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diff --git a/util/plot_gen.ipynb b/util/plot_gen.ipynb deleted file mode 100644 index 8e6913f..0000000 --- a/util/plot_gen.ipynb +++ /dev/null @@ -1,755 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Analysis of key generation data" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:38.893311Z", - "start_time": "2019-03-17T19:16:37.845017Z" - } - }, - "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\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": "2019-03-17T19:16:38.911566Z", - "start_time": "2019-03-17T19:16:38.900168Z" - } - }, - "outputs": [], - "source": [ - "# File name with output from ECTesterReader or ECTesterStandalone key generation.\n", - "fname = \"filename.csv\"\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", - "gen_unit = \"milli\" # Unit of key generation command\n", - "export_unit = \"milli\" # Unit of key export command\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": "2019-03-17T19:16:39.733575Z", - "start_time": "2019-03-17T19:16:39.728385Z" - } - }, - "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) not in (4, 5):\n", - " print(\"Bad data?\")\n", - " exit(1)\n", - "\n", - "# Load the data\n", - "\n", - "hx = lambda x: int(x, 16)\n", - "if len(header_names) == 4:\n", - " data = np.genfromtxt(fname, delimiter=\";\", skip_header=1, converters={2: unhexlify, 3: hx},\n", - " dtype=np.dtype([(\"index\", \"u4\"), (\"gen_time\", \"u4\"), (\"pub\", \"O\"), (\"priv\", \"O\")]))\n", - "else:\n", - " data = np.genfromtxt(fname, delimiter=\";\", skip_header=1, converters={3: unhexlify, 4: hx},\n", - " dtype=np.dtype([(\"index\", \"u4\"), (\"gen_time\", \"u4\"), (\"export_time\", \"u4\"),\n", - " (\"pub\", \"O\"), (\"priv\", \"O\")]))\n", - "\n", - "# Skip first (outliers?)\n", - "\n", - "data = data[skip_first:]\n", - "\n", - "# Setup the data\n", - "\n", - "# Convert time data\n", - "orig_gen_unit = header_names[1].split(\"[\")[1][:-1]\n", - "gen_disp_unit = time_scale(data[\"gen_time\"], orig_gen_unit, gen_unit, scaling_factor)\n", - "if len(header_names) == 5:\n", - " orig_export_unit = header_names[2].split(\"[\")[1][:-1]\n", - " export_disp_unit = time_scale(data[\"export_time\"], orig_export_unit, export_unit, scaling_factor)\n", - "\n", - "# Trim gen 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_gen = mquantiles(data[\"gen_time\"], prob=(quant_low_bound, 0.25, 0.5, 0.75, quant_high_bound))\n", - "if trim:\n", - " low_bound = quantiles_gen[0] if 0 <= trim_low <= 1 else trim_low\n", - " high_bound = quantiles_gen[4] if 0 <= trim_high <= 1 else trim_high\n", - " data_trimmed = data[np.logical_and(data[\"gen_time\"] >= low_bound,\n", - " data[\"gen_time\"] <= high_bound)]\n", - " quantiles_gen_trim = mquantiles(data_trimmed[\"gen_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_gen_trim = quantiles_gen\n", - "\n", - "description_gen = describe(data[\"gen_time\"])\n", - "description_gen_trim = describe(data_trimmed[\"gen_time\"])\n", - "\n", - "max_gen_time = description_gen.minmax[1]\n", - "min_gen_time = description_gen.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", - "if hist_size == \"sqrt\":\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: int(sqrt(n)) + 1\n", - "elif hist_size == \"sturges\":\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: int(log(n, 2)) + 1\n", - "elif hist_size == \"rice\":\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: int(2 * n**(1/3))\n", - "elif hist_size == \"scott\":\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: (xmax - xmin) // int((3.5 * sqrt(var)) / (n**(1/3)))\n", - "elif hist_size == \"fd\":\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: (xmax - xmin) // int(2 * (xupper - xlower) / (n**(1/3)))\n", - "else:\n", - " hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: hist_size\n", - "\n", - "hist_size_gen_time = hist_size_func(description_gen.nobs, min_gen_time, max_gen_time, description_gen.variance, quantiles_gen[1], quantiles_gen[3])\n", - "hist_size_gen_time_trim = hist_size_func(description_gen_trim.nobs, description_gen_trim.minmax[0], description_gen_trim.minmax[1], description_gen_trim.variance, quantiles_gen_trim[1], quantiles_gen_trim[3])\n", - "\n", - "if hist_size_gen_time < 30:\n", - " hist_size_gen_time = max_gen_time - min_gen_time\n", - "if hist_size_gen_time_trim < 30:\n", - " hist_size_gen_time_trim = description_gen_trim.minmax[1] - description_gen_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": "2019-03-17T19:16:43.343937Z", - "start_time": "2019-03-17T19:16:43.329900Z" - } - }, - "outputs": [], - "source": [ - "display(\"Raw\")\n", - "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n", - " description_gen]\n", - "display(HTML(tabulate.tabulate(desc, tablefmt=\"html\")))\n", - "display(\"Trimmed\")\n", - "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n", - " description_gen_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": "2019-03-17T19:16:44.058425Z", - "start_time": "2019-03-17T19:16:44.043877Z" - } - }, - "outputs": [], - "source": [ - "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n", - " list(map(lambda x: \"{} {}\".format(x, gen_disp_unit), quantiles_gen))]\n", - "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Info" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-19T13:41:01.468943Z", - "start_time": "2019-03-19T13:41:01.417360Z" - } - }, - "outputs": [], - "source": [ - "display(\"Bitsize:\", bit_size)\n", - "display(\"Histogram time bins: {}\".format(hist_size_gen_time))\n", - "display(\"Histogram time bins(trimmed): {}\".format(hist_size_gen_time_trim))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Private key MSB vs time heatmap\n", - "The heatmap should show uncorrelated variables." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:45.995145Z", - "start_time": "2019-03-17T19:16:45.802741Z" - } - }, - "outputs": [], - "source": [ - "fig_private = plt.figure(figsize=(10.5, 8), dpi=90)\n", - "axe_private = fig_private.add_subplot(1, 1, 1, title=\"Private key MSB vs keygen time\")\n", - "priv_msb = np.array(list(map(lambda x: x >> (bit_size - 8), data_trimmed[\"priv\"])), dtype=np.dtype(\"u1\"))\n", - "max_msb = max(priv_msb)\n", - "min_msb = min(priv_msb)\n", - "heatmap, xedges, yedges = np.histogram2d(priv_msb, data_trimmed[\"gen_time\"],\n", - " bins=[max_msb - min_msb + 1, hist_size_gen_time_trim])\n", - "extent = [min_msb, max_msb, yedges[0], yedges[-1]]\n", - "im = axe_private.imshow(heatmap.T, extent=extent, aspect=\"auto\", cmap=cmap, origin=\"low\",\n", - " interpolation=\"nearest\", norm=norm)\n", - "axe_private.set_xlabel(\"private key MSB value\")\n", - "axe_private.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n", - "fig_private.colorbar(im, ax=axe_private)\n", - "\n", - "fig_private.tight_layout()\n", - "del priv_msb" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Private key Hamming Weight vs time heatmap\n", - "The heatmap should show uncorrelated variables.\n", - "\n", - "Also contains a private key Hamming Weight histogram, which should be binomially distributed." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:49.890330Z", - "start_time": "2019-03-17T19:16:47.357225Z" - } - }, - "outputs": [], - "source": [ - "fig_priv_hist = plt.figure(figsize=(10.5, 12), dpi=90)\n", - "gs = gridspec.GridSpec(2, 1, height_ratios=[2.5, 1])\n", - "axe_priv_hist = fig_priv_hist.add_subplot(gs[0], title=\"Private key Hamming weight vs keygen time\")\n", - "axe_priv_hist_hw = fig_priv_hist.add_subplot(gs[1], sharex=axe_priv_hist, title=\"Private key Hamming weight\")\n", - "priv_hw = np.array(list(map(hw, data_trimmed[\"priv\"])), dtype=np.dtype(\"u2\"))\n", - "h, xe, ye = np.histogram2d(priv_hw, data_trimmed[\"gen_time\"], bins=[max(priv_hw) - min(priv_hw), hist_size_gen_time_trim])\n", - "im = axe_priv_hist.imshow(h.T, origin=\"low\", cmap=cmap, aspect=\"auto\", extent=[xe[0], xe[-1], ye[0], ye[-1]], norm=norm)\n", - "axe_priv_hist.axvline(x=bit_size//2, alpha=0.7, linestyle=\"dotted\", color=\"white\", label=str(bit_size//2) + \" bits\")\n", - "axe_priv_hist.set_xlabel(\"private key Hamming weight\")\n", - "axe_priv_hist.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n", - "axe_priv_hist.legend(loc=\"best\")\n", - "\n", - "plot_hist(axe_priv_hist_hw, priv_hw, \"private key Hamming weight\", log_scale, None)\n", - "\n", - "param = norm_dist.fit(priv_hw)\n", - "pdf_range = np.arange(min(priv_hw), max(priv_hw))\n", - "norm_pdf = norm_dist.pdf(pdf_range, *param[:-2], loc=param[-2], scale=param[-1]) * description_gen_trim.nobs\n", - "axe_priv_hist_hw.plot(pdf_range, norm_pdf, label=\"fitted normal distribution\")\n", - "axe_priv_hist_hw.legend(loc=\"best\")\n", - "\n", - "\n", - "display(HTML(\"<b>Private key Hamming weight fitted with normal distribution:</b>\"))\n", - "display(HTML(tabulate.tabulate([(\"Mean\", \"Variance\"), param], tablefmt=\"html\")))\n", - "\n", - "fig_priv_hist.tight_layout()\n", - "fig_priv_hist.colorbar(im, ax=[axe_priv_hist, axe_priv_hist_hw])\n", - "del priv_hw" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Key generation time histogram" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:52.605277Z", - "start_time": "2019-03-17T19:16:50.114281Z" - } - }, - "outputs": [], - "source": [ - "fig_kg_hist = plt.figure(figsize=(10.5, 8), dpi=90)\n", - "axe_hist_full = fig_kg_hist.add_subplot(2, 1, 1)\n", - "axe_hist_trim = fig_kg_hist.add_subplot(2, 1, 2)\n", - "plot_hist(axe_hist_full, data[\"gen_time\"], \"keygen time ({})\".format(gen_disp_unit), log_scale, hist_size_gen_time);\n", - "plot_hist(axe_hist_trim, data_trimmed[\"gen_time\"], \"keygen time ({})\".format(gen_disp_unit), log_scale, hist_size_gen_time_trim);\n", - "fig_kg_hist.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Key export time histogram\n", - "*Available only for ECTesterReader and keys generated on cards.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:52.610858Z", - "start_time": "2019-03-17T19:16:52.607191Z" - } - }, - "outputs": [], - "source": [ - "if \"export_time\" in data.dtype.names:\n", - " fig_exp_hist = plt.figure(figsize=(10.5, 8), dpi=90)\n", - " axe_hist_full = fig_exp_hist.add_subplot(2, 1, 1)\n", - " axe_hist_trim = fig_exp_hist.add_subplot(2, 1, 2)\n", - " plot_hist(axe_hist_full, data[\"export_time\"], \"export time ({})\".format(export_disp_unit), log_scale, hist_size_gen_time);\n", - " plot_hist(axe_hist_trim, data_trimmed[\"export_time\"], \"export time ({})\".format(export_disp_unit), log_scale, hist_size_gen_time_trim);\n", - " fig_exp_hist.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Moving averages of key generation time" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:54.504830Z", - "start_time": "2019-03-17T19:16:54.409189Z" - } - }, - "outputs": [], - "source": [ - "fig_avg = plt.figure(figsize=(10.5, 7), dpi=90)\n", - "axe_avg = fig_avg.add_subplot(1, 1, 1, title=\"Moving average of key generation time\")\n", - "avg_100 = moving_average(data[\"gen_time\"], 100)\n", - "avg_1000 = moving_average(data[\"gen_time\"], 1000)\n", - "axe_avg.plot(avg_100, label=\"window = 100\")\n", - "axe_avg.plot(avg_1000, label=\"window = 1000\")\n", - "if low_bound is not None:\n", - " axe_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_avg.axhline(y=high_bound, alpha=0.7, linestyle=\"dotted\", color=\"orange\", label=\"Hight trim bound = {}\".format(high_bound))\n", - "axe_avg.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n", - "axe_avg.set_xlabel(\"index\")\n", - "axe_avg.legend(loc=\"best\")\n", - "\n", - "fig_avg.tight_layout()\n", - "del avg_100, avg_1000" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Private key MSB and LSB histograms\n", - "Expected to be uniform over [0, 255]." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:16:55.155285Z", - "start_time": "2019-03-17T19:16:54.508407Z" - } - }, - "outputs": [], - "source": [ - "fig_priv_hists = plt.figure(figsize=(10.5, 8), dpi=90)\n", - "priv_msb = np.array(list(map(lambda x: x >> (bit_size - 8), data[\"priv\"])), dtype=np.dtype(\"u1\"))\n", - "priv_lsb = np.array(list(map(lambda x: x & 0xff, data[\"priv\"])), dtype=np.dtype(\"u1\"))\n", - "axe_msb_s_hist = fig_priv_hists.add_subplot(2, 1, 1, title=\"Private key MSB\")\n", - "axe_lsb_s_hist = fig_priv_hists.add_subplot(2, 1, 2, title=\"Private key LSB\")\n", - "plot_hist(axe_msb_s_hist, priv_msb, \"private key MSB\", log_scale)\n", - "plot_hist(axe_lsb_s_hist, priv_lsb, \"private key LSB\", log_scale)\n", - "\n", - "fig_priv_hists.tight_layout()\n", - "del priv_msb, priv_lsb" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Public key coordinate MSB and LSB histograms\n", - "Expected to be somewhat uniform over [0, 255]." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-17T19:17:06.443596Z", - "start_time": "2019-03-17T19:17:05.516616Z" - } - }, - "outputs": [], - "source": [ - "def _split(xy):\n", - " x = int.from_bytes(xy[1:byte_size + 1], byteorder=\"big\")\n", - " y = int.from_bytes(xy[1 + byte_size:], byteorder=\"big\")\n", - " return (x, y)\n", - "\n", - "pub_coords = np.array(list(map(_split, data[\"pub\"])), dtype=np.dtype(\"O\"))\n", - "xs = pub_coords[...,0]\n", - "ys = pub_coords[...,1]\n", - "fig_pub_hists = plt.figure(figsize=(10.5, 14), dpi=90)\n", - "\n", - "def _plot_coord(data, name, offset):\n", - " axe_msb_pub_hist = fig_pub_hists.add_subplot(4, 1, offset, title=\"{} coordinate MSB\".format(name))\n", - " axe_lsb_pub_hist = fig_pub_hists.add_subplot(4, 1, offset + 1, title=\"{} coordinate LSB\".format(name))\n", - " pub_msb = np.array(list(map(lambda x: x >> (bit_size - 8), data)))\n", - " pub_lsb = np.array(list(map(lambda x: x & 0xff, data)))\n", - " plot_hist(axe_msb_pub_hist, pub_msb, \"{} coordinate MSB\".format(name), log_scale)\n", - " plot_hist(axe_lsb_pub_hist, pub_lsb, \"{} coordinate LSB\".format(name), log_scale)\n", - " del pub_msb, pub_lsb\n", - "\n", - "_plot_coord(xs, \"X\", 1)\n", - "_plot_coord(ys, \"Y\", 3)\n", - "\n", - "fig_pub_hists.tight_layout()\n", - "\n", - "del pub_coords, xs, ys" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Private key bit length vs time heatmap\n", - "Also contains private key 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": "2019-03-17T19:25:51.126642Z", - "start_time": "2019-03-17T19:25:50.929170Z" - } - }, - "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=\"Private key bit length vs keygen time\")\n", - "axe_bl_hist = fig_bl.add_subplot(gs[1], sharex=axe_bl_heat, title=\"Private key bit length\")\n", - "\n", - "bl_data = np.array(list(map(lambda x: x.bit_length(), data_trimmed[\"priv\"])), dtype=np.dtype(\"u2\"))\n", - "\n", - "h, xe, ye = np.histogram2d(bl_data, data_trimmed[\"gen_time\"], bins=[max(bl_data) - min(bl_data), hist_size_gen_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(\"private key bit length\")\n", - "axe_bl_heat.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n", - "\n", - "plot_hist(axe_bl_hist, bl_data, \"Private key bit length\", log_scale, align=\"right\")\n", - "\n", - "fig_priv_hist.tight_layout()\n", - "fig_priv_hist.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n", - "\n", - "del bl_data" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Private key bit length histogram given time\n", - "Interactively shows the histogram of private key 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": {}, - "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[\"gen_time\"] <= upper_bnd,\n", - " data_trimmed[\"gen_time\"] >= lower_bnd)]\n", - " axe_bl_time.clear()\n", - " axe_bl_time.set_title(\"Private key bit length, given keygen time $\\in ({}, {})$ {}\".format(int(lower_bnd), int(upper_bnd), gen_disp_unit))\n", - " bl_data = np.array(list(map(lambda x: x.bit_length(), values[\"priv\"])), dtype=np.dtype(\"u2\"))\n", - " plot_hist(axe_bl_time, bl_data, \"private key 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[\"gen_time\"]),\n", - " max=max(data_trimmed[\"gen_time\"]),\n", - " step=1,\n", - " value=description_gen_trim.mean,\n", - " continuous_update=False,\n", - " description=\"center {}\".format(gen_disp_unit))\n", - "width_w = widgets.IntSlider(min=1, max=100, continuous_update=False,\n", - " description=\"width {}\".format(gen_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", - "This requires some information about the used curve, enter it below." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-18T18:27:02.748493Z", - "start_time": "2019-03-18T18:27:01.294850Z" - } - }, - "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": "2019-03-18T18:27:09.351619Z", - "start_time": "2019-03-18T18:27:08.674272Z" - } - }, - "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": {}, - "outputs": [], - "source": [ - "max_priv = max(data[\"priv\"])\n", - "\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(\"Private keys reach full bit length of order:\\t\\t\" + str(max_priv.bit_length() == r.bit_length()))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(\"Private key bit length (min, max):\" + str(min(data[\"priv\"]).bit_length()) + \", \" + str(max(data[\"priv\"]).bit_length()))" - ] - } - ], - "metadata": { - "@webio": { - "lastCommId": "62b9fbe51a4c472094fee49d62cdb7ec", - "lastKernelId": "a920ac21-57cb-406f-8aef-476c8b0e7df5" - }, - "hide_input": false, - "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": "3.7.4" - }, - "latex_envs": { - "LaTeX_envs_menu_present": true, - "autoclose": false, - "autocomplete": true, - "bibliofile": "biblio.bib", - "cite_by": "apalike", - "current_citInitial": 1, - "eqLabelWithNumbers": true, - "eqNumInitial": 1, - "hotkeys": { - "equation": "Ctrl-E", - "itemize": "Ctrl-I" - }, - "labels_anchors": false, - "latex_user_defs": false, - "report_style_numbering": false, - "user_envs_cfg": false - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": false - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} |