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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3232df80-2a65-47ce-bc77-6a64f44d2404",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pickle\n",
+    "import itertools\n",
+    "\n",
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "\n",
+    "from collections import Counter\n",
+    "from pathlib import Path\n",
+    "from random import randint\n",
+    "\n",
+    "from bs4 import BeautifulSoup\n",
+    "from tqdm.auto import tqdm, trange\n",
+    "\n",
+    "from common import MultIdent, MultResults"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2130254b-4b88-4928-9fa0-88fa58de9fc7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# All dbl-and-add multipliers from https://github.com/J08nY/pyecsca/blob/master/pyecsca/ec/mult\n",
+    "\n",
+    "window_mults = [\n",
+    "    MultIdent(SlidingWindowMultiplier, width=4),\n",
+    "    MultIdent(SlidingWindowMultiplier, width=5),\n",
+    "    MultIdent(SlidingWindowMultiplier, width=6),\n",
+    "    MultIdent(FixedWindowLTRMultiplier, m=2**4),\n",
+    "    MultIdent(FixedWindowLTRMultiplier, m=2**5),\n",
+    "    MultIdent(FixedWindowLTRMultiplier, m=2**6),\n",
+    "    MultIdent(WindowBoothMultiplier, width=4),\n",
+    "    MultIdent(WindowBoothMultiplier, width=5),\n",
+    "    MultIdent(WindowBoothMultiplier, width=6)\n",
+    "]\n",
+    "naf_mults = [\n",
+    "    MultIdent(WindowNAFMultiplier, width=4),\n",
+    "    MultIdent(WindowNAFMultiplier, width=5),\n",
+    "    MultIdent(WindowNAFMultiplier, width=6),\n",
+    "    MultIdent(BinaryNAFMultiplier)\n",
+    "]\n",
+    "comb_mults = [\n",
+    "    MultIdent(CombMultiplier, width=4),\n",
+    "    MultIdent(CombMultiplier, width=5),\n",
+    "    MultIdent(CombMultiplier, width=6),\n",
+    "    MultIdent(BGMWMultiplier, width=4),\n",
+    "    MultIdent(BGMWMultiplier, width=5),\n",
+    "    MultIdent(BGMWMultiplier, width=6)\n",
+    "]\n",
+    "binary_mults = [\n",
+    "    MultIdent(LTRMultiplier),\n",
+    "    MultIdent(RTLMultiplier),\n",
+    "    MultIdent(CoronMultiplier)\n",
+    "]\n",
+    "other_mults = [\n",
+    "    MultIdent(FullPrecompMultiplier),\n",
+    "    MultIdent(SimpleLadderMultiplier)\n",
+    "]\n",
+    "\n",
+    "with_precomputation = window_mults + naf_mults[:-1] + other_mults[:-1] + comb_mults\n",
+    "\n",
+    "all_mults = window_mults + naf_mults + binary_mults + other_mults + comb_mults"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2df8cd8c-9528-4755-83b5-10ecabaead54",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def divides_any(l: int, small_scalars: set[int]) -> bool:\n",
+    "    if l in small_scalars:\n",
+    "        return True\n",
+    "    for s in small_scalars:\n",
+    "        if s%l==0:\n",
+    "            return True\n",
+    "    return False\n",
+    "\n",
+    "def process_small_scalars(scalar_results: MultResults, divisors: set[int]) -> dict[int, float]:\n",
+    "    result = {}\n",
+    "    for divisor in tqdm(divisors, leave=False):\n",
+    "        count = 0\n",
+    "        for smult in scalar_results.multiplications:\n",
+    "            if divides_any(divisor, smult):\n",
+    "                count += 1\n",
+    "        result[divisor] = count / scalar_results.samples\n",
+    "    return result\n",
+    "\n",
+    "def merge_probs(*prob_maps: dict[int, float]) -> dict[int, float]:\n",
+    "    # Merge two or more maps of \"small-scalar\" -> \"probability\" together by averaging them.\n",
+    "    # This is correct if they were collected with the same amount of samples. If the\n",
+    "    # amount of samples differs a lot this will not update as much as it should, but will\n",
+    "    # update in the correct direction nonetheless.\n",
+    "    counter = Counter()\n",
+    "    nprobs = len(prob_maps)\n",
+    "    for prob_map in prob_maps:\n",
+    "        for k, v in prob_map.items():\n",
+    "            counter[k] += v\n",
+    "    return {k: v / nprobs for k, v in counter.items()}\n",
+    "\n",
+    "def mult_label(mult: MultIdent | ScalarMultiplier) -> str:\n",
+    "    if isinstance(mult, ScalarMultiplier):\n",
+    "        for attr in (\"width\", \"m\"):\n",
+    "            if not hasattr(mult, attr):\n",
+    "                continue\n",
+    "            return f\"{mult.__class__.__name__}_{getattr(mult, attr)}\"\n",
+    "        return mult.__class__.__name__\n",
+    "    elif isinstance(mult, MultIdent):\n",
+    "        return str(mult)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bab2a086-8b3d-4e76-bf5c-46ea2b617708",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def powers_of(k, max_power=10):\n",
+    "    return [k**i for i in range(1, max_power)]\n",
+    "\n",
+    "def prod_combine(one, other):\n",
+    "    return [a * b for a, b in itertools.product(one, other)]\n",
+    "\n",
+    "small_primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]\n",
+    "medium_primes = [211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397]\n",
+    "large_primes = [401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]\n",
+    "all_integers = list(range(1, 100))\n",
+    "\n",
+    "all_divisors = small_primes + medium_primes + large_primes #+ powers_of(2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "318ca5ac-66a6-4187-a01f-f0e2d27ba34e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load\n",
+    "with open(f\"multiples_{category}_{curve}_{bits}\", \"rb\") as f:\n",
+    "    multiples_mults = pickle.load(f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4d2a0f19-8275-4db8-b3fc-c930d8ba2177",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "selected_mults = all_mults\n",
+    "selected_divisors = all_divisors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6b42d25f-6ce1-477a-bc5f-d7c2a8af87a3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "distributions_mults = {}\n",
+    "for mult, results in tqdm(multiples_mults.items()):\n",
+    "    distributions_mults[mult] = process_small_scalars(results, selected_divisors)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "906b5d78-b3a4-4cbb-8051-092d411ba735",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot_mults = selected_mults\n",
+    "plot_divisors = selected_divisors\n",
+    "\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(plot_mults)))[i] for i,mult in enumerate(plot_mults)}\n",
+    "\n",
+    "fig = plt.subplots(figsize=(36, 12))\n",
+    "\n",
+    "L = len(plot_divisors)\n",
+    "plot_divisors = sorted(plot_divisors)\n",
+    "for mult in plot_mults:\n",
+    "    y_values = [distributions_mults[mult][l] for l in plot_divisors]\n",
+    "    plt.plot(list(range(L)), y_values, color=colors[mult], label=str(mult))\n",
+    "plt.plot(list(range(L)), var / np.max(var), label=\"cross-mult variance (normalized)\", ls=\"--\", lw=2, color=\"black\")\n",
+    "plt.xlabel(\"divisors\") \n",
+    "plt.ylabel(\"error probability\")\n",
+    "plt.xticks(list(range(L)), plot_divisors, rotation=90)\n",
+    "\n",
+    "plt.grid()\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/re.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b7fcd473-6cde-4913-9274-ff02f5ddb786",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plot_mults = [mult for mult in selected_mults if mult.klass not in (CombMultiplier, BGMWMultiplier)]\n",
+    "plot_divisors = selected_divisors\n",
+    "\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(plot_mults)))[i] for i,mult in enumerate(plot_mults)}\n",
+    "\n",
+    "fig = plt.subplots(figsize=(36, 12))\n",
+    "\n",
+    "L = len(plot_divisors)\n",
+    "N = len(plot_mults)\n",
+    "plot_divisors = sorted(plot_divisors)\n",
+    "vals = np.zeros((N, L))\n",
+    "for i, mult in enumerate(plot_mults):\n",
+    "    for j, m in enumerate(plot_divisors):\n",
+    "        y = distributions_mults[mult][m]\n",
+    "        vals[i, j] = y\n",
+    "var = np.var(vals, axis=0)\n",
+    "plt.plot(list(range(L)), var, label=\"cross-mult variance\", ls=\"--\", lw=2, color=\"black\")\n",
+    "\n",
+    "plt.xlabel(\"divisors\")\n",
+    "plt.ylabel(\"variance\")\n",
+    "plt.xticks(list(range(L)), plot_divisors, rotation=90)\n",
+    "\n",
+    "plt.grid()\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/cross_var.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8454cb7a-5308-43c6-9cd0-5de7946ec72a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# general_distributions = get_general_distributions(selected_divisors, bits, samples)\n",
+    "# general_n_distributions = get_general_n_distributions(selected_divisors, bits, 256, samples)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8eae8df8-0bf8-4a9d-a55e-deea6a9d6b07",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "selected_mults = all_mults#window_mults[0:1]+window_mults[5:6]+naf_mults[1:2]#[mult for mult in all_mults if not mult in comb_mults]\n",
+    "selected_divisors = all_divisors\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(distributions_mults_10k)))[i] for i,mult in enumerate(distributions_mults_10k)}\n",
+    "\n",
+    "\n",
+    "fig = plt.subplots(figsize =(36, 12)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "selected_divisors = sorted(selected_divisors)\n",
+    "for mult in distributions_mults_10k:\n",
+    "    y_values = [distributions_mults_10k[mult][l] for l in selected_divisors]\n",
+    "    plt.plot([l for l in range(L)],y_values,color = colors[mult], label = mult_label(mult))\n",
+    "\n",
+    "# mult = list(fixedwindow_dist.keys())[0]\n",
+    "# plt.plot([l for l in range(L)],[fixedwindow_dist[l] for l in selected_divisors],color = \"pink\", label = mult_label(mult))\n",
+    "\n",
+    "# measured_dist = measured_distribution(library,selected_divisors)\n",
+    "# mes_x, mes_y = [],[]\n",
+    "# for i,l in enumerate(selected_divisors):\n",
+    "#     if l in measured_dist:\n",
+    "#         mes_y.append(measured_dist[l])\n",
+    "#         mes_x.append(i)\n",
+    "# plt.scatter(mes_x,mes_y,color = \"black\", label = library)\n",
+    "\n",
+    "#attempts = 0\n",
+    "#fails =0\n",
+    "#for i in range(51):\n",
+    "#    with open(f\"cards/jcop/199_{i}.txt\") as f:\n",
+    "#        attempts += f.read().count(\"ALG_EC_SVDP_DH of remote pubkey and local privkey\")+1\n",
+    "#        fails += 1\n",
+    "#plt.scatter([selected_divisors.index(199)],[fails/attempts],s=[40],color = \"black\", label = \"jcop\")\n",
+    "\n",
+    "#plt.plot([l for l in range(L)],[general_distributions[l] for l in selected_divisors],color = \"black\", label = \"prime-distribution\")\n",
+    "\n",
+    "\n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/re.png\",dpi=300)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d240059f-9ed6-4864-b4bf-525de576272f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "selected_mults = with_precomputation\n",
+    "selected_divisors = all_divisors\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(selected_mults)))[i] for i,mult in enumerate(selected_mults)}\n",
+    "\n",
+    "\n",
+    "fig = plt.subplots(figsize =(24, 12)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "selected_divisors = sorted(selected_divisors)\n",
+    "for mult in selected_mults:\n",
+    "    plt.plot([l for l in range(L)],[distributions_mults_precomp[mult][l] for l in selected_divisors],color = colors[mult], label = mult_label(mult))\n",
+    "\n",
+    "\n",
+    "#measured_dist = measured_distribution(library,selected_divisors)\n",
+    "#mes_x, mes_y = [],[]\n",
+    "#for i,l in enumerate(selected_divisors):\n",
+    "#    if l in measured_dist:\n",
+    "#        mes_y.append(measured_dist[l])\n",
+    "#        mes_x.append(i)\n",
+    "#plt.scatter(mes_x,mes_y,color = \"black\", label = library)\n",
+    "\n",
+    "\n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.show() "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0da0eed4-a5dc-4dde-9bd1-8b519d02375e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def nok_ecdh(line):\n",
+    "    return int(line.split(\";\")[-1].strip(),16)==0\n",
+    "\n",
+    "def measured_distribution(library, selected_divisors):\n",
+    "    measured_distribution = {}\n",
+    "    counts = {order:0 for order in selected_divisors}\n",
+    "    for div in selected_divisors:\n",
+    "        errors = 0\n",
+    "        with open(f\"./ecdh/{library}/ecdh_{div}.txt\") as f:\n",
+    "            for line in f.readlines()[1:]:\n",
+    "                if nok_ecdh(line):\n",
+    "                    errors+=1\n",
+    "                counts[div]+=1\n",
+    "        measured_distribution[div] = errors\n",
+    "    \n",
+    "    for o,v in measured_distribution.items():\n",
+    "        if counts[o]!=0:\n",
+    "            measured_distribution[o] = v/counts[o]\n",
+    "    return measured_distribution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6f8b83e3-7e2e-409a-82bd-7d44316236c6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "selected_mults = other_mults[:1]+binary_mults[:1]+comb_mults[:1]+window_mults[:1]\n",
+    "selected_divisors = small_primes#all_divisors\n",
+    "library = \"tomcrypt\"\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(selected_mults)))[i] for i,mult in enumerate(selected_mults)}\n",
+    "\n",
+    "fig = plt.subplots(figsize =(24, 12)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "selected_divisors = sorted(selected_divisors)\n",
+    "for mult in selected_mults:\n",
+    "    plt.plot([l for l in range(L)],[distributions_mults[mult][l] for l in selected_divisors],color = colors[mult], label = mult_label(mult))\n",
+    "\n",
+    "\n",
+    "measured_dist = measured_distribution(library,selected_divisors)\n",
+    "mes_x, mes_y = [],[]\n",
+    "for i,l in enumerate(selected_divisors):\n",
+    "    if l in measured_dist:\n",
+    "        mes_y.append(measured_dist[l])\n",
+    "        mes_x.append(i)\n",
+    "plt.scatter(mes_x,mes_y,color = \"black\", label = library)\n",
+    "\n",
+    "\n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/{library}/re.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b7936e5b-76d2-410f-82b1-36333071bd12",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "selected_mults = [mult for mult in with_precomputation if mult in comb_mults]\n",
+    "selected_divisors = small_primes#all_divisors\n",
+    "library = \"mbedtls\"\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(selected_mults)))[i] for i,mult in enumerate(selected_mults)}\n",
+    "\n",
+    "fig = plt.subplots(figsize =(24, 12)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "selected_divisors = sorted(selected_divisors)\n",
+    "for mult in selected_mults:\n",
+    "    plt.plot([l for l in range(L)],[distributions_mults_precomp[mult][l] for l in selected_divisors],color = colors[mult], label = mult_label(mult))\n",
+    "\n",
+    "\n",
+    "measured_dist = measured_distribution(library,selected_divisors)\n",
+    "mes_x, mes_y = [],[]\n",
+    "for i,l in enumerate(selected_divisors):\n",
+    "    if l in measured_dist:\n",
+    "        mes_y.append(measured_dist[l])\n",
+    "        mes_x.append(i)\n",
+    "plt.scatter(mes_x,mes_y,color = \"black\", label = library)\n",
+    "\n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/{library}/re.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbdd0219-3937-4ef3-8cb3-b90f03af9977",
+   "metadata": {},
+   "source": [
+    "BouncyCastle\n",
+    " - WindowBooth-5?\n",
+    "\n",
+    "Mbedtls\n",
+    " - CombMultiplier-4\n",
+    " - confirmed in library\n",
+    "   \n",
+    "tomcrypt\n",
+    " - ladder or coron\n",
+    " - ladder confirmed in library\n",
+    "\n",
+    "OpenSSL, LibreSSL, Botan, Crypto++ and IPPCP followed the general distribution of divisibility by the primes. So they have some countermeasure.\n",
+    "\n",
+    "Note that some libraries for some orders output \"Invalid algorithm parameter: Not supported.\". For libcrypt, SunEC and Nettle it happened for all orders.\n",
+    "BoringSSL\n",
+    " - \"Invalid algorithm parameter: Error creating EC_GROUP, EC_GROUP_set_generator.\"\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "34609ae2-fa8c-4437-a601-cd25a0708a19",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def scatter(library, color):\n",
+    "    measured_dist = measured_distribution(library,selected_divisors)\n",
+    "    mes_x, mes_y = [],[]\n",
+    "    for i,l in enumerate(selected_divisors):\n",
+    "        if l in measured_dist:\n",
+    "            mes_y.append(measured_dist[l])\n",
+    "            mes_x.append(i)\n",
+    "    plt.scatter(mes_x,mes_y,color = color, label = library)\n",
+    "\n",
+    "selected_divisors = small_primes#all_divisors\n",
+    "\n",
+    "fig = plt.subplots(figsize =(24, 12)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "\n",
+    "colors = matplotlib.cm.tab20(range(6))\n",
+    "scatter(\"openssl\",colors[0])\n",
+    "scatter(\"libressl\",colors[1])\n",
+    "scatter(\"botan\",colors[2])\n",
+    "scatter(\"Crypto++\",colors[3])\n",
+    "scatter(\"ippcp\",colors[4])\n",
+    "\n",
+    "plt.plot([l for l in range(L)],[general_distributions[l] for l in selected_divisors],color = colors[5], label = \"prime-distribution\")\n",
+    "\n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/resistant.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1f403fa3-880d-45a8-aaf3-964b0fbc38d7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def scatter(library, color):\n",
+    "    measured_dist = measured_distribution(library,selected_divisors)\n",
+    "    mes_x, mes_y = [],[]\n",
+    "    for i,l in enumerate(selected_divisors):\n",
+    "        if l in measured_dist:\n",
+    "            mes_y.append(measured_dist[l])\n",
+    "            mes_x.append(i)\n",
+    "    # plt.scatter(mes_x,mes_y,color = color, label = library)\n",
+    "    plt.plot(mes_x,mes_y,color = color, linewidth = 1, label = library)\n",
+    "\n",
+    "selected_divisors = small_primes[:12]#all_divisors\n",
+    "\n",
+    "fig = plt.subplots(figsize =(10, 4)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "\n",
+    "colors = matplotlib.cm.tab20(range(9))\n",
+    "scatter(\"openssl\",colors[0])\n",
+    "scatter(\"libressl\",colors[1])\n",
+    "scatter(\"botan\",colors[2])\n",
+    "scatter(\"Crypto++\",colors[3])\n",
+    "scatter(\"mbedtls\",colors[4])\n",
+    "scatter(\"libressl\",colors[5])\n",
+    "scatter(\"BouncyCastle\",colors[6])\n",
+    "scatter(\"tomcrypt\",colors[7])\n",
+    "scatter(\"ippcp\",colors[8])\n",
+    "\n",
+    "\n",
+    "# plt.plot([l for l in range(L)],[general_distributions[l] for l in selected_divisors],color = colors[9], label = \"divison-distribution\")\n",
+    "\n",
+    "plt.xlabel('Input point order',fontsize=15) \n",
+    "plt.ylabel(\"Error rate\",fontsize=15) \n",
+    "plt.xticks([r for r in range(L)], [v if i%1==0 else \"\" for i,v in enumerate(selected_divisors)])\n",
+    "plt.legend(loc=\"center right\",prop={'size': 11})\n",
+    "plt.tight_layout()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/lib_dists.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a0415861-c9ee-4420-bb82-6fda216d401c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def bars(library, color,shift,width):\n",
+    "    measured_dist = measured_distribution(library,selected_divisors)\n",
+    "    mes_x, mes_y = [],[]\n",
+    "    for i,l in enumerate(selected_divisors):\n",
+    "        offset = width*shift\n",
+    "        if l in measured_dist:\n",
+    "            mes_y.append(measured_dist[l])\n",
+    "            mes_x.append(2*i+offset)\n",
+    "    plt.bar(mes_x,mes_y,width=0.1,color = color,align ='center', label = labels.get(library,library))\n",
+    "\n",
+    "selected_divisors = small_primes[:12]#all_divisors\n",
+    "\n",
+    "fig = plt.subplots(figsize =(10, 4)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "\n",
+    "colors = matplotlib.cm.tab20(range(9))\n",
+    "width = 0.2\n",
+    "for i,lib in enumerate((\"openssl\",\"libressl\",\"botan\",\"Crypto++\",\"mbedtls\",\"BouncyCastle\",\"tomcrypt\",\"ippcp\")):\n",
+    "    bars(lib,colors[i],i,width)\n",
+    "\n",
+    "\n",
+    "plt.plot([2*l+4*width for l in range(L)],[general_distributions[l] for l in selected_divisors],color = colors[8], label = \"expected distribution\")\n",
+    "\n",
+    "plt.xlabel('Input point order',fontsize=15) \n",
+    "plt.ylabel(\"Error rate\",fontsize=15) \n",
+    "plt.xticks([2*r+4*width for r in range(L)], [v if i%1==0 else \"\" for i,v in enumerate(selected_divisors)])\n",
+    "plt.legend(loc=\"upper right\",prop={'size': 11})\n",
+    "plt.tight_layout()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/lib_dists.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e5f036c8-3d47-4105-9a67-79b2b8e1ecdb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from math import sqrt\n",
+    "\n",
+    "selected_mults = all_mults#window_mults[0:1]+window_mults[5:6]+naf_mults[1:2]#[mult for mult in all_mults if not mult in comb_mults]\n",
+    "selected_divisors = small_primes#ll_divisors\n",
+    "colors = {mult:matplotlib.cm.tab20(range(len(selected_mults)))[i] for i,mult in enumerate(selected_mults)}\n",
+    "\n",
+    "\n",
+    "fig = plt.subplots(figsize =(30, 20)) \n",
+    "\n",
+    "L = len(selected_divisors)\n",
+    "selected_divisors = sorted(selected_divisors)\n",
+    "for mult in selected_mults:\n",
+    "    y_values,y_values_mstd, y_values_pstd = [],[],[]\n",
+    "    for l in selected_divisors:\n",
+    "        p = distributions_mults[mult][l]\n",
+    "        y_values.append(1/p)\n",
+    "        y_values_mstd.append(1/p-sqrt((1-p)/p**2))\n",
+    "        y_values_pstd.append(1/p+sqrt((1-p)/p**2))\n",
+    "    plt.plot([l for l in range(L)],y_values,color = colors[mult], label = mult_label(mult))\n",
+    "    plt.fill_between([l for l in range(L)], y_values_mstd , y_values_pstd, alpha = 0.1, color = colors[mult])\n",
+    "    \n",
+    "# mult = list(fixedwindow_dist.keys())[0]\n",
+    "# plt.plot([l for l in range(L)],[fixedwindow_dist[l] for l in selected_divisors],color = \"pink\", label = mult_label(mult))\n",
+    "\n",
+    "# measured_dist = measured_distribution(library,selected_divisors)\n",
+    "# mes_x, mes_y = [],[]\n",
+    "# for i,l in enumerate(selected_divisors):\n",
+    "#     if l in measured_dist:\n",
+    "#         mes_y.append(measured_dist[l])\n",
+    "#         mes_x.append(i)\n",
+    "# plt.scatter(mes_x,mes_y,color = \"black\", label = library)\n",
+    "\n",
+    "plt.plot([l for l in range(L)],[1/general_distributions[l] for l in selected_divisors],color = \"black\", label = \"prime-distribution\")\n",
+    "\n",
+    "steps_dist = {}\n",
+    "for i in range(51):\n",
+    "    with open(f\"cards/jcop/199_{i}.txt\") as f:\n",
+    "        steps = f.read().count(\"ALG_EC_SVDP_DH of remote pubkey and local privkey\")\n",
+    "    if not steps in steps_dist:\n",
+    "        steps_dist[steps] = 0\n",
+    "    steps_dist[steps]+=1\n",
+    "ys = sorted(list(steps_dist.keys()))\n",
+    "plt.scatter([selected_divisors.index(199)]*len(ys),ys, s=[steps_dist[y]*20 for y in ys],color=\"black\")\n",
+    "for i, y in enumerate(ys):\n",
+    "    plt.annotate(str(steps_dist[y]), (selected_divisors.index(199)-1, y))\n",
+    "avg = 0\n",
+    "for s,c in steps_dist.items():\n",
+    "    avg+=s*c\n",
+    "avg = avg/sum(steps_dist.values())\n",
+    "plt.scatter([selected_divisors.index(199)],[avg], s=[30],color=\"yellow\")\n",
+    "    \n",
+    "plt.xlabel('divisors') \n",
+    "plt.ylabel(\"prob\") \n",
+    "plt.yticks(range(12))\n",
+    "plt.xticks([r for r in range(L)], selected_divisors)\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.show() \n",
+    "fig[0].savefig(f\"graphs/re.png\",dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "37a64963-e63a-4c74-8414-6d29482e7151",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}