src/raw_data_processing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\n",
    "# Universite Jean Monnet\n",
    "# Laboratoire Hubert Curien\n",
    "# Saint-Etienne\n",
    "\n",
    "# Nathalie Bochard\n",
    "\n",
    "# PLL-based TRNG - sampled period reconstruction\n",
    "#\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "from pathlib import Path\n",
    "\n",
    "## #########################################\n",
    "## functions definition\n",
    "## #########################################\n",
    "\n",
    "\n",
    "def read_dff(filename, KM, KD):\n",
    "    ###############################\n",
    "    \"\"\"Read dff bits from the raw file. Return a matrix of shape (n_cycles, KD)\"\"\"\n",
    "    bytes_data = np.fromfile(filename, dtype=\"uint8\")  # read bytes\n",
    "    bits_data = np.unpackbits(bytes_data, axis=None, count=None, bitorder=\"little\")  # unpack to bits\n",
    "    bits_data = bits_data.reshape((-1, 32))[:, ::-1].ravel()  # reverse bits order in blocks of 32\n",
    "    bits_data = np.resize(bits_data, (len(bits_data) // KD, KD))  # reshape to cycles\n",
    "    return bits_data\n",
    "\n",
    "\n",
    "def get_rng_from_dff(filename, data, KM, KD):\n",
    "    #############################################\n",
    "    \"\"\"Compute rng data from dff and record it to a file that is NIST compatible\"\"\"\n",
    "    # counter of ones\n",
    "    nb_ones = np.sum(data, 1)\n",
    "    # sum inside Tq period\n",
    "    # lsb\n",
    "    rng = nb_ones % 2\n",
    "\n",
    "    fileoutname = filename[:-4] + \"_rng_nist_1bit.bin\"\n",
    "    rng = np.array(rng, dtype=\"uint8\")\n",
    "\n",
    "    # 1.000.000 bits are needed to pass NIST tests\n",
    "    while len(rng) < 1000000:\n",
    "        rng = np.concatenate([rng, rng])[:1000000]\n",
    "\n",
    "    rng.tofile(fileoutname)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data\n",
    "\n",
    "💡 To reproduce Fig 10 and Fig 11, use files `data/Regular/S6v11_2/B_1/acq_20230405133036_km464_kd475_dff.bin` and `data/Regular/S6v11_2/C_1/acq_20230405135452_km476_kd495_dff.bin`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "## #########################################\n",
    "## Setting variables\n",
    "## #########################################\n",
    "\n",
    "filename = \"../data/Regular/S6v11_2/C_1/acq_20230405135452_km476_kd495_dff.bin\"\n",
    "\n",
    "\n",
    "# Threshold for jittered points taken into account\n",
    "thr = 0.05\n",
    "# Step to display Tq\n",
    "# 1 to display every periods\n",
    "# 10 to display all 10 periods\n",
    "step = 20\n",
    "\n",
    "# Max number of computed Tq period\n",
    "# Nval_max = 2**19\n",
    "Nval_max = 8000\n",
    "\n",
    "# If Km and Kd are manually set\n",
    "KM = 476\n",
    "KD = 495"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## #########################################\n",
    "## Main section\n",
    "## #########################################\n",
    "\n",
    "# Read data from binary file, returns a matrix of bits\n",
    "full_data = read_dff(filename, KM, KD)  # N_CYCLES x KM\n",
    "\n",
    "# Compute rng data from dff and record it to a file that is NIST compatible\n",
    "# (uncomment the following line if you want to get the random bits)\n",
    "#get_rng_from_dff(filename, full_data, KM, KD)\n",
    "\n",
    "# Nb of periods : uncomment one of the 2 following lines (max possible periods or a fixed nb of periods)\n",
    "#Nsum = len(bin_data)//KD\n",
    "Nsum = Nval_max\n",
    "\n",
    "img = full_data[0:Nsum]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Re-ordered Period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nb of contributors: 11\n",
      "Distances between contributors : [ 13  13  13  13  13  13  13  13  13  13 365]\n"
     ]
    }
   ],
   "source": [
    "# Reorder samples inside period T_P, compute their probability value\n",
    "# ---------------------------------------------\n",
    "j = [(i * KM) % KD for i in range(KD)]\n",
    "# Reordered index\n",
    "somme = np.sum(img, 0)\n",
    "# Sum per period\n",
    "nsum = somme / len(img)\n",
    "# Normalized sum\n",
    "z = zip(j, nsum)\n",
    "# Zip position and values\n",
    "uz = list(zip(*sorted(z)))\n",
    "# Sort and unzip\n",
    "period = uz[1]\n",
    "\n",
    "# Plot period T_P with indices and thresholds\n",
    "# ---------------------------------------------\n",
    "x = range(0, KD)\n",
    "y = period\n",
    "title = \"Km = \" + str(KM) + \", Kd = \" + str(KD)\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "plt.plot(x, y, \"+\", markersize=4)\n",
    "plt.xlabel(\"$K_D$\", fontsize=12, family=\"serif\")\n",
    "plt.ylabel(\"P(X=1)\", fontsize=12, family=\"serif\")\n",
    "plt.title(title)\n",
    "plt.axhline(y=thr, color=\"r\", linestyle=\"dashed\")\n",
    "plt.axhline(y=1 - thr, color=\"r\", linestyle=\"dashed\")\n",
    "for ind in range(len(x)):\n",
    "    if y[ind] > thr and y[ind] < (1 - thr):\n",
    "        ax.text(x[ind], y[ind], j.index(ind), size=8)\n",
    "plt.show()\n",
    "\n",
    "# Compute distances between contributors\n",
    "# --------------------------------------\n",
    "\n",
    "npuz = np.array(uz)\n",
    "# j_jit: index of points on edges, with overflow on the last index to measure last distance\n",
    "j_jit = np.where((npuz[1] < (1 - thr)) & (npuz[1] > thr))[0]\n",
    "i_jit = []\n",
    "for w in j_jit:\n",
    "    i_jit.append(j.index(w))\n",
    "i_jit.sort()\n",
    "i_jit.append(i_jit[0] + KD)\n",
    "ijit = np.array(i_jit)\n",
    "d = ijit[1 : len(ijit)] - ijit[0 : (len(ijit) - 1)]\n",
    "\n",
    "print(\"Nb of contributors: \" + str(len(d)))\n",
    "print(\"Distances between contributors : \" + str(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bitmaps of Successive Periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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"
    },
    {
     "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": [
    "# Plot bitmap of successive periods\n",
    "# ---------------------------------\n",
    "# Image of successive periods T_P\n",
    "TqBitmap = pd.DataFrame(img, index=range(len(img)), columns=j)\n",
    "TqBitmap = TqBitmap.loc[::step]\n",
    "# Image of successive reordered periods\n",
    "periodeBitmap = TqBitmap.sort_index(axis=1, ascending=True)\n",
    "im1 = plt.imshow(TqBitmap, cmap=\"binary\")\n",
    "plt.show()\n",
    "im1 = plt.imshow(periodeBitmap, cmap=\"binary\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Online Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nval: 8000\n",
      "Mean: 247.26\n",
      "Median: 247.0\n",
      "Var: 1.01\n",
      "aVar: 1.00\n",
      "v from Pval: 1.79\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Online test: variance of the counter of ones\n",
    "# ----------------------------------------\n",
    "# Sum inside period T_P\n",
    "nb_ones = np.sum(img, 1).astype(np.int_)\n",
    "Mean = np.mean(nb_ones)\n",
    "Median = np.median(nb_ones)\n",
    "Var = np.var(nb_ones)\n",
    "aVar = np.sum((nb_ones[1:Nsum] - nb_ones[: Nsum - 1]) ** 2) / (2 * (Nsum - 1))\n",
    "# Compute variance from probability values\n",
    "Pval = somme / Nsum\n",
    "indPval = np.where((Pval < (1 - thr)) & (Pval > thr))\n",
    "jPval = Pval[indPval]\n",
    "v = np.sum(jPval * (1 - jPval))\n",
    "# Plot successive values and histogram with statistics\n",
    "plt.clf()\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(nb_ones, \"+\")\n",
    "plt.subplot(2, 1, 2)\n",
    "n_bins = nb_ones.max() - nb_ones.min() + 1\n",
    "h = plt.hist(nb_ones, n_bins)\n",
    "MyTxt = (\n",
    "    \"Nval: \"\n",
    "    + str(Nsum)\n",
    "    + \"\\nMean: \"\n",
    "    + str(\"%0.2f\" % Mean)\n",
    "    + \"\\nMedian: \"\n",
    "    + str(Median)\n",
    "    + \"\\nVar: \"\n",
    "    + str(\"%0.2f\" % Var)\n",
    "    + \"\\naVar: \"\n",
    "    + str(\"%0.2f\" % aVar)\n",
    "    + \"\\nv from Pval: \"\n",
    "    + str(\"%0.2f\" % v)\n",
    ")\n",
    "print(MyTxt)\n",
    "plt.figtext(0.7, 0.25, MyTxt)\n",
    "plt.show()"
   ]
  }
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