diff options
Diffstat (limited to 'util/plot_dsa.ipynb')
| -rw-r--r-- | util/plot_dsa.ipynb | 743 |
1 files changed, 0 insertions, 743 deletions
diff --git a/util/plot_dsa.ipynb b/util/plot_dsa.ipynb deleted file mode 100644 index abd6531..0000000 --- a/util/plot_dsa.ipynb +++ /dev/null @@ -1,743 +0,0 @@ -{ - "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\"])))" - ] - } - ], - "metadata": { - "@webio": { - "lastCommId": "a38f080b9a044da08882846212c38d91", - "lastKernelId": "4cad5b27-583d-4c4e-947c-f47bdf2d4754" - }, - "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 -} |