diff options
Diffstat (limited to 'util/plot_dh.ipynb')
| -rw-r--r-- | util/plot_dh.ipynb | 176 |
1 files changed, 119 insertions, 57 deletions
diff --git a/util/plot_dh.ipynb b/util/plot_dh.ipynb index 2e82292..e42b25c 100644 --- a/util/plot_dh.ipynb +++ b/util/plot_dh.ipynb @@ -9,11 +9,11 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:11.337869Z", - "start_time": "2019-03-18T18:35:11.331608Z" + "end_time": "2019-03-19T13:35:38.954375Z", + "start_time": "2019-03-19T13:35:38.578219Z" } }, "outputs": [], @@ -27,7 +27,7 @@ "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 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", @@ -48,8 +48,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:28.957529Z", - "start_time": "2019-03-18T18:35:28.952399Z" + "end_time": "2019-03-19T12:43:15.121139Z", + "start_time": "2019-03-19T12:43:15.117537Z" } }, "outputs": [], @@ -87,7 +87,7 @@ "\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 = \"rice\"" + "hist_size = \"sturges\"" ] }, { @@ -102,8 +102,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:30.394517Z", - "start_time": "2019-03-18T18:35:29.499890Z" + "end_time": "2019-03-19T12:43:16.687260Z", + "start_time": "2019-03-19T12:43:16.031604Z" } }, "outputs": [], @@ -170,21 +170,8 @@ "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_time = hist_size_func(description.nobs, min_time, max_time, description.variance, quantiles[1], quantiles[3])\n", - "hist_size_time_trim = hist_size_func(description_trim.nobs, description_trim.minmax[0], description_trim.minmax[1], description_trim.variance, quantiles_trim[1], quantiles_trim[3])\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", @@ -211,8 +198,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:31.158217Z", - "start_time": "2019-03-18T18:35:31.144280Z" + "end_time": "2019-03-19T12:43:17.706648Z", + "start_time": "2019-03-19T12:43:17.695215Z" } }, "outputs": [], @@ -239,8 +226,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:32.593550Z", - "start_time": "2019-03-18T18:35:32.588147Z" + "end_time": "2019-03-19T12:43:19.507884Z", + "start_time": "2019-03-19T12:43:19.502941Z" } }, "outputs": [], @@ -262,8 +249,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:33.252850Z", - "start_time": "2019-03-18T18:35:33.245928Z" + "end_time": "2019-03-19T12:43:20.963153Z", + "start_time": "2019-03-19T12:43:20.956502Z" } }, "outputs": [], @@ -293,14 +280,14 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:34.581846Z", - "start_time": "2019-03-18T18:35:34.472065Z" + "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)\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", @@ -313,6 +300,7 @@ "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" ] }, @@ -331,16 +319,16 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:39.673526Z", - "start_time": "2019-03-18T18:35:38.253945Z" + "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])\n", - "axe_priv_hist_hw = fig_priv_hist.add_subplot(gs[1], sharex = axe_priv_hist)\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", @@ -356,6 +344,8 @@ "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", @@ -376,8 +366,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:35:51.604298Z", - "start_time": "2019-03-18T18:35:40.980632Z" + "end_time": "2019-03-19T12:47:20.496134Z", + "start_time": "2019-03-19T12:47:20.360405Z" } }, "outputs": [], @@ -386,7 +376,9 @@ "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);" + "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()" ] }, { @@ -401,14 +393,14 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:36:00.467782Z", - "start_time": "2019-03-18T18:36:00.418942Z" + "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)\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", @@ -421,6 +413,7 @@ "axe_avg.set_xlabel(\"index\")\n", "axe_avg.legend(loc=\"best\")\n", "\n", + "fig_avg.tight_layout()\n", "del avg_100, avg_1000" ] }, @@ -437,8 +430,8 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:36:02.558769Z", - "start_time": "2019-03-18T18:36:02.216115Z" + "end_time": "2019-03-19T12:47:32.875112Z", + "start_time": "2019-03-19T12:47:32.542216Z" }, "hide_input": false }, @@ -447,11 +440,12 @@ "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)\n", - "axe_lsb_s_hist = fig_priv_hists.add_subplot(2, 1, 2)\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" ] }, @@ -468,16 +462,16 @@ "execution_count": null, "metadata": { "ExecuteTime": { - "end_time": "2019-03-18T18:36:04.445752Z", - "start_time": "2019-03-18T18:36:04.317542Z" + "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])\n", - "axe_bl_hist = fig_bl.add_subplot(gs[1], sharex=axe_bl_heat)\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", @@ -486,6 +480,8 @@ "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" @@ -495,6 +491,48 @@ "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), sign_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_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", @@ -530,7 +568,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "All of the following tests should pass (e.g. be true):" + "All of the following tests should pass (e.g. be true), given a large enough sample and run without the `--fixed` or `-priv/-npriv` flags:" ] }, { @@ -540,16 +578,40 @@ "outputs": [], "source": [ "max_priv = max(data[\"priv\"])\n", - "display(max_priv < r)\n", - "display(r <= p or max_priv > p)\n", - "display(max_priv.bit_length() == r.bit_length())" + "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": "73e8d2ab400746298b234c8983722e8e", - "lastKernelId": "cedfe41c-66b9-4611-ad6f-ab448422bbd2" + "lastCommId": "18de549d83f84e128074fc96e268d86f", + "lastKernelId": "875ada23-b504-4c96-8f24-68b5d72faab5" }, "hide_input": false, "kernelspec": { |