4 files changed, 351 insertions, 257 deletions

diff --git a/util/plot_dh.ipynb b/util/plot_dh.ipynb
index 4d4edbc..2e82292 100644
--- a/util/plot_dh.ipynb
+++ b/util/plot_dh.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Analysis of key generation data"
+    "# Analysis of key agreement data"
    ]
   },
   {
@@ -12,13 +12,13 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:51:29.892989Z",
-     "start_time": "2019-03-17T19:51:29.557783Z"
+     "end_time": "2019-03-18T18:35:11.337869Z",
+     "start_time": "2019-03-18T18:35:11.331608Z"
     }
    },
    "outputs": [],
    "source": [
-    " %matplotlib notebook \n",
+    "%matplotlib notebook\n",
     "import numpy as np\n",
     "from scipy.stats import describe\n",
     "from scipy.stats import norm as norm_dist\n",
@@ -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\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",
@@ -48,8 +48,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:57:52.012826Z",
-     "start_time": "2019-03-17T19:57:52.008374Z"
+     "end_time": "2019-03-18T18:35:28.957529Z",
+     "start_time": "2019-03-18T18:35:28.952399Z"
     }
    },
    "outputs": [],
@@ -57,6 +57,14 @@
     "# 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",
@@ -94,8 +102,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:51:36.973070Z",
-     "start_time": "2019-03-17T19:51:36.967369Z"
+     "end_time": "2019-03-18T18:35:30.394517Z",
+     "start_time": "2019-03-18T18:35:29.499890Z"
     }
    },
    "outputs": [],
@@ -111,20 +119,8 @@
     "if log_scale:\n",
     "    norm = colors.LogNorm()\n",
     "else:\n",
-    "    norm = colors.Normalize()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T19:51:39.208449Z",
-     "start_time": "2019-03-17T19:51:37.430702Z"
-    }
-   },
-   "outputs": [],
-   "source": [
+    "    norm = colors.Normalize()\n",
+    "\n",
     "# Read the header line.\n",
     "\n",
     "with open(fname, \"r\") as f:\n",
@@ -140,31 +136,14 @@
     "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",
-    "time_unit = \"ms\""
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T19:57:56.363502Z",
-     "start_time": "2019-03-17T19:57:56.331005Z"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "# Setup the data\n",
-    "\n",
     "# Skip first (outliers?)\n",
     "\n",
     "data = data[skip_first:]\n",
     "\n",
-    "# If in nanoseconds, scale to microseconds\n",
-    "if header_names[1].endswith(\"[nano]\") and time_unit == \"ms\":\n",
-    "    time_unit = r\"$\\mu s$\"\n",
-    "    np.floor_divide(data[\"time\"], 1000, out=data[\"time\"])\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",
@@ -189,6 +168,7 @@
     "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",
     "if hist_size == \"sqrt\":\n",
     "    hist_size_func = lambda n, xmin, xmax, var, xlower, xupper: int(sqrt(n)) + 1\n",
@@ -231,8 +211,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:57:59.534102Z",
-     "start_time": "2019-03-17T19:57:59.507172Z"
+     "end_time": "2019-03-18T18:35:31.158217Z",
+     "start_time": "2019-03-18T18:35:31.144280Z"
     }
    },
    "outputs": [],
@@ -259,14 +239,14 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:58:00.833677Z",
-     "start_time": "2019-03-17T19:58:00.827736Z"
+     "end_time": "2019-03-18T18:35:32.593550Z",
+     "start_time": "2019-03-18T18:35:32.588147Z"
     }
    },
    "outputs": [],
    "source": [
     "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n",
-    "       list(map(lambda x: \"{} {}\".format(x, time_unit), quantiles))]\n",
+    "       list(map(lambda x: \"{} {}\".format(x, time_disp_unit), quantiles))]\n",
     "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))"
    ]
   },
@@ -282,8 +262,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:58:01.954382Z",
-     "start_time": "2019-03-17T19:58:01.947339Z"
+     "end_time": "2019-03-18T18:35:33.252850Z",
+     "start_time": "2019-03-18T18:35:33.245928Z"
     }
    },
    "outputs": [],
@@ -304,7 +284,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key MSB vs time heatmap"
+    "### Private key MSB vs time heatmap\n",
+    "The heatmap should show uncorrelated variables."
    ]
   },
   {
@@ -312,8 +293,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:58:03.641387Z",
-     "start_time": "2019-03-17T19:58:03.572612Z"
+     "end_time": "2019-03-18T18:35:34.581846Z",
+     "start_time": "2019-03-18T18:35:34.472065Z"
     }
    },
    "outputs": [],
@@ -329,7 +310,7 @@
     "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_unit))\n",
+    "axe_private.set_ylabel(\"key agreement time ({})\".format(time_disp_unit))\n",
     "fig_private.colorbar(im, ax=axe_private)\n",
     "\n",
     "del priv_msb"
@@ -339,7 +320,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key Hamming Weight vs time heatmap"
+    "### 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."
    ]
   },
   {
@@ -347,8 +331,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:58:07.768683Z",
-     "start_time": "2019-03-17T19:58:06.938237Z"
+     "end_time": "2019-03-18T18:35:39.673526Z",
+     "start_time": "2019-03-18T18:35:38.253945Z"
     }
    },
    "outputs": [],
@@ -362,7 +346,7 @@
     "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_unit))\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",
@@ -392,8 +376,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:58:17.986917Z",
-     "start_time": "2019-03-17T19:58:11.101449Z"
+     "end_time": "2019-03-18T18:35:51.604298Z",
+     "start_time": "2019-03-18T18:35:40.980632Z"
     }
    },
    "outputs": [],
@@ -401,8 +385,8 @@
     "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_unit), log_scale, hist_size_time);\n",
-    "plot_hist(axe_hist_trim, data_trimmed[\"time\"], \"key agreement time ({})\".format(time_unit), log_scale, hist_size_time_trim);"
+    "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);"
    ]
   },
   {
@@ -417,8 +401,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:51:57.934476Z",
-     "start_time": "2019-03-17T19:51:57.877729Z"
+     "end_time": "2019-03-18T18:36:00.467782Z",
+     "start_time": "2019-03-18T18:36:00.418942Z"
     }
    },
    "outputs": [],
@@ -433,7 +417,7 @@
     "    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_unit))\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",
@@ -444,7 +428,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key MSB and LSB histograms"
+    "### Private key MSB and LSB histograms\n",
+    "Expected to be uniform over [0, 255]."
    ]
   },
   {
@@ -452,8 +437,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:51:58.466578Z",
-     "start_time": "2019-03-17T19:51:57.937797Z"
+     "end_time": "2019-03-18T18:36:02.558769Z",
+     "start_time": "2019-03-18T18:36:02.216115Z"
     },
     "hide_input": false
    },
@@ -474,7 +459,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Public key coordinate MSB and LSB histograms"
+    "### 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."
    ]
   },
   {
@@ -482,42 +468,37 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:52:21.184705Z",
-     "start_time": "2019-03-17T19:52:20.589707Z"
+     "end_time": "2019-03-18T18:36:04.445752Z",
+     "start_time": "2019-03-18T18:36:04.317542Z"
     }
    },
    "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",
+    "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",
+    "bl_data = np.array(list(map(lambda x: x.bit_length(), data_trimmed[\"priv\"])), dtype=np.dtype(\"u2\"))\n",
     "\n",
-    "def _plot_coord(data, name, offset):\n",
-    "    axe_msb_pub_hist = fig_pub_hists.add_subplot(4, 1, offset)\n",
-    "    axe_lsb_pub_hist = fig_pub_hists.add_subplot(4, 1, offset + 1)\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",
+    "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_coord(xs, \"X\", 1)\n",
-    "_plot_coord(ys, \"Y\", 3)\n",
+    "plot_hist(axe_bl_hist, bl_data, \"Private key bit length\", log_scale, align=\"right\")\n",
+    "fig_bl.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n",
     "\n",
-    "del pub_coords, xs, ys"
+    "del bl_data"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key bit length histogram"
+    "## 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."
    ]
   },
   {
@@ -525,27 +506,14 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T19:52:07.657216Z",
-     "start_time": "2019-03-17T19:52:07.549731Z"
+     "end_time": "2019-03-18T18:36:15.492599Z",
+     "start_time": "2019-03-18T18:36:12.008827Z"
     }
    },
    "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",
-    "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_unit))\n",
-    "\n",
-    "plot_hist(axe_bl_hist, bl_data, \"Private key bit length\", log_scale, align=\"right\")\n",
-    "fig_bl.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n",
-    "\n",
-    "del bl_data"
+    "p_str = input(\"The prime specifying the finite field:\")\n",
+    "p = int(p_str, 16) if p_str.startswith(\"0x\") else int(p_str)"
    ]
   },
   {
@@ -553,13 +521,35 @@
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "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):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "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())"
+   ]
   }
  ],
  "metadata": {
   "@webio": {
-   "lastCommId": "954c1f99782e402895d668a42553e22f",
-   "lastKernelId": "0b8e59f0-d640-4f72-ae7f-1b327e75910b"
+   "lastCommId": "73e8d2ab400746298b234c8983722e8e",
+   "lastKernelId": "cedfe41c-66b9-4611-ad6f-ab448422bbd2"
   },
   "hide_input": false,
   "kernelspec": {
diff --git a/util/plot_dsa.ipynb b/util/plot_dsa.ipynb
index dbfb38b..503bde8 100644
--- a/util/plot_dsa.ipynb
+++ b/util/plot_dsa.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Analysis of key generation data"
+    "# Analysis of signature data"
    ]
   },
   {
@@ -12,13 +12,13 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:25.518989Z",
-     "start_time": "2019-03-17T23:00:24.501601Z"
+     "end_time": "2019-03-18T18:08:10.526799Z",
+     "start_time": "2019-03-18T18:08:10.073972Z"
     }
    },
    "outputs": [],
    "source": [
-    " %matplotlib notebook \n",
+    "%matplotlib notebook\n",
     "import numpy as np\n",
     "from scipy.stats import describe\n",
     "from scipy.stats import norm as norm_dist\n",
@@ -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\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",
@@ -48,8 +48,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:06:29.704432Z",
-     "start_time": "2019-03-17T23:06:29.694540Z"
+     "end_time": "2019-03-18T18:15:54.067732Z",
+     "start_time": "2019-03-18T18:15:54.063679Z"
     }
    },
    "outputs": [],
@@ -57,8 +57,17 @@
     "# File name with output from ECTesterReader or ECTesterStandalone signatures.\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",
+    "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",
+    "skip_first = 100\n",
     "\n",
     "# Whether to plot things in logarithmic scale or not.\n",
     "log_scale = False\n",
@@ -94,8 +103,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:06:30.551732Z",
-     "start_time": "2019-03-17T23:06:30.545202Z"
+     "end_time": "2019-03-18T18:15:55.985799Z",
+     "start_time": "2019-03-18T18:15:55.495414Z"
     }
    },
    "outputs": [],
@@ -111,20 +120,8 @@
     "if log_scale:\n",
     "    norm = colors.LogNorm()\n",
     "else:\n",
-    "    norm = colors.Normalize()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:38.023486Z",
-     "start_time": "2019-03-17T23:00:27.178465Z"
-    }
-   },
-   "outputs": [],
-   "source": [
+    "    norm = colors.Normalize()\n",
+    "\n",
     "# Read the header line.\n",
     "\n",
     "with open(fname, \"r\") as f:\n",
@@ -142,39 +139,18 @@
     "                                                                      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",
-    "\n",
-    "    \n",
-    "sign_unit = \"ms\"\n",
-    "verify_unit = \"ms\"\n",
-    "# Setup the datatrimmed = False"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:38.465677Z",
-     "start_time": "2019-03-17T23:00:38.025692Z"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "# Setup the data\n",
-    "\n",
+    "                                     (\"nonce\", \"O\"), (\"valid\", \"b\")]))\n",
     "# Skip first (outliers?)\n",
     "\n",
     "data = data[skip_first:]\n",
     "\n",
-    "# If in nanoseconds, scale to microseconds\n",
-    "if header_names[1].endswith(\"[nano]\") and sign_unit == \"ms\":\n",
-    "    sign_unit = r\"$\\mu s$\"\n",
-    "    np.floor_divide(data[\"sign_time\"], 1000, out=data[\"sign_time\"])\n",
+    "# Setup the data\n",
     "\n",
-    "if header_names[2].endswith(\"[nano]\") and verify_unit == \"ms\":\n",
-    "    verify_unit = r\"$\\mu s$\"\n",
-    "    np.floor_divide(data[\"verify_time\"], 1000, out=data[\"verify_time\"])\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",
     "# Trim times\n",
     "quant_low_bound = trim_low if 0 <= trim_low <= 1 else 0.01\n",
@@ -242,8 +218,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:39.540701Z",
-     "start_time": "2019-03-17T23:00:39.511019Z"
+     "end_time": "2019-03-18T18:15:57.175564Z",
+     "start_time": "2019-03-18T18:15:57.161611Z"
     }
    },
    "outputs": [],
@@ -270,14 +246,14 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:40.974497Z",
-     "start_time": "2019-03-17T23:00:40.953755Z"
+     "end_time": "2019-03-18T18:15:58.257820Z",
+     "start_time": "2019-03-18T18:15:58.254036Z"
     }
    },
    "outputs": [],
    "source": [
     "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n",
-    "       list(map(lambda x: \"{} {}\".format(x, sign_unit), quantiles_sign))]\n",
+    "       list(map(lambda x: \"{} {}\".format(x, sign_disp_unit), quantiles_sign))]\n",
     "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))"
    ]
   },
@@ -293,8 +269,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:00:41.961541Z",
-     "start_time": "2019-03-17T23:00:41.949385Z"
+     "end_time": "2019-03-18T18:15:58.917927Z",
+     "start_time": "2019-03-18T18:15:58.909693Z"
     }
    },
    "outputs": [],
@@ -313,7 +289,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Nonce MSB vs signature time heatmap"
+    "### Nonce MSB vs signature time heatmap\n",
+    "The heatmap should show uncorrelated variables."
    ]
   },
   {
@@ -321,8 +298,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:06:34.030472Z",
-     "start_time": "2019-03-17T23:06:33.761991Z"
+     "end_time": "2019-03-18T18:15:59.977656Z",
+     "start_time": "2019-03-18T18:15:59.926337Z"
     }
    },
    "outputs": [],
@@ -338,7 +315,7 @@
     "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 key MSB value\")\n",
-    "axe_nonce.set_ylabel(\"signature time ({})\".format(sign_unit))\n",
+    "axe_nonce.set_ylabel(\"signature time ({})\".format(sign_disp_unit))\n",
     "fig_nonce.colorbar(im, ax=axe_nonce)\n",
     "\n",
     "del nonce_msb"
@@ -348,7 +325,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Nonce Hamming Weight vs signature time heatmap"
+    "### 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."
    ]
   },
   {
@@ -356,8 +336,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:26.804859Z",
-     "start_time": "2019-03-17T23:05:18.214110Z"
+     "end_time": "2019-03-18T18:16:01.977710Z",
+     "start_time": "2019-03-18T18:16:01.717704Z"
     }
    },
    "outputs": [],
@@ -371,7 +351,7 @@
     "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_unit))\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",
@@ -401,8 +381,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:32.395983Z",
-     "start_time": "2019-03-17T23:05:32.068823Z"
+     "end_time": "2019-03-18T18:16:03.232728Z",
+     "start_time": "2019-03-18T18:16:03.134237Z"
     }
    },
    "outputs": [],
@@ -410,8 +390,8 @@
     "fig_sig_hist = plt.figure(figsize=(10.5, 8), dpi=90)\n",
     "axe_hist_full = fig_sig_hist.add_subplot(2, 1, 1)\n",
     "axe_hist_trim = fig_sig_hist.add_subplot(2, 1, 2)\n",
-    "plot_hist(axe_hist_full, data[\"sign_time\"], \"signature time ({})\".format(sign_unit), log_scale, hist_size_sign_time);\n",
-    "plot_hist(axe_hist_trim, data_trimmed[\"sign_time\"], \"signature time ({})\".format(sign_unit), log_scale, hist_size_sign_time_trim);"
+    "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);"
    ]
   },
   {
@@ -426,15 +406,15 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:33.358613Z",
-     "start_time": "2019-03-17T23:05:32.963791Z"
+     "end_time": "2019-03-18T18:16:04.380116Z",
+     "start_time": "2019-03-18T18:16:04.227481Z"
     }
    },
    "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)\n",
-    "plot_hist(axe_hist_full, data[\"verify_time\"], \"verification time ({})\".format(verify_unit), log_scale, hist_size_sign_time);"
+    "plot_hist(axe_hist_full, data[\"verify_time\"], \"verification time ({})\".format(verify_disp_unit), log_scale, hist_size_sign_time);"
    ]
   },
   {
@@ -449,8 +429,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:33.971385Z",
-     "start_time": "2019-03-17T23:05:33.732857Z"
+     "end_time": "2019-03-18T18:16:05.236199Z",
+     "start_time": "2019-03-18T18:16:05.123540Z"
     }
    },
    "outputs": [],
@@ -466,7 +446,7 @@
     "    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_unit))\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",
@@ -474,7 +454,7 @@
     "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_unit))\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",
@@ -485,7 +465,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Nonce MSB and LSB histograms"
+    "### Nonce MSB and LSB histograms\n",
+    "Expected to be uniform over [0, 255]."
    ]
   },
   {
@@ -493,8 +474,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:36.256032Z",
-     "start_time": "2019-03-17T23:05:35.302194Z"
+     "end_time": "2019-03-18T18:16:06.352067Z",
+     "start_time": "2019-03-18T18:16:06.059476Z"
     }
    },
    "outputs": [],
@@ -514,7 +495,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Nonce bit length histogram"
+    "### 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."
    ]
   },
   {
@@ -522,8 +504,8 @@
    "execution_count": null,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2019-03-17T23:05:45.320760Z",
-     "start_time": "2019-03-17T23:05:44.951189Z"
+     "end_time": "2019-03-18T18:16:07.625289Z",
+     "start_time": "2019-03-18T18:16:07.544334Z"
     }
    },
    "outputs": [],
@@ -537,7 +519,7 @@
     "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_unit))\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",
     "fig_bl.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n",
@@ -546,6 +528,74 @@
    ]
   },
   {
+   "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": "2019-03-18T18:16:48.791656Z",
+     "start_time": "2019-03-18T18:16:45.435426Z"
+    }
+   },
+   "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": "2019-03-18T18:16:55.343989Z",
+     "start_time": "2019-03-18T18:16:49.543154Z"
+    }
+   },
+   "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):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2019-03-18T18:16:56.289305Z",
+     "start_time": "2019-03-18T18:16:56.278296Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "max_priv = max(data[\"priv\"])\n",
+    "max_nonce = max(data[\"nonce\"])\n",
+    "display(max_priv < r)\n",
+    "display(r <= p or max_priv > p)\n",
+    "display(max_nonce < r)\n",
+    "display(r <= p or max_nonce > p)\n",
+    "display(max_priv.bit_length() == r.bit_length())\n",
+    "display(max_nonce.bit_length() == r.bit_length())"
+   ]
+  },
+  {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
@@ -555,8 +605,8 @@
  ],
  "metadata": {
   "@webio": {
-   "lastCommId": "2218f80b2f784436bce6ffed5d971ea3",
-   "lastKernelId": "1c06331a-17dd-4743-9e31-832000e597c8"
+   "lastCommId": "7c4c5d836a8d43e5846df95890bbafa3",
+   "lastKernelId": "b01f6c07-c08b-4348-a503-dc2c9cf1db89"
   },
   "hide_input": false,
   "kernelspec": {
diff --git a/util/plot_gen.ipynb b/util/plot_gen.ipynb
index 5f02a00..db618cc 100644
--- a/util/plot_gen.ipynb
+++ b/util/plot_gen.ipynb
@@ -18,7 +18,7 @@
    },
    "outputs": [],
    "source": [
-    " %matplotlib notebook \n",
+    "%matplotlib notebook\n",
     "import numpy as np\n",
     "from scipy.stats import describe\n",
     "from scipy.stats import norm as norm_dist\n",
@@ -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\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",
@@ -57,6 +57,15 @@
     "# 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",
@@ -111,20 +120,8 @@
     "if log_scale:\n",
     "    norm = colors.LogNorm()\n",
     "else:\n",
-    "    norm = colors.Normalize()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T19:16:42.300146Z",
-     "start_time": "2019-03-17T19:16:40.259135Z"
-    }
-   },
-   "outputs": [],
-   "source": [
+    "    norm = colors.Normalize()\n",
+    "\n",
     "# Read the header line.\n",
     "\n",
     "with open(fname, \"r\") as f:\n",
@@ -144,37 +141,19 @@
     "    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",
-    "gen_unit = \"ms\"\n",
-    "export_unit = \"ms\"\n",
-    "# Setup the datatrimmed = False"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2019-03-17T19:16:42.417415Z",
-     "start_time": "2019-03-17T19:16:42.302353Z"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "# Setup the data\n",
     "\n",
     "# Skip first (outliers?)\n",
     "\n",
     "data = data[skip_first:]\n",
     "\n",
-    "# If in nanoseconds, scale to microseconds\n",
-    "if header_names[1].endswith(\"[nano]\") and gen_unit == \"ms\":\n",
-    "    gen_unit = r\"$\\mu s$\"\n",
-    "    np.floor_divide(data[\"gen_time\"], 1000, out=data[\"gen_time\"])\n",
+    "# Setup the data\n",
     "\n",
-    "if len(header_names) == 5 and header_names[2].endswith(\"[nano]\") and export_unit == \"ms\":\n",
-    "    export_unit = r\"$\\mu s$\"\n",
-    "    np.floor_divide(data[\"export_time\"], 1000, out=data[\"export_time\"])\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",
@@ -199,6 +178,7 @@
     "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",
@@ -276,7 +256,7 @@
    "outputs": [],
    "source": [
     "tbl = [(quant_low_bound, \"0.25\", \"0.5\", \"0.75\", quant_high_bound),\n",
-    "       list(map(lambda x: \"{} {}\".format(x, gen_unit), quantiles_gen))]\n",
+    "       list(map(lambda x: \"{} {}\".format(x, gen_disp_unit), quantiles_gen))]\n",
     "display(HTML(tabulate.tabulate(tbl, tablefmt=\"html\")))"
    ]
   },
@@ -312,7 +292,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key MSB vs time heatmap"
+    "### Private key MSB vs time heatmap\n",
+    "The heatmap should show uncorrelated variables."
    ]
   },
   {
@@ -337,7 +318,7 @@
     "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_unit))\n",
+    "axe_private.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n",
     "fig_private.colorbar(im, ax=axe_private)\n",
     "\n",
     "del priv_msb"
@@ -347,7 +328,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key Hamming Weight vs time heatmap"
+    "### 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."
    ]
   },
   {
@@ -370,7 +354,7 @@
     "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_unit))\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",
@@ -409,8 +393,8 @@
     "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_unit), log_scale, hist_size_gen_time);\n",
-    "plot_hist(axe_hist_trim, data_trimmed[\"gen_time\"], \"keygen time ({})\".format(gen_unit), log_scale, hist_size_gen_time_trim);"
+    "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);"
    ]
   },
   {
@@ -436,8 +420,8 @@
     "    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_unit), log_scale, hist_size_gen_time);\n",
-    "    plot_hist(axe_hist_trim, data_trimmed[\"export_time\"], \"export time ({})\".format(export_unit), log_scale, hist_size_gen_time_trim);"
+    "    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);"
    ]
   },
   {
@@ -468,7 +452,7 @@
     "    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_unit))\n",
+    "axe_avg.set_ylabel(\"keygen time ({})\".format(gen_disp_unit))\n",
     "axe_avg.set_xlabel(\"index\")\n",
     "axe_avg.legend(loc=\"best\")\n",
     "del avg_100, avg_1000"
@@ -478,7 +462,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key MSB and LSB histograms"
+    "### Private key MSB and LSB histograms\n",
+    "Expected to be uniform over [0, 255]."
    ]
   },
   {
@@ -506,7 +491,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Public key coordinate MSB and LSB histograms"
+    "### Public key coordinate MSB and LSB histograms\n",
+    "Expected to be somewhat uniform over [0, 255]."
    ]
   },
   {
@@ -549,7 +535,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Private key bit length vs time heatmap"
+    "### 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."
    ]
   },
   {
@@ -573,7 +560,7 @@
     "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_unit))\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",
     "fig_priv_hist.colorbar(im, ax=[axe_bl_heat, axe_bl_hist])\n",
@@ -582,17 +569,69 @@
    ]
   },
   {
+   "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):"
+   ]
+  },
+  {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "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())"
+   ]
   }
  ],
  "metadata": {
   "@webio": {
-   "lastCommId": "eaf134b2342a4b71afa1ac9334e37e07",
-   "lastKernelId": "95d0d16c-1dde-451e-94cb-8bd0fefb8378"
+   "lastCommId": "a0b5176ec9b441fc87297b9ed343c5b3",
+   "lastKernelId": "a6864201-5c88-44d7-8438-ea96f7295d78"
   },
   "hide_input": false,
   "kernelspec": {
diff --git a/util/utils.py b/util/utils.py
index d6b9aed..5359988 100644
--- a/util/utils.py
+++ b/util/utils.py
@@ -16,6 +16,21 @@ def moving_average(a, n) :
     return ret[n - 1:] / n
 
 
+def time_scale(data, orig_unit, target_unit, scaling_factor):
+    units = {
+        "milli": ("ms", 1000000),
+        "micro": (r"$\mu s$", 1000),
+        "nano":  ("ns", 1)
+    }
+    upper = units[orig_unit][1]
+    lower = units[target_unit][1] * scaling_factor
+    if upper > lower:
+        data *= upper // lower
+    elif lower > upper:
+        np.floor_divide(data, lower // upper, data)
+    return (r"$\frac{1}{" + str(scaling_factor) + "}$" if scaling_factor != 1 else "") + units[target_unit][0]
+
+
 def plot_hist(axes, data, xlabel=None, log=False, avg=True, median=True, bins=None, **kwargs):
     time_max = max(data)
     time_min = min(data)