{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis of signature data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:04:46.257111Z",
     "start_time": "2019-03-22T09:04:43.955081Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "from scipy.stats import describe\n",
    "from scipy.stats import norm as norm_dist\n",
    "from scipy.stats.mstats import mquantiles\n",
    "from math import log, sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import ticker, colors, gridspec\n",
    "from copy import deepcopy\n",
    "from utils import plot_hist, moving_average, hw, time_scale, hist_size_func, recompute_nonces\n",
    "from binascii import unhexlify\n",
    "from IPython.display import display, HTML\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "import tabulate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings\n",
    "Enter your input below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:02.399284Z",
     "start_time": "2019-03-22T09:05:02.391509Z"
    }
   },
   "outputs": [],
   "source": [
    "# File name with output from ECTesterReader or ECTesterStandalone signatures.\n",
    "fname = \"filename.csv\"\n",
    "\n",
    "# A hash algorithm used\n",
    "hash_algo = \"SHA1\" # e.g. \"SHA1\" or None for no hash, raw data signatures\n",
    "\n",
    "# A curve name or a path to curve file, used to recompute the random nonces used in signing, if they are not present\n",
    "# in the file. (ECTester was not able to recompute them for some reason)\n",
    "curve = None # e.g. \"secg/secp256r1\" or \"secp256r1.csv\" or None for no curve.\n",
    "\n",
    "# The time unit used in displaying the plots. One of \"milli\", \"micro\", \"nano\".\n",
    "# WARNING: Using nano might lead to very large plots/histograms and to the\n",
    "#          notebook to freeze or run out of memory, as well as bad visualization\n",
    "#          quality, due to noise and low density.\n",
    "sign_unit = \"milli\"\n",
    "verify_unit = \"milli\"\n",
    "# A number which will be used to divide the time into sub-units, e.g. for 5, time will be in fifths of units\n",
    "scaling_factor = 1\n",
    "\n",
    "# The amount of entries skipped from the beginning of the file, as they are usually outliers.\n",
    "skip_first = 10\n",
    "\n",
    "# Whether to plot things in logarithmic scale or not.\n",
    "log_scale = False\n",
    "\n",
    "# Whether to trim the time data outside the 1 - 99 percentile range (adjust below). Quite useful.\n",
    "trim = True\n",
    "\n",
    "# How much to trim? Either a number in [0,1] signifying a quantile, or an absolute value signifying a threshold\n",
    "trim_low = 0.01\n",
    "trim_high = 0.99\n",
    "\n",
    "# Graphical (matplotlib) style name\n",
    "style = \"ggplot\"\n",
    "\n",
    "# Color map to use, and what color to assign to \"bad\" values (necessary for log_scale)\n",
    "color_map = plt.cm.viridis\n",
    "color_map_bad = \"black\"\n",
    "\n",
    "# What function to use to calculate number of histogram bins of time\n",
    "# one of \"sqrt\", \"sturges\", \"rice\", \"scott\" and \"fd\" or a number specifying the number of bins\n",
    "hist_size = \"sturges\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:04.270940Z",
     "start_time": "2019-03-22T09:05:03.059822Z"
    }
   },
   "outputs": [],
   "source": [
    "# Setup plot style\n",
    "\n",
    "plt.style.use(style)\n",
    "\n",
    "cmap = deepcopy(color_map)\n",
    "cmap.set_bad(color_map_bad)\n",
    "\n",
    "# Normalization, linear or log.\n",
    "if log_scale:\n",
    "    norm = colors.LogNorm()\n",
    "else:\n",
    "    norm = colors.Normalize()\n",
    "\n",
    "# Read the header line.\n",
    "\n",
    "with open(fname, \"r\") as f:\n",
    "    header = f.readline()\n",
    "header_names = header.split(\";\")\n",
    "if len(header_names) != 9:\n",
    "    print(\"Bad data?\")\n",
    "    exit(1)\n",
    "\n",
    "# Load the data\n",
    "\n",
    "hx = lambda x: int(x, 16)\n",
    "data = np.genfromtxt(fname, delimiter=\";\", skip_header=1, converters={3: unhexlify, 4: unhexlify,\n",
    "                                                                      5: hx, 6: unhexlify, 7: hx,\n",
    "                                                                      8: lambda b: bool(int(b))},\n",
    "                     dtype=np.dtype([(\"index\", \"u4\"), (\"sign_time\", \"u4\"), (\"verify_time\", \"u4\"),\n",
    "                                     (\"data\", \"O\"), (\"pub\", \"O\"), (\"priv\", \"O\"), (\"signature\", \"O\"),\n",
    "                                     (\"nonce\", \"O\"), (\"valid\", \"b\")]))\n",
    "# Skip first (outliers?)\n",
    "\n",
    "data = data[skip_first:]\n",
    "\n",
    "# Setup the data\n",
    "\n",
    "# Convert time data\n",
    "orig_sign_unit = header_names[1].split(\"[\")[1][:-1]\n",
    "orig_verify_unit = header_names[2].split(\"[\")[1][:-1]\n",
    "sign_disp_unit = time_scale(data[\"sign_time\"], orig_sign_unit, sign_unit, scaling_factor)\n",
    "verify_disp_unit = time_scale(data[\"verify_time\"], orig_verify_unit, verify_unit, scaling_factor)\n",
    "\n",
    "if np.any(data[\"nonce\"] == None):\n",
    "    recompute_nonces(data, curve, hash_algo)\n",
    "\n",
    "# Trim times\n",
    "quant_low_bound = trim_low if 0 <= trim_low <= 1 else 0.01\n",
    "quant_high_bound = trim_high if 0 <= trim_high <= 1 else 0.95\n",
    "quantiles_sign = mquantiles(data[\"sign_time\"], prob=(quant_low_bound, 0.25, 0.5, 0.75, quant_high_bound))\n",
    "if trim:\n",
    "    low_bound = quantiles_sign[0] if 0 <= trim_low <= 1 else trim_low\n",
    "    high_bound = quantiles_sign[4] if 0 <= trim_high <= 1 else trim_high\n",
    "    data_trimmed = data[np.logical_and(data[\"sign_time\"] >= low_bound,\n",
    "                                       data[\"sign_time\"] <= high_bound)]\n",
    "    quantiles_sign_trim = mquantiles(data_trimmed[\"sign_time\"], prob=(quant_low_bound, 0.25, 0.5, 0.75, quant_high_bound))\n",
    "else:\n",
    "    low_bound = None\n",
    "    high_bound = None\n",
    "    data_trimmed = data\n",
    "    quantiles_sign_trim = quantiles_sign\n",
    "\n",
    "description_sign = describe(data[\"sign_time\"])\n",
    "description_sign_trim = describe(data_trimmed[\"sign_time\"])\n",
    "\n",
    "max_sign_time = description_sign.minmax[1]\n",
    "min_sign_time = description_sign.minmax[0]\n",
    "bit_size = len(bin(max(data[\"priv\"]))) - 2\n",
    "byte_size = (bit_size + 7) // 8\n",
    "bit_size = byte_size * 8\n",
    "\n",
    "hist_size_sign_time = hist_size_func(hist_size)(description_sign.nobs, min_sign_time, max_sign_time, description_sign.variance, quantiles_sign[1], quantiles_sign[3])\n",
    "hist_size_sign_time_trim = hist_size_func(hist_size)(description_sign_trim.nobs, description_sign_trim.minmax[0], description_sign_trim.minmax[1], description_sign_trim.variance, quantiles_sign_trim[1], quantiles_sign_trim[3])\n",
    "\n",
    "if hist_size_sign_time < 30:\n",
    "    hist_size_sign_time = max_sign_time - min_sign_time\n",
    "if hist_size_sign_time_trim < 30:\n",
    "    hist_size_sign_time_trim = description_sign_trim.minmax[1] - description_sign_trim.minmax[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:04.817352Z",
     "start_time": "2019-03-22T09:05:04.804639Z"
    }
   },
   "outputs": [],
   "source": [
    "display(\"Raw\")\n",
    "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n",
    "        description_sign]\n",
    "display(HTML(tabulate.tabulate(desc, tablefmt=\"html\")))\n",
    "display(\"Trimmed\")\n",
    "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n",
    "        description_sign_trim]\n",
    "display(HTML(tabulate.tabulate(desc, tablefmt=\"html\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selected quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:06.106323Z",
     "start_time": "2019-03-22T09:05:06.090706Z"
    }
   },
   "outputs": [],
   "source": [
    "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n",
    "       list(map(lambda x: \"{} {}\".format(x, sign_disp_unit), quantiles_sign))]\n",
    "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:06.799992Z",
     "start_time": "2019-03-22T09:05:06.790754Z"
    }
   },
   "outputs": [],
   "source": [
    "display(\"Bitsize:\", bit_size)\n",
    "display(\"Histogram time bins: {}\".format(hist_size_sign_time))\n",
    "display(\"Histogram time bins(trimmed): {}\".format(hist_size_sign_time_trim))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonce MSB vs signature time heatmap\n",
    "The heatmap should show uncorrelated variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:08.567129Z",
     "start_time": "2019-03-22T09:05:07.948181Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_nonce = plt.figure(figsize=(10.5, 8), dpi=90)\n",
    "axe_nonce = fig_nonce.add_subplot(1, 1, 1, title=\"Nonce MSB vs signature time\")\n",
    "nonce_msb = np.array(list(map(lambda x: x >> (bit_size - 8), data_trimmed[\"nonce\"])), dtype=np.dtype(\"u1\"))\n",
    "max_msb = max(nonce_msb)\n",
    "min_msb = min(nonce_msb)\n",
    "heatmap, xedges, yedges = np.histogram2d(nonce_msb, data_trimmed[\"sign_time\"],\n",
    "                                         bins=[max_msb - min_msb + 1, hist_size_sign_time_trim])\n",
    "extent = [min_msb, max_msb, yedges[0], yedges[-1]]\n",
    "im = axe_nonce.imshow(heatmap.T, extent=extent, aspect=\"auto\", cmap=cmap, origin=\"low\",\n",
    "                   interpolation=\"nearest\", norm=norm)\n",
    "axe_nonce.set_xlabel(\"nonce MSB value\")\n",
    "axe_nonce.set_ylabel(\"signature time ({})\".format(sign_disp_unit))\n",
    "fig_nonce.colorbar(im, ax=axe_nonce)\n",
    "\n",
    "fig_nonce.tight_layout()\n",
    "del nonce_msb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonce Hamming Weight vs signature time heatmap\n",
    "The heatmap should show uncorrelated variables.\n",
    "\n",
    "Also contains a nonce Hamming Weight histogram, which should be binomially distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:17.416586Z",
     "start_time": "2019-03-22T09:05:16.928355Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_nonce_hist = plt.figure(figsize=(10.5, 12), dpi=90)\n",
    "gs = gridspec.GridSpec(2, 1, height_ratios=[2.5, 1])\n",
    "axe_nonce_hist = fig_nonce_hist.add_subplot(gs[0], title=\"Nonce Hamming weight vs signature time\")\n",
    "axe_nonce_hist_hw = fig_nonce_hist.add_subplot(gs[1], sharex=axe_nonce_hist, title=\"Nonce Hamming weight\")\n",
    "nonce_hw = np.array(list(map(hw, data_trimmed[\"nonce\"])), dtype=np.dtype(\"u2\"))\n",
    "h, xe, ye = np.histogram2d(nonce_hw, data_trimmed[\"sign_time\"], bins=[max(nonce_hw) - min(nonce_hw), hist_size_sign_time_trim])\n",
    "im = axe_nonce_hist.imshow(h.T, origin=\"low\", cmap=cmap, aspect=\"auto\", extent=[xe[0], xe[-1], ye[0], ye[-1]], norm=norm)\n",
    "axe_nonce_hist.axvline(x=bit_size//2, alpha=0.7, linestyle=\"dotted\", color=\"white\", label=str(bit_size//2) + \" bits\")\n",
    "axe_nonce_hist.set_xlabel(\"nonce Hamming weight\")\n",
    "axe_nonce_hist.set_ylabel(\"signature time ({})\".format(sign_disp_unit))\n",
    "axe_nonce_hist.legend(loc=\"best\")\n",
    "\n",
    "plot_hist(axe_nonce_hist_hw, nonce_hw, \"nonce Hamming weight\", log_scale, True, True)\n",
    "\n",
    "param = norm_dist.fit(nonce_hw)\n",
    "pdf_range = np.arange(min(nonce_hw), max(nonce_hw))\n",
    "norm_pdf = norm_dist.pdf(pdf_range, *param[:-2], loc=param[-2], scale=param[-1]) * description_sign_trim.nobs\n",
    "axe_nonce_hist_hw.plot(pdf_range, norm_pdf, label=\"fitted normal distribution\")\n",
    "axe_nonce_hist_hw.legend(loc=\"best\")\n",
    "\n",
    "\n",
    "display(HTML(\"<b>Nonce Hamming weight fitted with normal distribution:</b>\"))\n",
    "display(HTML(tabulate.tabulate([(\"Mean\", \"Variance\"), param], tablefmt=\"html\")))\n",
    "\n",
    "fig_nonce_hist.tight_layout()\n",
    "fig_nonce_hist.colorbar(im, ax=[axe_nonce_hist, axe_nonce_hist_hw])\n",
    "del nonce_hw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Signature time histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T16:18:48.188494Z",
     "start_time": "2019-03-21T16:18:39.850301Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_sig_hist = plt.figure(figsize=(10.5, 8), dpi=90)\n",
    "axe_hist_full = fig_sig_hist.add_subplot(2, 1, 1, title=\"Signature time\")\n",
    "axe_hist_trim = fig_sig_hist.add_subplot(2, 1, 2, title=\"Signature time (trimmed)\")\n",
    "plot_hist(axe_hist_full, data[\"sign_time\"], \"signature time ({})\".format(sign_disp_unit), log_scale, hist_size_sign_time);\n",
    "plot_hist(axe_hist_trim, data_trimmed[\"sign_time\"], \"signature time ({})\".format(sign_disp_unit), log_scale, hist_size_sign_time_trim);\n",
    "fig_sig_hist.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verification time histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T16:19:05.618320Z",
     "start_time": "2019-03-21T16:18:53.161932Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_vrfy_hist = plt.figure(figsize=(10.5, 5), dpi=90)\n",
    "axe_hist_full = fig_vrfy_hist.add_subplot(1, 1, 1, title=\"Verification time\")\n",
    "plot_hist(axe_hist_full, data[\"verify_time\"], \"verification time ({})\".format(verify_disp_unit), log_scale, hist_size_sign_time);\n",
    "fig_vrfy_hist.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moving averages of signature and verification times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:24.311923Z",
     "start_time": "2019-03-22T09:05:24.063585Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_avg = plt.figure(figsize=(10.5, 8), dpi=90)\n",
    "axe_sign_avg = fig_avg.add_subplot(2, 1, 1, title=\"Moving average of signature time\")\n",
    "axe_vrfy_avg = fig_avg.add_subplot(2, 1, 2, sharex=axe_sign_avg, title=\"Moving average of verification time\")\n",
    "avg_sign_100 = moving_average(data[\"sign_time\"], 100)\n",
    "avg_sign_1000 = moving_average(data[\"sign_time\"], 1000)\n",
    "axe_sign_avg.plot(avg_sign_100, label=\"window = 100\")\n",
    "axe_sign_avg.plot(avg_sign_1000, label=\"window = 1000\")\n",
    "if low_bound is not None:\n",
    "    axe_sign_avg.axhline(y=low_bound, alpha=0.7, linestyle=\"dotted\", color=\"green\", label=\"Low trim bound = {}\".format(low_bound))\n",
    "if high_bound is not None:\n",
    "    axe_sign_avg.axhline(y=high_bound, alpha=0.7, linestyle=\"dotted\", color=\"orange\", label=\"Hight trim bound = {}\".format(high_bound))\n",
    "axe_sign_avg.set_ylabel(\"signature time ({})\".format(sign_disp_unit))\n",
    "axe_sign_avg.set_xlabel(\"index\")\n",
    "axe_sign_avg.legend(loc=\"best\")\n",
    "\n",
    "avg_vrfy_100 = moving_average(data[\"verify_time\"], 100)\n",
    "avg_vrfy_1000 = moving_average(data[\"verify_time\"], 1000)\n",
    "axe_vrfy_avg.plot(avg_vrfy_100, label=\"window = 100\")\n",
    "axe_vrfy_avg.plot(avg_vrfy_1000, label=\"window = 1000\")\n",
    "axe_vrfy_avg.set_ylabel(\"verification time ({})\".format(verify_disp_unit))\n",
    "axe_vrfy_avg.set_xlabel(\"index\")\n",
    "axe_vrfy_avg.legend(loc=\"best\")\n",
    "\n",
    "fig_avg.tight_layout()\n",
    "\n",
    "del avg_sign_100, avg_sign_1000, avg_vrfy_100, avg_vrfy_1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonce MSB and LSB histograms\n",
    "Expected to be uniform over [0, 255]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:05:29.427210Z",
     "start_time": "2019-03-22T09:05:28.768399Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_nonce_hists = plt.figure(figsize=(10.5, 8), dpi=90)\n",
    "nonce_msb = np.array(list(map(lambda x: x >> (bit_size - 8), data[\"nonce\"])), dtype=np.dtype(\"u1\"))\n",
    "nonce_lsb = np.array(list(map(lambda x: x & 0xff, data[\"nonce\"])), dtype=np.dtype(\"u1\"))\n",
    "axe_msb_n_hist = fig_nonce_hists.add_subplot(2, 1, 1, title=\"Nonce MSB\")\n",
    "axe_lsb_n_hist = fig_nonce_hists.add_subplot(2, 1, 2, title=\"Nonce LSB\")\n",
    "plot_hist(axe_msb_n_hist, nonce_msb, \"nonce MSB\", log_scale, False, False)\n",
    "plot_hist(axe_lsb_n_hist, nonce_lsb, \"nonce LSB\", log_scale, False, False)\n",
    "\n",
    "fig_nonce_hists.tight_layout()\n",
    "del nonce_msb, nonce_lsb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonce bit length vs signature time heatmap\n",
    "Also contains nonce bit length histogram, which is expected to be axis flipped geometric distribution with $p = \\frac{1}{2}$ peaking at the bit size of the order of the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:06:00.061206Z",
     "start_time": "2019-03-22T09:05:59.817227Z"
    }
   },
   "outputs": [],
   "source": [
    "fig_bl = plt.figure(figsize=(10.5, 12), dpi=90)\n",
    "gs = gridspec.GridSpec(2, 1, height_ratios=[2.5, 1])\n",
    "axe_bl_heat = fig_bl.add_subplot(gs[0], title=\"Nonce bit length vs signature time\")\n",
    "axe_bl_hist = fig_bl.add_subplot(gs[1], sharex=axe_bl_heat, title=\"Nonce bit length\")\n",
    "bl_data = np.array(list(map(lambda x: x.bit_length(), data_trimmed[\"nonce\"])), dtype=np.dtype(\"u2\"))\n",
    "\n",
    "h, xe, ye = np.histogram2d(bl_data, data_trimmed[\"sign_time\"], bins=[max(bl_data) - min(bl_data), hist_size_sign_time_trim])\n",
    "im = axe_bl_heat.imshow(h.T, origin=\"low\", cmap=cmap, aspect=\"auto\", extent=[xe[0], xe[-1], ye[0], ye[-1]], norm=norm)\n",
    "axe_bl_heat.set_xlabel(\"nonce bit length\")\n",
    "axe_bl_heat.set_ylabel(\"signature time ({})\".format(sign_disp_unit))\n",
    "\n",
    "plot_hist(axe_bl_hist, bl_data, \"nonce bit length\", log_scale, align=\"right\")\n",
    "\n",
    "fig_bl.tight_layout()\n",
    "fig_bl.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n",
    "\n",
    "del bl_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonce bit length histogram given time\n",
    "Interactively shows the histogram of nonce bit length given a selected time range centered around `center` of width `width`. Ideally, the means of these conditional distributions are equal, while the variances can vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-22T09:06:16.571781Z",
     "start_time": "2019-03-22T09:06:16.336312Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "fig_bl_time = plt.figure(figsize=(10.5, 5), dpi=90)\n",
    "axe_bl_time = fig_bl_time.add_subplot(111)\n",
    "axe_bl_time.set_autoscalex_on(False)\n",
    "def f(center, width):\n",
    "    lower_bnd = center - width/2\n",
    "    upper_bnd = center + width/2\n",
    "    values = data_trimmed[np.logical_and(data_trimmed[\"sign_time\"] <= upper_bnd,\n",
    "                                         data_trimmed[\"sign_time\"] >= lower_bnd)]\n",
    "    axe_bl_time.clear()\n",
    "    axe_bl_time.set_title(\"Nonce bit length, given signature time $\\in ({}, {})$ {}\".format(int(lower_bnd), int(upper_bnd), sign_disp_unit))\n",
    "    bl_data = np.array(list(map(lambda x: x.bit_length(), values[\"nonce\"])), dtype=np.dtype(\"u2\"))\n",
    "    plot_hist(axe_bl_time, bl_data, \"nonce bit length\", bins=11, range=(bit_size-10, bit_size+1), align=\"left\")\n",
    "    axe_bl_time.set_xlim((bit_size-10, bit_size))\n",
    "    fig_bl_time.tight_layout()\n",
    "\n",
    "center_w = widgets.IntSlider(min=min(data_trimmed[\"sign_time\"]),\n",
    "                             max=max(data_trimmed[\"sign_time\"]),\n",
    "                             step=1,\n",
    "                             value=description_sign_trim.mean,\n",
    "                             continuous_update=False,\n",
    "                             description=\"center {}\".format(sign_disp_unit))\n",
    "width_w = widgets.IntSlider(min=1, max=100, continuous_update=False,\n",
    "                             description=\"width {}\".format(sign_disp_unit))\n",
    "w = interactive(f, center=center_w,\n",
    "                width=width_w)\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation\n",
    "Perform some tests on the produced data and compare to expected results.\n",
    "\n",
    "\n",
    "This requires some information about the used curve, enter it below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T15:24:57.397880Z",
     "start_time": "2019-03-21T15:24:37.395614Z"
    }
   },
   "outputs": [],
   "source": [
    "p_str = input(\"The prime specifying the finite field:\")\n",
    "p = int(p_str, 16) if p_str.startswith(\"0x\") else int(p_str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T15:25:05.137250Z",
     "start_time": "2019-03-21T15:24:59.218945Z"
    }
   },
   "outputs": [],
   "source": [
    "r_str = input(\"The order of the curve:\")\n",
    "r = int(r_str, 16) if r_str.startswith(\"0x\") else int(r_str)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of the following tests should pass (e.g. be true), given a large enough sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T16:23:08.618543Z",
     "start_time": "2019-03-21T16:23:08.451827Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "max_priv = max(data[\"priv\"])\n",
    "max_nonce = max(data[\"nonce\"])\n",
    "un = len(np.unique(data[\"priv\"])) != 1\n",
    "if un:\n",
    "    print(\"Private keys are smaller than order:\\t\\t\\t\" + str(max_priv < r))\n",
    "    print(\"Private keys are larger than prime(if order > prime):\\t\" + str(r <= p or max_priv > p))\n",
    "print(\"Nonces are smaller than order:\\t\\t\\t\\t\" + str(max_nonce < r))\n",
    "print(\"Nonces are larger than prime(if order > prime):\\t\\t\" + str(r <= p or max_nonce > p))\n",
    "if un:\n",
    "    print(\"Private keys reach full bit length of order:\\t\\t\" + str(max_priv.bit_length() == r.bit_length()))\n",
    "print(\"Nonces reach full bit length of order:\\t\\t\\t\" + str(max_nonce.bit_length() == r.bit_length()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-21T16:23:09.355514Z",
     "start_time": "2019-03-21T16:23:09.315702Z"
    }
   },
   "outputs": [],
   "source": [
    "if un:\n",
    "    print(\"Private key bit length (min, max):\" + str(min(data[\"priv\"]).bit_length()) + \", \" + str(max(data[\"priv\"]).bit_length()))\n",
    "print(\"Nonce bit length (min, max):\" + str(min(data[\"nonce\"]).bit_length()) + \", \" + str(max(data[\"nonce\"]).bit_length()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"Nonce uniqueness (no duplicates):\" + str(len(np.unique(data[\"nonce\"])) == len(data[\"nonce\"])))"
   ]
  }
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