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Diffstat (limited to 'util/plot_dh.ipynb')
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diff --git a/util/plot_dh.ipynb b/util/plot_dh.ipynb deleted file mode 100644 index f43d631..0000000 --- a/util/plot_dh.ipynb +++ /dev/null @@ -1,668 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Analysis of key agreement data" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-19T13:35:38.954375Z", - "start_time": "2019-03-19T13:35:38.578219Z" - } - }, - "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\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": "2019-03-19T12:43:15.121139Z", - "start_time": "2019-03-19T12:43:15.117537Z" - } - }, - "outputs": [], - "source": [ - "# File name with output from ECTesterReader or ECTesterStandalone ECDH.\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", - "time_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": "2019-03-19T12:43:16.687260Z", - "start_time": "2019-03-19T12:43:16.031604Z" - } - }, - "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) != 5:\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={2: unhexlify, 3: hx, 4: hx},\n", - " dtype=np.dtype([(\"index\", \"u4\"), (\"time\", \"u4\"), (\"pub\", \"O\"), (\"priv\", \"O\"), (\"secret\", \"O\")]))\n", - "\n", - "# Skip first (outliers?)\n", - "\n", - "data = data[skip_first:]\n", - "\n", - "# Setup the data\n", - "\n", - "orig_time_unit = header_names[1].split(\"[\")[1][:-1]\n", - "time_disp_unit = time_scale(data[\"time\"], orig_time_unit, time_unit, scaling_factor)\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 = mquantiles(data[\"time\"], prob=(quant_low_bound, 0.25, 0.5, 0.75, quant_high_bound))\n", - "if trim:\n", - " low_bound = quantiles[0] if 0 <= trim_low <= 1 else trim_low\n", - " high_bound = quantiles[4] if 0 <= trim_high <= 1 else trim_high\n", - " data_trimmed = data[np.logical_and(data[\"time\"] >= low_bound,\n", - " data[\"time\"] <= high_bound)]\n", - " quantiles_trim = mquantiles(data_trimmed[\"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_trim = quantiles_gen\n", - "\n", - "description = describe(data[\"time\"])\n", - "description_trim = describe(data_trimmed[\"time\"])\n", - "\n", - "max_time = description.minmax[1]\n", - "min_time = description.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_time = hist_size_func(hist_size)(description.nobs, min_time, max_time, description.variance, quantiles[1], quantiles[3])\n", - "hist_size_time_trim = hist_size_func(hist_size)(description_trim.nobs, description_trim.minmax[0], description_trim.minmax[1], description_trim.variance, quantiles_trim[1], quantiles_trim[3])\n", - "\n", - "if hist_size_time < 30:\n", - " hist_size_time = max_time - min_time\n", - "if hist_size_time_trim < 30:\n", - " hist_size_time_trim = description_trim.minmax[1] - description_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": "2019-03-19T12:43:17.706648Z", - "start_time": "2019-03-19T12:43:17.695215Z" - } - }, - "outputs": [], - "source": [ - "display(\"Raw\")\n", - "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n", - " description]\n", - "display(HTML(tabulate.tabulate(desc, tablefmt=\"html\")))\n", - "display(\"Trimmed\")\n", - "desc = [(\"N\", \"min, max\", \"mean\", \"variance\", \"skewness\", \"kurtosis\"),\n", - " description_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": "2019-03-19T12:43:19.507884Z", - "start_time": "2019-03-19T12:43:19.502941Z" - } - }, - "outputs": [], - "source": [ - "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n", - " list(map(lambda x: \"{} {}\".format(x, time_disp_unit), quantiles))]\n", - "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Info" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-19T12:43:20.963153Z", - "start_time": "2019-03-19T12:43:20.956502Z" - } - }, - "outputs": [], - "source": [ - "display(\"Bitsize: {}\".format(bit_size))\n", - "display(\"Histogram time bins: {}\".format(hist_size_time))\n", - "display(\"Histogram time bins(trimmed): {}\".format(hist_size_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": "2019-03-19T12:43:22.063050Z", - "start_time": "2019-03-19T12:43:21.967845Z" - } - }, - "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 key agreement 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[\"time\"],\n", - " bins=[max_msb - min_msb + 1, hist_size_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(\"key agreement time ({})\".format(time_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": "2019-03-19T12:47:12.436692Z", - "start_time": "2019-03-19T12:47:11.310271Z" - } - }, - "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 key agreement 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[\"time\"], bins=[max(priv_hw) - min(priv_hw), hist_size_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(\"key agreement time ({})\".format(time_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_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", - "fig_priv_hist.tight_layout()\n", - "fig_priv_hist.colorbar(im, ax=[axe_priv_hist, axe_priv_hist_hw])\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", - "del priv_hw" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Key agreement time histogram" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-19T12:47:20.496134Z", - "start_time": "2019-03-19T12:47:20.360405Z" - } - }, - "outputs": [], - "source": [ - "fig_ka_hist = plt.figure(figsize=(10.5, 8), dpi=90)\n", - "axe_hist_full = fig_ka_hist.add_subplot(2, 1, 1)\n", - "axe_hist_trim = fig_ka_hist.add_subplot(2, 1, 2)\n", - "plot_hist(axe_hist_full, data[\"time\"], \"key agreement time ({})\".format(time_disp_unit), log_scale, hist_size_time);\n", - "plot_hist(axe_hist_trim, data_trimmed[\"time\"], \"key agreement time ({})\".format(time_disp_unit), log_scale, hist_size_time_trim);\n", - "\n", - "fig_ka_hist.tight_layout()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Moving averages of key agreement time" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "ExecuteTime": { - "end_time": "2019-03-19T12:47:21.706585Z", - "start_time": "2019-03-19T12:47:21.658363Z" - } - }, - "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 agreement time\")\n", - "avg_100 = moving_average(data[\"time\"], 100)\n", - "avg_1000 = moving_average(data[\"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(\"key agreement time ({})\".format(time_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": "2019-03-19T12:47:32.875112Z", - "start_time": "2019-03-19T12:47:32.542216Z" - }, - "hide_input": false - }, - "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", - "msb_h = plot_hist(axe_msb_s_hist, priv_msb, \"private key MSB\", log_scale, False, False)\n", - "lsb_h = plot_hist(axe_lsb_s_hist, priv_lsb, \"private key LSB\", log_scale, False, False)\n", - "\n", - "fig_priv_hists.tight_layout()\n", - "del priv_msb, priv_lsb" - ] - }, - { - "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": "2019-03-19T12:47:34.638019Z", - "start_time": "2019-03-19T12:47:34.479903Z" - } - }, - "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", - "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[\"time\"], bins=[max(bl_data) - min(bl_data), hist_size_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(\"key agreement time ({})\".format(time_disp_unit))\n", - "\n", - "plot_hist(axe_bl_hist, bl_data, \"Private key 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": [ - "### 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[\"time\"] <= upper_bnd,\n", - " data_trimmed[\"time\"] >= lower_bnd)]\n", - " axe_bl_time.clear()\n", - " axe_bl_time.set_title(\"Private key bit length, given key agreement time $\\in ({}, {})$ {}\".format(int(lower_bnd), int(upper_bnd), time_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[\"time\"]),\n", - " max=max(data_trimmed[\"time\"]),\n", - " step=1,\n", - " value=description_trim.mean,\n", - " continuous_update=False,\n", - " description=\"center {}\".format(time_disp_unit))\n", - "width_w = widgets.IntSlider(min=1, max=100, continuous_update=False,\n", - " description=\"width {}\".format(time_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": "2019-03-18T18:36:15.492599Z", - "start_time": "2019-03-18T18:36:12.008827Z" - } - }, - "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": {}, - "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", - "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(\"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": { - "ExecuteTime": { - "end_time": "2019-03-19T12:53:48.777395Z", - "start_time": "2019-03-19T12:53:48.766190Z" - } - }, - "outputs": [], - "source": [ - "if un:\n", - " print(\"Private key bit length (min, max):\" + str(min(data[\"priv\"]).bit_length()) + \", \" + str(max(data[\"priv\"]).bit_length()))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "@webio": { - "lastCommId": "709d7f1e9dab427486f950933d243d24", - "lastKernelId": "cf0cea00-5a1b-4e6e-b81a-40a069517c67" - }, - "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 -} |