timing_attack.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "from sympy import randprime, isprime, Mod\n",
    "\n",
    "def egcd(a, b):\n",
    "    if a == 0:\n",
    "        return (b, 0, 1)\n",
    "    else:\n",
    "        g, y, x = egcd(b % a, a)\n",
    "        return (g, x - (b // a) * y, y)\n",
    "\n",
    "def modinv(a, m):\n",
    "    g, x, y = egcd(a, m)\n",
    "    if g != 1:\n",
    "        raise Exception('modular inverse does not exist')\n",
    "    else:\n",
    "        return x % m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "def GenModulus(w):\n",
    "    n = len(w) // 2\n",
    "    p = randprime(2 ** n, 2 ** (n+1))\n",
    "    q = randprime(2 ** n, 2 ** (n+1))\n",
    "    N = p * q\n",
    "    return N, p, q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "def GenRSA(w):\n",
    "    n = len(w)\n",
    "    N, p, q = GenModulus(w)\n",
    "    m = (p-1) * (q-1)\n",
    "    e = 2 ** 16 + 1\n",
    "    d = modinv(e, m)\n",
    "    return N, e, d, p, q\n",
    "# N, e - public key\n",
    "# N, d - private key\n",
    "\n",
    "def enc(x, N, e):\n",
    "    return x ** e % N\n",
    "\n",
    "def dec(c, N, d):\n",
    "    return c ** d % N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "N, e, d, p, q = GenRSA(\"111111111111111111111\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "message = random.randint(2, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "y = enc(message, N, e)\n",
    "\n",
    "x = dec(y, N, d)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "87361 90572 87361 True\n"
     ]
    }
   ],
   "source": [
    "print(message, y, x, message == x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1709873 110100001011100110001\n"
     ]
    }
   ],
   "source": [
    "d_bin = \"{0:b}\".format(d)\n",
    "print(d, d_bin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "def fast_pow(c, d, N):\n",
    "    d_bin = \"{0:b}\".format(d)\n",
    "    d_len = len(d_bin)\n",
    "    reduced = 0\n",
    "    d_ham = 0\n",
    "    x = c\n",
    "    for j in range(1, d_len):\n",
    "        x, r = mod_reduce(x ** 2, N)\n",
    "        reduced = reduced + r\n",
    "        if d_bin[j] == \"1\":\n",
    "            x, r = mod_reduce(x * c, N)\n",
    "            reduced = reduced + r\n",
    "            d_ham = d_ham + 1\n",
    "            #print(\"A\")\n",
    "    return x, reduced, d_ham\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "87361 29 9\n"
     ]
    }
   ],
   "source": [
    "xx, r, h = fast_pow(y, d, N)\n",
    "print(xx, r, h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [],
   "source": [
    "def mod_reduce(a, b):\n",
    "    reduced = 0\n",
    "    if a >= b:\n",
    "        a = a % b\n",
    "        reduced = 1\n",
    "        #print(\"\\tB\")\n",
    "    return a, reduced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29 9\n"
     ]
    }
   ],
   "source": [
    "c = random.randint(2, N)\n",
    "m, r, h = fast_pow(c, d, N)\n",
    "print(r, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dostarczamy kryptogramy dwóch \"rodzajów\":\n",
    "1. y: $y^3 < N$\n",
    "2. z: $z^2 < N < z^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "89.1899742061465"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N ** (1/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "842.3140744401699"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N ** (1/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27 9\n"
     ]
    }
   ],
   "source": [
    "y = random.randint(2, math.floor(N ** (1/3)))\n",
    "m, r, h = fast_pow(y, d, N)\n",
    "print(r, h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26 9\n"
     ]
    }
   ],
   "source": [
    "z = random.randint(math.floor(N ** (1/3)), math.floor(N ** (1/2)))\n",
    "m, r, h = fast_pow(z, d, N)\n",
    "print(r, h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dec_blinded(c, d, N):\n",
    "    r = random.randint(2, N)\n",
    "    re = enc(r, N, e)\n",
    "    dec_1, r, h = fast_pow((c * re) % N, d, N)\n",
    "    print(r)\n",
    "    r_inv = modinv(r, N)\n",
    "    return (dec_1 * r_inv) % N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29\n"
     ]
    }
   ],
   "source": [
    "m = dec_blinded(z, d, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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