "p = 8461 q = 8447 --- 3.848 seconds ---\n",
      "p = 8527 q = 8537 --- 7.3203 seconds ---\n",
      "p = 8581 q = 8597 --- 7.0945 seconds ---\n",
      "p = 8641 q = 8629 --- 8.0469 seconds ---\n",
      "p = 8681 q = 8689 --- 5.2722 seconds ---\n",
      "p = 8731 q = 8719 --- 2.7894 seconds ---\n",
      "p = 8779 q = 8761 --- 8.7932 seconds ---\n",
      "p = 8821 q = 8831 --- 8.3634 seconds ---\n",
      "p = 8867 q = 8863 --- 4.2257 seconds ---\n",
      "p = 8933 q = 8941 --- 8.1676 seconds ---\n",
      "p = 9001 q = 8999 --- 9.1473 seconds ---\n",
      "p = 9041 q = 9043 --- 8.9529 seconds ---\n",
      "p = 9109 q = 9103 --- 8.5302 seconds ---\n",
      "p = 9157 q = 9161 --- 0.9873 seconds ---\n",
      "p = 9203 q = 9209 --- 7.154 seconds ---\n",
      "p = 9257 q = 9277 --- 8.718 seconds ---\n",
      "p = 9323 q = 9319 --- 8.8168 seconds ---\n",
      "p = 9377 q = 9371 --- 7.4632 seconds ---\n",
      "p = 9421 q = 9419 --- 9.6378 seconds ---\n",
      "p = 9461 q = 9463 --- 9.7119 seconds ---\n",
      "p = 9511 q = 9497 --- 4.9794 seconds ---\n",
      "p = 9551 q = 9587 --- 7.7513 seconds ---\n",
      "p = 9629 q = 9631 --- 10.0945 seconds ---\n",
      "p = 9689 q = 9679 --- 2.4043 seconds ---\n",
      "p = 9739 q = 9743 --- 10.14 seconds ---\n",
      "p = 9791 q = 9787 --- 8.3726 seconds ---\n",
      "p = 9833 q = 9839 --- 9.4439 seconds ---\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p = 9883 q = 9887 --- 5.0642 seconds ---\n",
      "p = 9941 q = 9931 --- 11.7723 seconds ---\n",
      "Sucess rate: 204/1\n",
      "[0.0, 0.0001, 0.0001, 0.0003, 0.0004, 0.002, 0.0014, 0.0014, 0.0041, 0.006, 0.0036, 0.0046, 0.008, 0.0094, 0.033, 0.0632, 0.0231, 0.031, 0.0397, 0.0437, 0.0044, 0.0156, 0.0134, 0.0617, 0.0184, 0.0563, 0.023, 0.0354, 0.1056, 0.0385, 0.096, 0.0651, 0.1273, 0.1291, 0.1366, 0.1263, 0.2031, 0.1926, 0.1158, 0.1707, 0.0909, 0.204, 0.2791, 0.2203, 0.2238, 0.2472, 0.3098, 0.0928, 0.3845, 0.2068, 0.3155, 0.1581, 0.4563, 0.3377, 0.1804, 0.519, 0.3667, 0.4719, 0.5813, 0.6932, 0.3275, 0.3046, 0.536, 0.7167, 0.7343, 0.1892, 0.8748, 1.0008, 0.3681, 0.6453, 0.8349, 1.1105, 0.7153, 0.3381, 0.7408, 0.568, 0.3978, 1.1865, 1.2833, 1.1893, 0.8729, 1.2592, 0.5885, 0.666, 1.1524, 0.2501, 1.1979, 1.2562, 0.3884, 1.2955, 0.7928, 1.3546, 1.1817, 0.6251, 0.895, 1.3439, 2.3946, 1.3941, 0.9617, 2.111, 1.6716, 1.5865, 1.0624, 1.6358, 0.5568, 2.2821, 1.7256, 1.6052, 2.4228, 2.61, 1.2661, 0.9145, 2.1749, 2.0014, 2.1727, 2.3122, 2.4056, 2.4887, 2.2141, 0.575, 1.5444, 1.5692, 3.8608, 2.4163, 1.179, 0.8513, 0.6209, 0.6184, 2.0154, 3.1882, 1.8549, 1.377, 3.4297, 3.7233, 3.0797, 4.143, 3.3847, 2.9502, 3.4369, 3.1508, 1.2056, 3.8109, 1.6167, 4.5226, 4.6041, 2.4568, 3.9863, 4.0207, 3.5522, 4.1298, 3.7884, 3.8576, 2.6149, 2.6349, 4.0403, 1.8681, 4.6666, 1.4185, 5.1119, 3.1749, 3.1424, 0.6872, 3.0022, 1.52, 5.171, 5.2182, 5.2881, 3.4815, 5.5457, 5.5328, 3.0669, 3.4166, 2.9992, 7.0471, 1.796, 3.848, 7.3203, 7.0945, 8.0469, 5.2722, 2.7894, 8.7932, 8.3634, 4.2257, 8.1676, 9.1473, 8.9529, 8.5302, 0.9873, 7.154, 8.718, 8.8168, 7.4632, 9.6378, 9.7119, 4.9794, 7.7513, 10.0945, 2.4043, 10.14, 8.3726, 9.4439, 5.0642, 11.7723]\n",
      "[6, 323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 223693, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 8797147, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57380621, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]\n"
     ]
    }
   ],
   "source": [
    "if not skip_live_benchmarking:\n",
    "    time_array_p_1, prime_array_p_1 = tm.time_crack(p_1_pollard.crack_primes, 10000)\n",
    "else:\n",
    "    print(\"Skipping live benchmarking.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reflected-locking",
   "metadata": {},
   "source": [
    "Expected success rate: 204/1  \n",
    "Pre-calculated values for up to 10000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "authentic-norwegian",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_array_p_1 = [0.0, 0.0001, 0.0001, 0.0003, 0.0003, 0.002, 0.0019, 0.0016, 0.0046, 0.0072, 0.005, 0.0053, 0.0144, 0.0109, 0.0171, 0.0541, 0.0183, 0.0255, 0.037, 0.0454, 0.0045, 0.0133, 0.0113, 0.0588, 0.0243, 0.0584, 0.021, 0.034, 0.0951, 0.0446, 0.0951, 0.0576, 0.1095, 0.1182, 0.1576, 0.134, 0.1823, 0.1921, 0.1415, 0.1626, 0.0801, 0.2095, 0.281, 0.2093, 0.2318, 0.3549, 0.3266, 0.087, 0.4357, 0.2272, 0.3207, 0.1417, 0.467, 0.3688, 0.1994, 0.4994, 0.3407, 0.4379, 0.5269, 0.6485, 0.3285, 0.2821, 0.5315, 0.7108, 0.8379, 0.1919, 0.8199, 0.9006, 0.3154, 0.6876, 0.7778, 1.2373, 0.8053, 0.3737, 0.8271, 0.8183, 0.6564, 1.2104, 1.3017, 1.2963, 1.1832, 1.259, 0.7239, 0.6696, 1.1632, 0.2398, 1.2053, 1.3875, 0.4172, 1.4002, 0.8907, 1.3152, 1.3812, 0.577, 0.892, 1.4087, 2.6808, 1.4096, 0.924, 2.1559, 1.97, 1.5635, 1.2707, 1.7319, 0.7735, 2.4481, 1.7858, 1.6227, 2.6543, 2.9991, 1.3164, 0.9631, 2.2616, 1.9545, 2.2084, 2.3113, 2.6392, 2.5502, 2.4239, 0.602, 1.6834, 1.7443, 4.0155, 2.5827, 1.1642, 0.896, 0.5716, 0.5781, 2.1127, 3.8943, 1.9005, 1.4171, 3.4037, 3.8823, 3.0669, 4.4261, 3.6036, 3.1638, 3.6444, 2.9615, 1.12, 3.4972, 1.6108, 4.4809, 4.7448, 2.7512, 4.0245, 3.9428, 3.4408, 4.3342, 4.0228, 4.0749, 2.7078, 2.7202, 4.4515, 1.9519, 5.6055, 1.5651, 5.4449, 3.4822, 3.3174, 0.7313, 3.065, 1.7151, 5.3468, 5.7065, 5.5176, 3.5401, 5.4838, 5.9387, 3.1999, 4.0808, 4.1737, 7.4243, 1.8565, 4.9708, 8.4855, 6.8496, 9.9372, 5.8576, 3.0353, 8.4402, 8.5004, 4.5633, 8.3461, 9.6529, 9.353, 8.9358, 0.9723, 8.1987, 9.5935, 9.6645, 8.8883, 11.5081, 12.6517, 5.6759, 8.6167, 11.0262, 2.4345, 10.6413, 9.1108, 9.8131, 5.4559, 12.1245]\n",
    "prime_array_p_1 = [6, 323, 1763, 4757, 9797, 16637, 25591, 36863, 51983, 67591, 82919, 111547, 136891, 164009, 194477, 223693, 265189, 320347, 359999, 404471, 444853, 509771, 568507, 644773, 695531, 772637, 853751, 938957, 1022117, 1089911, 1185917, 1254391, 1382951, 1488391, 1607743, 1687397, 2005007, 2099597, 2205221, 2331713, 2461757, 2585663, 2712509, 2883203, 3041527, 3196943, 3437267, 3549431, 3767417, 3980021, 4112783, 4334723, 4498577, 4652633, 4968377, 5157437, 5336099, 5541307, 5716877, 5948717, 6199931, 6502499, 6827753, 7080917, 7241477, 7420151, 7683959, 7901657, 8173877, 8485553, 8797147, 9126437, 9443293, 9790577, 10169717, 10497479, 10889999, 11088899, 11370383, 11840417, 12110279, 12467957, 12709189, 13068221, 13432189, 13727009, 14167687, 14531263, 14884139, 15319387, 15563021, 16080091, 16434907, 16850989, 17264021, 17791523, 18113527, 18429833, 19009591, 19554083, 19998703, 20412323, 20930561, 21511043, 21790199, 22335067, 22924943, 23270927, 24068827, 24472793, 24900091, 25220483, 25847047, 26347493, 26967233, 27551857, 28153627, 28987447, 29354723, 29811479, 30305021, 30913591, 31708097, 32012963, 32558411, 33223471, 33837473, 34269307, 34680257, 35604893, 36481591, 37015031, 37601423, 38415203, 38912563, 39463499, 40018267, 40500487, 41267767, 42068171, 43007339, 43599593, 44448853, 44970427, 45846377, 46580621, 47141947, 47803387, 48566957, 49098013, 49885933, 50808383, 51839951, 52417591, 53406863, 54169519, 55562107, 56160011, 56836517, 57380621, 57972947, 58936313, 59598391, 60434851, 61575373, 62283583, 63091213, 64224187, 65351047, 65934391, 66994189, 67815221, 68707517, 69572137, 70626991, 71470067, 72794999, 73770857, 74563189, 75429209, 76125589, 76912819, 77898251, 78588221, 79869953, 80999999, 81757763, 82919227, 83887277, 84750427, 85877189, 86881037, 87871867, 88736399, 89529443, 90325967, 91565437, 92736899, 93779831, 94887077, 95824517, 96746887, 97713221, 98724071]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "altered-thursday",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, p_1 = plt.subplots()\n",
    "\n",
    "p_1.plot(prime_array_p_1, time_array_p_1, 'o')\n",
    "p_1.set(xlabel = \"n (module de chiffrement)\",\n",
    "        ylabel = \"time (s)\",\n",
    "        title = \"Pollard's p-1 Algorithm\")\n",
    "p_1.grid()\n",
    "\n",
    "plt.xscale(\"log\")\n",
    "# fig.savefig(\"p_one_big.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compact-valve",
   "metadata": {},
   "source": [
    "Pre calulcated values for big numbers not done in the notebook (because it's too slow)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "saved-hacker",
   "metadata": {},
   "outputs": [],
   "source": [
    "bits_p_1 = [6, 8, 10, 12, 14, 16, 18, 20, 22, 26, 28, 30, 32, 34, 36, 42, 48, 56, 62] \n",
    "time_p_1 =  [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.02, 0.0815, 0.052, 0.0011, 0.0013, 0.0409, 0.4159, 0.6083, 1.2154, 1.0691, 0.1458]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "applicable-preserve",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Z1A+gAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdCklEQVR4nO3de5RcZZnv8e/PTpg0BGhInB7SCQY0BDOAxPQBRR07iiY4CBxhuAniHDFrjrLUNZpZBBUcxAuT8XoG8UQOooBkAsaAEIyOpA9HkVuMQwKZhgzCQEeMIA02NNAJz/lj74ZKUd1dldSu2/591uqV2u9+a9fzVHfqqf2++6KIwMzM8utV9Q7AzMzqy4XAzCznXAjMzHLOhcDMLOdcCMzMcs6FwMws51wIrC4kPSTp6PTx5yRdVcVtXyHpomptrx4khaTXZbTtmyWdNcb6pn//rDIuBLZL0g/0IUmDkn6ffohMrndcIyT1SOqtweucLOk2Sc+W+3qSDpD0oqRLMw5vBxFxTER8L43hg5J+UcvXt8bjQmDV8N6ImAy8EegGPlOrF5bUVqvXGscfga8DX67gOR8AngROkfRnWQRVSAn/n7dX8B+FVU1E9AM3A4cASDpO0r2SBiT1Snp9OduRdK2kxyQ9JelWSX9ZsO4KSZdKWi3pGWC+pLmSfi3pT5L+FZg0ynYl6WuStkp6WtIGSYeM0rdX0pck3Zn2vV7SvmPk/m8RsQLYUmaOIikEnwGGgfeO0XeKpB+ncdwl6aLCb/GSjkrbn0r/Paoojy9I+iXwLHBg2nZ2+vv4NvDmdI9uoOBl95F0U/qe3iHptQXbDEkfkfRAuv7zkl6b7hE9LWmFpN3KeR+sMbgQWNVImgG8B1gv6SDgGuATwKuB1cCPy/yAuBmYBfw58Gvg6qL1pwNfAPYE7gRWAVcC+wLXAieOdIyI3ojoSRffDfwVcBCwN3Ay8MQYcXwA+B/AfsA24JtlxF6utwLTgeXACmDUMXvgEuAZ4C/Sfi/1TYvTTWlsU4CvAjdJmlLw/DOBRSTv18MjjRGxCfg74FcRMTkiOgqecyrwj8A+wGaS97vQAmAe8CbgH4BlwBnADJIvAqeNk781EBcCq4ZV6bfJXwD/F/gicApwU0T8LCKGgX8G2oGjRt1KKiIuj4g/RcTzwOeAN0jau6DL9RHxy4h4ETgcmAh8PSKGI+I64K5RNj1M8mF4MKCI2BQRvxsjlCsjYmNEPAN8Fji5ikNRZwE3R8STwA+AhZL+vLhT+nonAhdExLMRcR/wvYIufw08EBFXRsS2iLgG+A923MO4IiLuTdcPlxnfjyLizojYRlKIDy9a/08R8XRE3AtsBH4aEQ9GxFMkhXxuma9jDcCFwKrhhIjoiIjXRMRHImIImMaO3z5fBB4BusbakKQ2SV+W9J+SngYeSldNLej2SMHjaUB/7Hj1xIcpISJuAf6F5Bv2VknLJO01RjiFr/MwScGZKunb6VDKoKTzxsqnFEntwN+Q7ulExK+A/yLZ0yn2amBCUSzF+Rfn+zA7vs+PULnHCh4/CxQfAPD7gsdDJZYb5oABG58LgWVlC/CakYV0THwG0D/O804HjgeOJhm+mTmyiYI+hR/6vwO60u2P2H+0jUfENyNiHjCHZIho8RixzCja5jDweET8XTqUMjkivjhOPqX8d2Av4FvpXMhjJB/cpYaH/kAyLDV9lLh2eJ8LYi18n8e6xLAvP2wuBJaZFcBfS3qnpInAJ4HngdvGed6eab8ngN1JhpnG8iuSD8qPSZoo6X3AEaU6Svpvko5M43kGeA54cYxtnyFpjqTdgQuB6yJi+yjbbpM0ieTb+6skTUpfp5SzgMuBQ0mGXA4H3kIyBHZoYcf09VYCn5O0u6SDSeYuRqwGDpJ0uqQJkk4hKXI3jpFXod8D0z25m28uBJaJiOgjmTz8X8DjJGPW742IF8Z56vdJhjb6gfuA28d5nReA9wEfJDmE8xSSD85S9gK+Q3LI5sMkxWbpGJu/EriCZJhkEvCxMfqeSTIkcinwtvTxd4o7SeoC3kkyp/FYwc864CeU3is4h2Tv6LE0pmtIiiUR8QRwLEmhfYJk4vbYiHh8jFgL3QLcCzwmqdznWIuRb0xj9kpKTgq7KiIuq3csxSRdDPxFRIx1pJFZ2bxHYNbgJB0s6bD0PIgjgA8BP6p3XNY6JtQ7ADMb154kw0HTSMb0vwJcX9eIrKV4aMjMLOc8NGRmlnNNNzQ0derUmDlzZr3D2MEzzzzDHnvsUe8wMtGquTmv5tOqudUqr3Xr1j0eEa8uta7pCsHMmTO5++676x3GDnp7e+np6al3GJlo1dycV/Np1dxqlZekkmfcg4eGzMxyz4XAzCznXAjMzHLOhcDMLOdcCMzMcq7pjhoys+a3an0/S9f0sWVgiGkd7SxeMJsT5o55qwrLkAuBmdXUqvX9LFm5gaHh5Ire/QNDLFm5AcDFoE48NGRmNbV0Td9LRWDE0PB2lq7pq1NEllkhkHS5pK2SNo6y/v2S7pG0QdJtkt6QVSxm1ji2DAxV1G7Zy3KP4Apg4Rjrfwu8PSIOBT4PLMswFjNrENM62itqt+xlVggi4laSO0aNtv62iHgyXbydHe/JamYtavGC2bRPbNuhrX1iG4sXzK5TRJbpZaglzQRujIhDxun3KeDgiDh7lPWLgEUAnZ2d85YvX17tUHfJ4OAgkydPrncYmWjV3JxXfd22ZZgf3j/ME88FUyaJEw+ayFHTRrvFc6JZcqtUrfKaP3/+uojoLrkyIjL7AWYCG8fpMx/YBEwpZ5vz5s2LRrN27dp6h5CZVs3NeTWfVs2tVnkBd8con6t1PXxU0mHAZcAxkdyE28zMaqxuh49K2h9YCZwZEffXKw4zs7zLbI9A0jVADzBV0qPABcBEgIj4NnA+MAX4liSAbTHa+JWZmWUms0IQEaeNs/5soOTksJmZ1Y7PLDYzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5yr6/0IzMwa3ar1/Sxd08eWgSGmdbSzeMFsTpjbVe+wqsqFwMxsFKvW97Nk5QaGhrcD0D8wxJKVGwBaqhh4aMjMbBRL1/S9VARGDA1vZ+mavjpFlA0XAjOzUWwZGKqovVm5EJiZjWJaR3tF7c3KhcDMbBSLF8ymfWLbDm3tE9tYvGB2nSLKhieLzcxGMTIh7KOGzMxy7IS5XS33wV/MQ0NmZjnnQmBmlnMuBGZmOZdZIZB0uaStkjaOsl6Svilps6R7JL0xq1jMzGx0We4RXAEsHGP9McCs9GcRcGmGsZiZ2SgyKwQRcSvwxzG6HA98PxK3Ax2S9ssqHjMzK62eh492AY8ULD+atv2uuKOkRSR7DXR2dtLb21uL+Mo2ODjYcDFVS6vm5ryaT6vm1gh5NcV5BBGxDFgG0N3dHT09PfUNqEhvby+NFlO1tGpuzqv5tGpujZBXPY8a6gdmFCxPT9vMzKyG6lkIbgA+kB499CbgqYh4xbCQmZllK7OhIUnXAD3AVEmPAhcAEwEi4tvAauA9wGbgWeBvs4rFzMxGl1khiIjTxlkfwEezen0zMyuPzyw2M8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7Ocy7QQSFooqU/SZknnlli/v6S1ktZLukfSe7KMx8zMXimzQiCpDbgEOAaYA5wmaU5Rt88AKyJiLnAq8K2s4jEzs9Ky3CM4AtgcEQ9GxAvAcuD4oj4B7JU+3hvYkmE8ZmZWgiIimw1LJwELI+LsdPlM4MiIOKegz37AT4F9gD2AoyNiXYltLQIWAXR2ds5bvnx5JjHvrMHBQSZPnlzvMDLRqrk5r+bTqrnVKq/58+evi4juUusmZP7qYzsNuCIiviLpzcCVkg6JiBcLO0XEMmAZQHd3d/T09NQ+0jH09vbSaDFVS6vm5ryaT6vm1gh5ZTk01A/MKFienrYV+hCwAiAifgVMAqZmGJOZmRXJshDcBcySdICk3Ugmg28o6vNfwDsBJL2epBD8IcOYzMysSGaFICK2AecAa4BNJEcH3SvpQknHpd0+CXxY0r8D1wAfjKwmLczMrKRM5wgiYjWwuqjt/ILH9wFvyTIGMzMbm88sNjPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXAjOznHMhMDPLORcCM7OcG/eEMknTSS4P8TZgGjAEbARuAm4uvkCcmZk1lzELgaTvAl3AjcDFwFaS6wEdBCwEPi3p3Ii4NetAzcwsG+PtEXwlIjaWaN8IrEwvJrd/9cMyM7NaGXOOoFQRkLSPpMPS9S9ExOasgjMzs+yVNVksqVfSXpL2BX4NfEfS17INzczMaqHco4b2joingfcB34+II0nvI2BmZs2t3EIwIb2/8MkkE8dmZtYiyi0EF5LcYGZzRNwl6UDggezCMjOzWinrxjQRcS1wbcHyg8CJWQVlZma1M+YegaTPpBPEo61/h6Rjqx+WmZnVynh7BBuAH0t6juRooT+QnFA2Czgc+Dfgi1kGaGZm2RqzEETE9cD1kmaR3Ft4P+Bp4CpgUUQMZR+imZllqdw5ggfw5LCZWUvy1UfNzHKurD0CM2sdq9b3s3RNH1sGhpjW0c7iBbM5YW5XvcOyOsp0j0DSQkl9kjZLOneUPidLuk/SvZJ+kGU8Znm3an0/S1ZuoH9giAD6B4ZYsnIDq9b31zs0q6NyrzV0kKSfS9qYLh8m6TPjPKcNuAQ4BpgDnCZpTlGfWcAS4C0R8ZfAJypPwczKtXRNH0PD23doGxreztI1fXWKyBpBuXsE3yH5wB4GiIh7SG5WM5YjSM5EfjAiXgCWA8cX9fkwcElEPJlud2u5gZtZ5bYMlD7Qb7R2y4dy5wh2j4g7JRW2bRvnOV3AIwXLjwJHFvU5CEDSL4E24HMR8ZPiDUlaBCwC6OzspLe3t8ywa2NwcLDhYqqWVs0tr3ntO0k88VyUbG/09yOvv7NaKLcQPC7ptUAASDoJ+F2VXn8W0ANMB26VdGhEDBR2iohlwDKA7u7u6OnpqcJLV09vby+NFlO1tGpuec3rs3sncwSFw0PtE9v47PGH0tPgE8Z5/Z3VQrmF4KMkH8QHS+oHfgucMc5z+oEZBcvT07ZCjwJ3RMQw8FtJ95MUhrvKjMvMKjBydJCPGrJC5Z5Q9iBwtKQ9gFdFxJ/KeNpdwCxJB5AUgFOB04v6rAJOA74raSrJUNGDZcZuZjvhhLld/uC3HZRVCCR1AB8AZpLcmwCAiPjYaM+JiG2SziG5fHUbcHlE3CvpQuDuiLghXfduSfcB24HFEfHEzqdjZmaVKndoaDVwO8lF6F4sd+MRsTp9bmHb+QWPA/j79MfMzOqg3EIwKSL8YW1m1oLKPY/gSkkflrSfpH1HfjKNzMzMaqLcPYIXgKXAp0kPIU3/PTCLoMzMrHbKLQSfBF4XEY9nGYyZmdVeuUNDm4FnswzEzMzqo9w9gmeA30haCzw/0jjW4aNmZtYcyi0Eq9IfMzNrMeWeWfy9rAMxM7P6GLMQSFoRESdL2sDLRwu9JCIOyywyMzOrifH2CD6e/nts1oGYmVl9jHnUUESMXGr6IxHxcOEP8JHswzMzs6yVe/jou0q0HVPNQMzMrD7GmyP4nyTf/A+UdE/Bqj2BX2YZmJmZ1cZ4cwQ/AG4GvgScW9D+p4j4Y2ZRmZlZzYxZCCLiKeApkpvHmJlZCyp3jsDMzFqUC4GZWc65EJiZ5ZwLgZlZzrkQmJnlnAuBmVnOlXsZajOrglXr+1m6po8tA0NM62hn8YLZnDC3q95hWc65EJjVyKr1/SxZuYGh4e0A9A8MsWTlBgAXA6srDw2Z1cjSNX0vFYERQ8PbWbqmr04RmSUyLQSSFkrqk7RZ0rlj9DtRUkjqzjIes3raMjBUUbtZrWRWCCS1AZeQXKV0DnCapDkl+u1Jct+DO7KKxawRTOtor6jdrFay3CM4AtgcEQ9GxAvAcuD4Ev0+D1wMPJdhLGZ1t3jBbNontu3Q1j6xjcULZtcpIrOEIl5xB8rqbFg6CVgYEWeny2cCR0bEOQV93gh8OiJOlNQLfCoi7i6xrUXAIoDOzs55y5cvzyTmnTU4OMjkyZPrHUYmWjW3euV125Zhfnj/ME88F0yZJE48aCJHTZtYte236u8LWje3WuU1f/78dRFRcvi9bkcNSXoV8FXgg+P1jYhlwDKA7u7u6OnpyTS2SvX29tJoMVVLq+ZWr7x6gPMy3H6r/r6gdXNrhLyyHBrqB2YULE9P20bsCRwC9Ep6CHgTcIMnjM3MaivLQnAXMEvSAZJ2A04FbhhZGRFPRcTUiJgZETOB24HjSg0NmZlZdjIrBBGxDTgHWANsAlZExL2SLpR0XFava2Zmlcl0jiAiVgOri9rOH6VvT5axmJlZaT6z2Mws51wIzMxyzoXAzCznXAjMzHLOhcDMLOdcCMzMcs6FwMws51wIzMxyzoXAzCznXAjMzHLOhcDMLOdcCMzMcs6FwMws51wIzMxyzoXAzCznXAjMzHLOhcDMLOdcCMzMcs6FwMws51wIzMxyzoXAzCznXAjMzHLOhcDMLOcyLQSSFkrqk7RZ0rkl1v+9pPsk3SPp55Jek2U8Zmb2SpkVAkltwCXAMcAc4DRJc4q6rQe6I+Iw4Drgn7KKx8zMSstyj+AIYHNEPBgRLwDLgeMLO0TE2oh4Nl28HZieYTxmZlaCIiKbDUsnAQsj4ux0+UzgyIg4Z5T+/wI8FhEXlVi3CFgE0NnZOW/58uWZxLyzBgcHmTx5cr3DyESr5ua8mk+r5larvObPn78uIrpLrZuQ+auXQdIZQDfw9lLrI2IZsAygu7s7enp6ahdcGXp7e2m0mKqlVXNzXs2nVXNrhLyyLAT9wIyC5elp2w4kHQ18Gnh7RDyfYTxmZlZClnMEdwGzJB0gaTfgVOCGwg6S5gL/GzguIrZmGIuZmY0is0IQEduAc4A1wCZgRUTcK+lCScel3ZYCk4FrJf1G0g2jbM7MzDKS6RxBRKwGVhe1nV/w+OgsX9/MzMbXEJPFZmY2ulXr+1m6po8tA0NM62hn8YLZnDC3q2rbdyEwM2tgq9b3s2TlBoaGtwPQPzDEkpUbAKpWDHytITOzBrZ0Td9LRWDE0PB2lq7pq9pruBCYmTWwLQNDFbXvDBcCM7MGNq2jvaL2neFCYGbWwBYvmE37xLYd2tontrF4weyqvYYni83MGtjIhLCPGjIzy7ET5nZV9YO/mIeGzMxyzoXAzCznXAjMzHLOcwTWkLI+pd7MXuZCYA2nFqfUm9nLPDRkDacWp9Sb2ctcCKzh1OKUejN7mYeGrOFM62inv8SH/min1Hs+wWzXeI/AGk4lp9SPzCf0DwwRvDyfsGr9K26PbWaj8B6BNZxKTqkfaz6hlnsF3iuxZuZCYA2p3FPqG2E+wUc5WbPz0JA1tVpconc8PsrJmp0LgTW1WlyidzyNsFditis8NGS7pN5j47W4RO94Kj3KyazRuBDYTmuUsfGsL9E7nsULZu/wPkDt90rMdoWHhmyneWw8ccLcLr70vkPp6mhHQFdHO19636GeKLamkekegaSFwDeANuCyiPhy0fo/A74PzAOeAE6JiIeqHUclwxc707d/YIiu22+p+nYboe9YuTXj2HhWv7N675WY7YrMCoGkNuAS4F3Ao8Bdkm6IiPsKun0IeDIiXifpVOBi4JRqxlHJ8IX7Vta32cbGs3q/zJpdlkNDRwCbI+LBiHgBWA4cX9TneOB76ePrgHdKUjWDqGT4wn0r69sIR+xUIqv3y6zZZTk01AU8UrD8KHDkaH0iYpukp4ApwOOFnSQtAhYBdHZ20tvbW3YQpb6xjrQXb8d9K+vbAZz5+jZ+eP+LPPFcMGWSOPGgNjqeeoDe3gdKbqOesnq/Gsng4GBDx7crWjW3RsirKY4aiohlwDKA7u7u6OnpKfu5XbffUvI/dVdHO8Xbcd/K+/YA572iZ2PK6j1oJL29vQ0d365o1dwaIa8sh4b6gRkFy9PTtpJ9JE0A9iaZNK6aSoYv3Lfyvs3E74FZaVnuEdwFzJJ0AMkH/qnA6UV9bgDOAn4FnATcEhFRzSAqOeFoZ/v2DwzRlcF2G6HveLk1k6x+Z2ZNLyIy+wHeA9wP/Cfw6bTtQuC49PEk4FpgM3AncOB425w3b140mrVr19Y7hMy0am7Oq/m0am61ygu4O0b5XM10jiAiVgOri9rOL3j8HPA3WcZgZmZj85nFZmY550JgZpZzLgRmZjnnQmBmlnOK6h6tmTlJfwAernccRaZSdDZ0C2nV3JxX82nV3GqV12si4tWlVjRdIWhEku6OiO56x5GFVs3NeTWfVs2tEfLy0JCZWc65EJiZ5ZwLQXUsq3cAGWrV3JxX82nV3Oqel+cIzMxyznsEZmY550JgZpZzLgQVknS5pK2SNha07SvpZ5IeSP/dp54x7gxJMyStlXSfpHslfTxtb+rcJE2SdKekf0/z+se0/QBJd0jaLOlfJe1W71h3hqQ2Sesl3Zgut0peD0naIOk3ku5O25r6bxFAUoek6yT9h6RNkt7cCHm5EFTuCmBhUdu5wM8jYhbw83S52WwDPhkRc4A3AR+VNIfmz+154B0R8QbgcGChpDcBFwNfi4jXAU8CH6pfiLvk48CmguVWyQtgfkQcXnCMfbP/LQJ8A/hJRBwMvIHkd1f/vEa7PrV/xrzPwkxgY8FyH7Bf+ng/oK/eMVYhx+uBd7VSbsDuwK9J7p39ODAhbX8zsKbe8e1EPtNJPjjeAdwIqBXySmN/CJha1NbUf4skd2D8LelBOo2Ul/cIqqMzIn6XPn4M6KxnMLtK0kxgLnAHLZBbOnzyG2Ar8DOSGyUNRMS2tMujQDPeeuzrwD8AL6bLU2iNvAAC+KmkdZIWpW3N/rd4APAH4LvpcN5lkvagAfJyIaiySMp60x6TK2ky8EPgExHxdOG6Zs0tIrZHxOEk36CPAA6ub0S7TtKxwNaIWFfvWDLy1oh4I3AMyTDlXxWubNK/xQnAG4FLI2Iu8AxFw0D1ysuFoDp+L2k/gPTfrXWOZ6dImkhSBK6OiJVpc0vkBhARA8BakiGTDkkjd+ibTnJf7WbyFuA4SQ8By0mGh75B8+cFQET0p/9uBX5EUsCb/W/xUeDRiLgjXb6OpDDUPS8Xguq4ATgrfXwWyfh6U5Ek4P8AmyLiqwWrmjo3Sa+W1JE+bieZ99hEUhBOSrs1XV4RsSQipkfETOBU4JaIeD9NnheApD0k7TnyGHg3sJEm/1uMiMeARyTNTpveCdxHA+TlM4srJOkaoIfk0rG/By4AVgErgP1JLpF9ckT8sU4h7hRJbwX+H7CBl8eczyOZJ2ja3CQdBnwPaCP54rMiIi6UdCDJN+l9gfXAGRHxfP0i3XmSeoBPRcSxrZBXmsOP0sUJwA8i4guSptDEf4sAkg4HLgN2Ax4E/pb075I65uVCYGaWcx4aMjPLORcCM7OccyEwM8s5FwIzs5xzITAzyzkXArMySZpZeNXZgvbL0gv0Iem82kdmtmt8+KhZmdJrMN0YEYeM0WcwIibXLiqzXec9ArPKTJB0dXot+esk7S6pV1K3pC8D7ek19K9Oz5C9Kb0XwkZJp9Q7eLNSXAjMKjMb+FZEvB54GvjIyIqIOBcYiuQa+u8nuW/Floh4Q7oX8ZO6RGw2DhcCs8o8EhG/TB9fBbx1jL4bgHdJuljS2yLiqezDM6ucC4FZZYon1UadZIuI+0muLrkBuEjS+VkGZrazXAjMKrO/pDenj08HflG0fji9nDeSpgHPRsRVwFKSomDWcFwIzCrTR3KjlE3APsClReuXAfdIuho4FLgzvTvaBcBFtQzUrFw+fNTMLOe8R2BmlnMuBGZmOedCYGaWcy4EZmY550JgZpZzLgRmZjnnQmBmlnP/H7VAc8EITCMGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, p_1 = plt.subplots()\n",
    "\n",
    "p_1.plot(bits_p_1, time_p_1, 'o')\n",
    "p_1.set(xlabel = \"bits\",\n",
    "        ylabel = \"time (s)\",\n",
    "        title = \"Pollard's p-1 Algorithm\")\n",
    "p_1.grid()\n",
    "\n",
    "# fig.savefig(\"p_one_small.png\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}