models/Isthmus_Bx_big_bang_model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical simulation for upper bound on dynamic blocksize expansion\n",
    "\n",
    "Mitchell / Isthmus - Sept 2018, updated Jan 2019\n",
    "\n",
    "## Abstract:\n",
    "\n",
    "The current bound on expansion of the Monero block(/chain) is that each block cannot be larger than the median size of the previous 100 blocks. Given the 2-minute block time, this means that the protocol has a few-hour memory, which performs well for most use cases and conditions. \n",
    "\n",
    "However, it is prudent to consider edge cases as well, and the current absence of medium or long-term memory comes with a significant risk. Under the current protocol, sustained high transaction volume (due to rapid adoption or a well-funded spammer) induces a rapid exponential increase in resource requirements (disk space, bandwidth, etc) that would exceed the capacities of the extant Monero infrastructure on the scale of hours\n",
    "\n",
    "This notebook quantifies the scale of damage in the worst-case-scenarios that could arise from overwhelming adoption or a deliberate spam attack. The current system (short-term memory only) is compared to two proposed mitigation strategies: a two point long/short-term memory, and an additive limit.\n",
    "\n",
    "## Background Reading:\n",
    "\n",
    "-  Jolly Mort's [Monero Dynamic Block Size and Dynamic Minimum Fee](https://github.com/JollyMort/monero-research/blob/master/Monero%20Dynamic%20Block%20Size%20and%20Dynamic%20Minimum%20Fee/Monero%20Dynamic%20Block%20Size%20and%20Dynamic%20Minimum%20Fee%20-%20DRAFT.md)\n",
    "-  ArticMine's [BitcoinTalk discussion](https://bitcointalk.org/index.php?topic=753252.msg13591241#msg13591241) about oversize block attacks.\n",
    "\n",
    "The topic of blockchain bloat has been discussed in many communities for many years. This notebook is not the first mention of the idea, it simply seeks to quantify the rate and scale of increasing resource demand, and test strategies proposed to protect the Monero cryptocurrency.\n",
    "\n",
    "## Risk:\n",
    "\n",
    "The block size can be maximized by any set of transactions in the memory pool whose:\n",
    "-  Net fee > coinbase\n",
    "-  Net size ~ 2*median(last 100 blocks)\n",
    "\n",
    "*Note: depending on assumptions about miner software and transaction selection methodology, a net fee of 4x coinbase may be necessary to induce a maximum-size block.*\n",
    "\n",
    "We'll consider \"Icarus adoption\" to be any scenario (whether benignly or maliciously induced) that causes a flood of transactions that increases resource requirements beyond the capacity of the Monero infrastructure (e.g. exceeding the disk space or bandwidth of most nodes and miners).\n",
    "\n",
    "## Result:\n",
    "\n",
    "Under the current system, the *block size* doubles every 51 blocks (i.e. doubling 14 times each day) indefinitely. The *blockchain size* doubles in less than a day and grows catastrophically large shortly thereafter.\n",
    "\n",
    "## Conclusions:\n",
    "\n",
    "Most cryptoeconomic schemes include fee/reward mechanisms designed to discourage undesired behavior from financially-rational parties under economic equilibrium conditions. However all protocols must include secondary fail-safe mechanisms to protect the network against literally \"overwhelming\" adoption and/or adversaries whose external agendas override economic motivations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "General state information about simulation and cost estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulation parameters\n",
    "initial_blocksize = 600 # kB # penalty-free up to 300 kB\n",
    "num_blocks_simulate = 36*30+1 # just over 36 hours\n",
    "current_blockchain_size_GB = 65 # GB\n",
    "circulating_supply = 16697487 # XMR\n",
    "\n",
    "# Economic parameters\n",
    "cost_of_1_XMR = 50 # EUR\n",
    "current_reward = 2 # XMR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the timescale and growth bound for two-point short/long term memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For 2-point short/long-term memory\n",
    "short_term_max_growth = 1.4 # multiplier\n",
    "short_term_memory = 100 # blocks\n",
    "long_term_max_growth = 50 # multiplier\n",
    "long_term_memory = 100000 # blocks\n",
    "\n",
    "# Make a note of the legend for figures\n",
    "LSTM_legend = '2-point memory: min['+str(short_term_max_growth)+'*M('+str(short_term_memory)+'), '+str(long_term_max_growth)+'*M('+str(long_term_memory)+')'+']'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the number of (exponentially-distributed) time scales to be used in the span multi-timescale memory model. For example, `index_offset = 7` and `index_set_size = 6` checks the growth in the last $2^7$ blocks, last $2^8$ blocks, ..., last $2^{13}$ blocks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For span memory (multi-timescale)\n",
    "index_offset = 7\n",
    "index_set_size = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the size for temporary fixed cap (not optimal solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "fixed_cap_kB = 5000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also model additive growth since this results in a linear expansion instead of exponential blowup. Set the maximum expansion per block."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "additive_allowance_kB = 300"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize with lowball estimate that last 100 blocks were 100 kB in size\n",
    "pre_length = max(100, long_term_memory, 2**(7+index_set_size))\n",
    "\n",
    "height_vector = list(range(-pre_length,num_blocks_simulate)) \n",
    "block_sizes = (pre_length+num_blocks_simulate)*[initial_blocksize] # For regular model\n",
    "block_sizes_LSTM = (pre_length+num_blocks_simulate)*[initial_blocksize] # For 2-point memory\n",
    "block_sizes_span = (pre_length+num_blocks_simulate)*[initial_blocksize] # For span memory\n",
    "block_sizes_cap = (pre_length+num_blocks_simulate)*[initial_blocksize] # For temporary cap\n",
    "block_sizes_add = (pre_length+num_blocks_simulate)*[initial_blocksize] # For additive approach\n",
    "block_sizes_ETH = (pre_length+num_blocks_simulate)*[initial_blocksize] # For additive approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run simulation\n",
    "Simulation loops over heights, and models three possible boundings:\n",
    "-  Short term memory only (current implementation)\n",
    "-  Two-point short/long-term memory\n",
    "-  Span memory, a generalization to more than 2 points/timescales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "LSTM_long_cap_triggered = (pre_length+num_blocks_simulate)*[0]\n",
    "\n",
    "for attack_block_num in range(pre_length, pre_length + num_blocks_simulate):\n",
    "        \n",
    "    # Model short-term memory (current method)\n",
    "    last_blocks = block_sizes[(attack_block_num-100):attack_block_num]\n",
    "    median_prev = np.median(last_blocks)\n",
    "    next_size = 2*median_prev\n",
    "    block_sizes[attack_block_num] = next_size\n",
    "    \n",
    "    # Model ETH\n",
    "    last_block_ETH = block_sizes_ETH[attack_block_num-1]\n",
    "    next_size_ETH = ((1+1/1024)**(120/15))*last_block_ETH\n",
    "    block_sizes_ETH[attack_block_num] = next_size_ETH\n",
    "    \n",
    "    # Model two-point short/long-term memory   \n",
    "    last_blocks_short = block_sizes_LSTM[(attack_block_num-short_term_memory):attack_block_num]\n",
    "    median_prev_short = np.median(last_blocks_short)\n",
    "    next_size_short = short_term_max_growth*median_prev_short\n",
    "    last_blocks_long = block_sizes_LSTM[(attack_block_num-long_term_memory):attack_block_num]\n",
    "    median_prev_long = np.median(last_blocks_long)\n",
    "    next_size_long = long_term_max_growth*median_prev_long\n",
    "    next_size_LSTM = min(next_size_short, next_size_long)\n",
    "    if next_size_long < next_size_short:\n",
    "        LSTM_long_cap_triggered[attack_block_num] = 1\n",
    "        # ^ Mark when we switch from short-limited growth to long-limited\n",
    "    block_sizes_LSTM[attack_block_num] = next_size_LSTM  \n",
    "    \n",
    "    # Model span multi-timescale memory\n",
    "    size_list = index_set_size*[np.inf]\n",
    "    c = 0\n",
    "    for k in range(index_offset, index_offset + index_set_size):\n",
    "        this_memory_len = 2**k\n",
    "        last_blocks_span = block_sizes_span[(attack_block_num-this_memory_len):attack_block_num]\n",
    "        median_prev_span = np.median(last_blocks_span) \n",
    "        this_B = (2+c/index_set_size)*median_prev_span\n",
    "        size_list[c] = this_B\n",
    "        c = c + 1\n",
    "    block_sizes_span[attack_block_num] = min(size_list)\n",
    "        \n",
    "    # Model cap\n",
    "    last_blocks_cap = block_sizes_cap[(attack_block_num-100):attack_block_num]\n",
    "    median_prev_cap = np.median(last_blocks_cap)\n",
    "    next_size_cap = min(2*median_prev_cap, fixed_cap_kB)\n",
    "    block_sizes_cap[attack_block_num] = next_size_cap\n",
    "    \n",
    "    # Model additive\n",
    "    last_blocks_add = block_sizes_add[(attack_block_num-100):attack_block_num]\n",
    "    median_prev_add = np.median(last_blocks_add)\n",
    "    next_size_add = median_prev_add + additive_allowance_kB\n",
    "    block_sizes_add[attack_block_num] = next_size_add\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Block size increase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5.5,3))\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(height_vector, block_sizes,'r', label='Original method: 2x every 100 blocks')\n",
    "plt.plot(height_vector, block_sizes_add,'g', label = 'Additive limit: ' + str(additive_allowance_kB) + ' kB increase per block')\n",
    "#plt.plot(height_vector, block_sizes_LSTM,'c', label = LSTM_legend)\n",
    "plt.plot(height_vector, block_sizes_ETH,'b', label = 'x(1+1/1024) each block')\n",
    "plt.set_yscale = 'log'\n",
    "plt.xlabel('time (blocks)', fontsize='12')\n",
    "plt.ylabel('blocksize (kB)',  fontsize='12')\n",
    "plt.title('Block size limit (kB)',  fontsize='18')\n",
    "plt.grid(True)\n",
    "ax.legend(loc='best', fontsize='10')\n",
    "ax.set_xlim(0, num_blocks_simulate)\n",
    "ax.set_yscale('log')\n",
    "#ax.set_ylim(1,block_sizes[num_blocks_simulate])\n",
    "ax.set_ylim(1e2,1e6)\n",
    "plt.xticks(size = 12)\n",
    "plt.yticks(size = 12)\n",
    "#plt.text(200, 2, 'Isthmus', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Blockchain size bloat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5.5,3))\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(height_vector, current_blockchain_size_GB + np.cumsum(block_sizes)/1e6,'r', label='Original method: 2x every 100 blocks')\n",
    "plt.plot(height_vector, current_blockchain_size_GB + np.cumsum(block_sizes_add)/1e6,'g',  label = 'Additive limit: ' + str(additive_allowance_kB) + ' kB increase per block')\n",
    "plt.plot(height_vector, current_blockchain_size_GB + np.cumsum(block_sizes_ETH)/1e6,'b',  label = 'x(1+1/1024) each block')\n",
    "# plt.plot(height_vector, current_blockchain_size_GB + np.cumsum(block_sizes_LSTM)/1e6,'c', label = LSTM_legend)\n",
    "plt.set_yscale = 'log'\n",
    "plt.xlabel('time (blocks)', fontsize='12')\n",
    "plt.ylabel('Blockchain size (GB)',  fontsize='12')\n",
    "plt.title('Blockchain size limit (GB)',  fontsize='18')\n",
    "plt.grid(True)\n",
    "ax.legend(loc='best', fontsize='10')\n",
    "ax.set_xlim(0, num_blocks_simulate)\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([65,1e3])\n",
    "plt.xticks(size = 12)\n",
    "plt.yticks(size = 12)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cost analysis (GB bloat per €)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5))\n",
    "ax = fig.add_subplot(111)\n",
    "cost_vector = [h*(cost_of_1_XMR*current_reward) for h in height_vector]\n",
    "cum_curr_GB =  current_blockchain_size_GB + np.cumsum(block_sizes)/1e6;\n",
    "plt.plot(cost_vector, current_blockchain_size_GB + np.cumsum(block_sizes)/1e6,'r', label='Curent method: 2x every 100 blocks')\n",
    "plt.plot(cost_vector, current_blockchain_size_GB + np.cumsum(block_sizes_add)/1e6, 'g', label = 'Additive limit: ' + str(additive_allowance_kB) + ' kB increase per block')\n",
    "plt.plot(cost_vector, current_blockchain_size_GB + np.cumsum(block_sizes_ETH)/1e6,'b', label = 'x(1+1/1024) each block')\n",
    "\n",
    "plt.xlabel('Net budget (EUR)', fontsize='12')\n",
    "plt.ylabel('Blockchain size (GB)',  fontsize='12')\n",
    "plt.set_yscale = 'log'\n",
    "plt.title('Net fees (GB bloat per €)',  fontsize='18')\n",
    "plt.grid(True)\n",
    "ax.legend(loc='best', fontsize='10')\n",
    "ax.set_xlim(1, max(cost_vector))\n",
    "ax.set_ylim(65,1e5)\n",
    "ax.set_yscale('log')\n",
    "plt.xticks(size = 12)\n",
    "plt.yticks(size = 12)\n",
    "#plt.text(20000, 100, 'Isthmus', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check out some key times, sizes, costs\n",
    "This is a bunch of verbose text output, if desired. Commented out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "*************************\n",
      "At the end of the 6th hour:\n",
      "-\n",
      "# Current algorithm\n",
      "Blocksize = 9600.0 kB\n",
      ">>> Blockchain size = 65.6978 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 2304.9599999999996 kB\n",
      "Blockchain size = 65.25064256 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 1400.0 kB\n",
      "Blockchain size = 65.2328 GB\n",
      "-\n",
      "# Additive cap\n",
      "300 kB additive allowance\n",
      "Blocksize = 1800.0 kB\n",
      "Blockchain size = 65.2331 GB\n",
      "-\n",
      "Net fees ~ 360 XMR\n",
      "Net fees ~ 18000 EUR\n",
      "stake ~ 0.002%\n",
      "\n",
      "*************************\n",
      "At the end of the 12th hour:\n",
      "-\n",
      "# Current algorithm\n",
      "Blocksize = 153600.0 kB\n",
      ">>> Blockchain size = 73.6946 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 8854.734335999996 kB\n",
      "Blockchain size = 66.06941598310401 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 1500.0 kB\n",
      "Blockchain size = 65.4952 GB\n",
      "-\n",
      "# Additive cap\n",
      "300 kB additive allowance\n",
      "Blocksize = 3000.0 kB\n",
      "Blockchain size = 65.6558 GB\n",
      "-\n",
      "Net fees ~ 720 XMR\n",
      "Net fees ~ 36000 EUR\n",
      "stake ~ 0.004%\n",
      "\n",
      "*************************\n",
      "At the end of the 18th hour:\n",
      "-\n",
      "# Current algorithm\n",
      "Blocksize = 1228800.0 kB\n",
      ">>> Blockchain size = 170.0018 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 24297.39101798398 kB\n",
      "Blockchain size = 68.81190430164992 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 1600.0 kB\n",
      "Blockchain size = 65.768 GB\n",
      "-\n",
      "# Additive cap\n",
      "300 kB additive allowance\n",
      "Blocksize = 3900.0 kB\n",
      "Blockchain size = 66.27275 GB\n",
      "-\n",
      "Net fees ~ 1080 XMR\n",
      "Net fees ~ 54000 EUR\n",
      "stake ~ 0.006%\n",
      "\n",
      "*************************\n",
      "At the end of the 24th hour:\n",
      "-\n",
      "# Current algorithm\n",
      "Blocksize = 19660800.0 kB\n",
      ">>> Blockchain size = 1313.4002 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 30000.0 kB\n",
      "Blockchain size = 74.12966967671738 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 1600.0 kB\n",
      "Blockchain size = 66.056 GB\n",
      "-\n",
      "# Additive cap\n",
      "300 kB additive allowance\n",
      "Blocksize = 5100.0 kB\n",
      "Blockchain size = 67.08125 GB\n",
      "-\n",
      "Net fees ~ 1440 XMR\n",
      "Net fees ~ 72000 EUR\n",
      "stake ~ 0.009000000000000001%\n",
      "\n",
      "*************************\n",
      "At the end of the 36th hour:\n",
      "-\n",
      "# Current algorithm\n",
      "Blocksize = 2516582400.0 kB\n",
      ">>> Blockchain size = 176225.7074 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 30000.0 kB\n",
      "Blockchain size = 84.92966967671738 GB\n",
      "-\n",
      "# Two-point short/long-term algorithm\n",
      "Blocksize = 1700.0 kB\n",
      "Blockchain size = 66.6376 GB\n",
      "-\n",
      "# Additive cap\n",
      "300 kB additive allowance\n",
      "Blocksize = 7200.0 kB\n",
      "Blockchain size = 69.27635 GB\n",
      "-\n",
      "Net fees ~ 2160 XMR\n",
      "Net fees ~ 108000 EUR\n",
      "stake ~ 0.013%\n"
     ]
    }
   ],
   "source": [
    "skip_me = 0\n",
    "\n",
    "if skip_me < 1:\n",
    "#    time_dict = {30: '1st hour', 9*30:'9th hour', 18*30:'18th hour', 24*30:'1st day', 36*30:'36th hour', 2*24*30:'2nd day', 7*24*30:'1st week'}\n",
    "    time_dict = {6*30: '6', 12*30:'12', 18*30:'18', 24*30:'24', 36*30:'36'}\n",
    "\n",
    "    for time_in_blocks in time_dict:\n",
    "        print('\\n' + 25*'*')\n",
    "        print('At the end of the ' + time_dict[time_in_blocks] + 'th hour:')\n",
    "        print('-')\n",
    "        print('# Current algorithm')\n",
    "        print('Blocksize = ' + str(block_sizes[pre_length + time_in_blocks]) + ' kB')\n",
    "        print('>>> Blockchain size = ' + str(current_blockchain_size_GB + sum(block_sizes[pre_length:(pre_length + time_in_blocks)])/1e6) + ' GB')\n",
    "        print('-')\n",
    "        \n",
    "        print('# Two-point short/long-term algorithm')\n",
    "        print('Blocksize = ' + str(block_sizes_LSTM[pre_length + time_in_blocks]) + ' kB')\n",
    "        print('Blockchain size = ' + str(current_blockchain_size_GB + sum(block_sizes_LSTM[pre_length:(pre_length + time_in_blocks)])/1e6) + ' GB')\n",
    "        print('-')\n",
    "        print('# Two-point short/long-term algorithm')\n",
    "        print('Blocksize = ' + str(block_sizes_span[pre_length + time_in_blocks]) + ' kB')\n",
    "        print('Blockchain size = ' + str(current_blockchain_size_GB + sum(block_sizes_span[pre_length:(pre_length + time_in_blocks)])/1e6) + ' GB')\n",
    "        print('-')        \n",
    "        \n",
    "        print('# Additive cap')\n",
    "        print(str(additive_allowance_kB) + ' kB additive allowance')\n",
    "        print('Blocksize = ' + str(block_sizes_add[pre_length + time_in_blocks]) + ' kB')\n",
    "        print('Blockchain size = ' + str(current_blockchain_size_GB + sum(block_sizes_add[pre_length:(pre_length + time_in_blocks)])/1e6) + ' GB')\n",
    "        print('-')\n",
    "        \n",
    "        # print('# Hard cap')\n",
    "        # print(str(fixed_cap_kB) + ' kB hard cap')\n",
    "        # print('Blocksize = ' + str(block_sizes_cap[pre_length + time_in_blocks]) + ' kB')\n",
    "        # print('Blockchain size = ' + str(current_blockchain_size_GB + sum(block_sizes_cap[pre_length:(pre_length + time_in_blocks)])/1e6) + ' GB')\n",
    "        # print('-')\n",
    "         \n",
    "        print('Net fees ~ ' + str(current_reward*time_in_blocks) + ' XMR')\n",
    "        print('Net fees ~ ' + str(cost_of_1_XMR*current_reward*time_in_blocks) + ' EUR')\n",
    "        print('stake ~ ' + str(round(current_reward*time_in_blocks/circulating_supply,5)*100) + '%')\n"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## Observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Icarus adoption could blast the Monero blocksize to 10 TB in less than 2 days. If the attack started Friday evening, almost all full nodes would be knocked off the network before Monday morning. See [The Ethereum-blockchain size has exceeded 1TB, and yes, it’s an issue](https://hackernoon.com/the-ethereum-blockchain-size-has-exceeded-1tb-and-yes-its-an-issue-2b650b5f4f62) for more discussion of this topic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## FAQ\n",
    "\n",
    "Q: Won't miners voluntarily avoid mining large blocks?\n",
    "\n",
    "A1: The timescale of this attack can be mind-bogglingly FAST! In 36 hours, the blockchain explodes to 30 TB. To stop an in-progress attack, it would be necessary to modify major mining and pool software, and roll out updates across the ecosystem and dozens of platforms. The permanent damage would be on the order of tens of terabytes, even if every Monero engineer mobilized instantly with deft DevOps ability. I don't know if every random botnet operator is going to be following Reddit 24/7 and race to fix their mining pools in the middle of the night.\n",
    "\n",
    "A2: Voluntarily avoiding large blocks means voluntarily mining blocks with less profit. Some software/people are greedy.\n",
    "\n",
    "A3: Cryptocurrencies are designed to be resistant to block censorship, so any ideas to have the nodes or users reject large blocks will run into a lot of practical issues.\n",
    "\n",
    "--- \n",
    "Q: Why would somebody do this intentionally? Isn't this more expensive than a 51% attack?\n",
    "\n",
    "A1: A 51% is a totally different threat/consequence model. The blockchain big bang knocks nodes off the network, leaves permanent scars in the blockchain, and wreaks obvious major havoc in everybody's face with severe service disruptions. In contrast, a 51% attack on Monero is totally unnoticable to the rest of the ecosystem, causing no disruption to Monero's services, network, or community. \n",
    "\n",
    "A2: While the two attacks may cost the same *on paper*, there is a big logistical difference. Converting 200,000 EUR into purchasing half of the mining equipment / hashrate in the world is a huge endeavor. Converting 200,000 EUR into a blockchain big bang spam attack requires a few hours of coding open source software, and a laptop.\n",
    "\n",
    "---\n",
    "Q: We need a dynamic blocksize! What about an influx of legitimate transactions?\n",
    "\n",
    "A: We will definitely not remove dynamic blocksizes. Dynamic protocols can be designed to allow short-term flexibility without having to allow unbounded extremes.\n",
    "\n",
    "Temporary high fees are better than a permanantly-broken network.\n",
    "\n",
    "---\n",
    "Q: What happens if we implement an upper bound, but no adoption/attacks ever cause the upper limit to be triggered?\n",
    "\n",
    "A: That's an ideal outcome! In systems handling large amounts of money, it's better to be safe than sorry - properly implementing safeguards are always better than leaving any feature or process unbounded and up to fate. \n",
    "\n",
    "--- \n",
    "Q: How can we possibly adjust the blocksize algorithm?\n",
    "\n",
    "A: The current block size algorithm should be subject to improvement just like every other aspect of the cryptocurrency. Belief that the first iteration of any system is perfect tends to be limiting, and often dangerous if it preserves vulnerabilities. \n",
    "\n",
    "---\n",
    "Q: Isn't this a pretty big decision?\n",
    "\n",
    "A: **YES, absolutely**. The discussion and development of mitigation strategies must include many different facets of the community - software engineers, economists, researchers, modelers, designers of the current algorithm, etc. This is a big undertaking that must be done deliberately. Each different strategy (or lack of one!) entails different consequences, and we must work together to make sure the community's solution does not introduce other issues / edge cases with financial incentives around mining, fees, etc. \n",
    "\n",
    "We should avoid both non-action and careless action.\n",
    "\n",
    "---\n",
    "Q: Have you thought about XXX mitigation strategy?\n",
    "\n",
    "A: Not yet, so please share your ideas with us in Noncesense Research Lab ([website](https://noncesense-research-lab.github.io/), [IRC](https://www.irccloud.com/invite?channel=%23noncesense-research-lab&hostname=chat.freenode.net&port=6697&ssl=1)) or the Monero Research Lab ([website](https://www.getmonero.org/resources/research-lab/), [IRC](https://www.irccloud.com/invite?channel=%23monero-research-lab&hostname=chat.freenode.net&port=6697&ssl=1))"
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  }
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