TLS statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MultipleLocator, FormatStrFormatter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "We are testing the randomness of the stack pointer in an ELF file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "addresses = []\n",
    "addresses_bytes = []\n",
    "\n",
    "with open('rsp_rnd.log', 'r') as f:\n",
    "    for address_value in f:\n",
    "        addresses.append(int(address_value, 16))\n",
    "        value = address_value.replace('0x', '').replace('\\n', '')\n",
    "        addresses_bytes.append([int(_, 16) for _ in (value[-2:], value[-4:-2], value[-6:-4], value[:-6])])\n",
    "\n",
    "s_addresses = stats.describe(addresses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DescribeResult(nobs=15184852, minmax=(4286555040, 4294953968), mean=4290755616.867121, variance=5866256680718.409, skewness=-7.78734814298478e-05, kurtosis=-1.2003548301655678)\n",
      "DescribeResult(nobs=15184852, minmax=(0, 240), mean=119.99774301389306, variance=5439.430016313532, skewness=-0.00014000867759740704, kurtosis=-1.2090314769565125)\n",
      "# addresses: 15184852\n",
      "max: 0xffffcbf0 min: 0xff7fa3a0\n",
      "delta: 802850\n",
      "delta: 802\n"
     ]
    }
   ],
   "source": [
    "first_byte_statistics  = [_[0] for _ in addresses_bytes]\n",
    "second_byte_statistics = [_[1] for _ in addresses_bytes]\n",
    "third_byte_statistics  = [_[2] for _ in addresses_bytes]\n",
    "fourth_byte_statistics = [_[3] for _ in addresses_bytes]\n",
    "\n",
    "print(s_addresses)\n",
    "print(stats.describe(first_byte_statistics))\n",
    "n_total = len(addresses)\n",
    "min, max = s_addresses.minmax\n",
    "print(\"# addresses: %d\" % n_total)\n",
    "print(\"max: 0x%08x min: 0x%08x\" % (max, min))\n",
    "print(\"delta: %x\" % (max - min))\n",
    "print(\"delta: %x\" % ((max - min) >> 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# example from here <http://matplotlib.org/examples/pylab_examples/major_minor_demo1.html>\n",
    "def plot_statistics(data):\n",
    "    plt.figure(figsize=(20,6))\n",
    "    s = stats.describe(data)\n",
    "\n",
    "    min = s.minmax[0]\n",
    "    max = s.minmax[1]\n",
    "    delta = max - min\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    #if delta != 0:\n",
    "    plt.xticks(np.arange(0, 0xff, 0x10), rotation='vertical')\n",
    "    plt.xlim(0, 0xff + 1)\n",
    "    plt.hist(data, bins=0xff, density=True)\n",
    "    plt.plot()\n",
    "\n",
    "    #if delta != 0:\n",
    "    # print out hex values for the ticks\n",
    "    majorFormatter = FormatStrFormatter('%02x')\n",
    "    ax.xaxis.set_major_formatter(majorFormatter)\n",
    "\n",
    "    plt.show()\n",
    "    print('#: %d min: 0x%08x max: 0x%08x delta: 0x%08x' % (len(addresses), min, max, delta))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/matplotlib/figure.py:98: MatplotlibDeprecationWarning: \n",
      "Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
      "  \"Adding an axes using the same arguments as a previous axes \"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bins=7415\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,6))\n",
    "counts, bins, patches = plt.hist(addresses, bins=int(n_total/0x800), density=True)\n",
    "plt.xlabel('addresses')\n",
    "plt.axes().set_xlim(left=max - 0x5000, right=max)\n",
    "plt.axvline(max - 0x2000, color='k')\n",
    "plt.axvline(max - 0x1000, color='r')\n",
    "#plt.xaxis.set_major_formatter(FormatStrFormatter('%08x'))\n",
    "plt.axes().yaxis.grid()\n",
    "print('bins={}'.format(len(bins)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's possible to notice a little step at the right of the distribution, if we expand the histogram doing a \"zoom\" we can observe something interesting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bins=257\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# http://synesthesiam.com/posts/matplotlib-and-numpy-double-trouble.html\n",
    "plt.figure(figsize=(20,6))\n",
    "limit = 0x8000\n",
    "bins_size = 0x80\n",
    "counts, bins, patches = plt.hist(addresses, range=(max - limit, max), bins=int(limit/bins_size), density=True)\n",
    "plt.axvline(max - 0x3000, color='k')\n",
    "plt.axvline(max - 0x2000, color='k')\n",
    "plt.axvline(max - 0x1000, color='k')\n",
    "plt.xlabel('addresses')\n",
    "plt.xticks(np.arange(max - limit, max + 0x1000, 0x1000), rotation='vertical')\n",
    "plt.axes().yaxis.grid()\n",
    "plt.axes().xaxis.set_major_formatter(FormatStrFormatter('%08x'))\n",
    "print('bins={}'.format(len(bins)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "it seems that there are three regions on the right $ \\hbox{stack_top} - 0x1000 < x < \\hbox{stack_top}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1440x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#: 15184852 min: 0x00000000 max: 0x000000f0 delta: 0x000000f0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1440x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#: 15184852 min: 0x00000000 max: 0x000000ff delta: 0x000000ff\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1440x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#: 15184852 min: 0x0000007f max: 0x000000ff delta: 0x00000080\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1440x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#: 15184852 min: 0x000000ff max: 0x000000ff delta: 0x00000000\n"
     ]
    }
   ],
   "source": [
    "plot_statistics(first_byte_statistics)\n",
    "plot_statistics(second_byte_statistics)\n",
    "plot_statistics(third_byte_statistics)\n",
    "plot_statistics(fourth_byte_statistics)"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}