A notebook in SAGE Math showing prime number calculation via Miller Rabin, based upon example in Stallings' "Cryptography and Network Security"

Miller-Rabin.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MILLER_RABIN_TEST(n):\n",
    "    R = IntegerModRing(n);\n",
    "    q = n-1\n",
    "    k = 0\n",
    "    while (1 == (q % 2)):\n",
    "        k += 1\n",
    "        q = q.quo_rem(2)[0]\n",
    "        \n",
    "    a = randint(1,n-1)\n",
    "    # integers congruent to a\n",
    "    a = R(a)\n",
    "    # sage provides simple syntac for modular exponentiation:\n",
    "    if (1 == a^q):\n",
    "        return False\n",
    "    \n",
    "    e = q\n",
    "    for j in range(k):\n",
    "        if (n-1) == (a^e):\n",
    "            return False\n",
    "        e = 2*e\n",
    "        \n",
    "    return True\n",
    "\n",
    "# prime tests rounds times (default 10) \n",
    "def prime(n, rounds = 10):\n",
    "    for i in range(rounds):\n",
    "        if MILLER_RABIN_TEST(n):\n",
    "            return false\n",
    "    return true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "primes = []\n",
    "for i in range(500000, 1000000):\n",
    "    if prime(i):\n",
    "        primes.append(i)\n",
    "print(primes)"
   ]
  }
 ],
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