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LeakLWE2
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Fork of the official github repository of the framework Leaky-LWE-Estimator, a Sage Toolkit to attack and estimate the hardness of LWE with Side Information. https://github.com/lducas/leaky-LWE-Estimator
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LeakLWE2/Sec6_applications/TEST.ipynb

TEST.ipynb 55KB
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  1. {

  2.  "cells": [

  3.   {

  4.    "cell_type": "code",

  5.    "execution_count": 1,

  6.    "metadata": {},

  7.    "outputs": [],

  8.    "source": [

  9.     "load(\"../framework/instance_gen.sage\")"

  10.    ]

  11.   },

  12.   {

  13.    "cell_type": "code",

  14.    "execution_count": 2,

  15.    "metadata": {},

  16.    "outputs": [

  17.     {

  18.      "name": "stdout",

  19.      "output_type": "stream",

  20.      "text": [

  21.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  22.       "\u001b[1;33m n= 70 \t m= 70 \t q=3301 \u001b[0m\n",

  23.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  24.       "\u001b[1;33m dim=141 \t δ=1.012362 \t β=45.40  \u001b[0m\n",

  25.       "\u001b[0m  \u001b[0m\n"

  26.      ]

  27.     }

  28.    ],

  29.    "source": [

  30.     "n = 70\n",

  31.     "m = n\n",

  32.     "q = 3301\n",

  33.     "D_s = build_centered_binomial_law(40)\n",

  34.     "D_e = D_s\n",

  35.     "A, b, dbdd = initialize_from_LWE_instance(DBDD, n, q, m, D_e, D_s)\n",

  36.     "# In such parameter range, no need to integrate q-vectors\n",

  37.     "beta, delta = dbdd.estimate_attack()"

  38.    ]

  39.   },

  40.   {

  41.    "cell_type": "code",

  42.    "execution_count": 14,

  43.    "metadata": {},

  44.    "outputs": [

  45.     {

  46.      "name": "stdout",

  47.      "output_type": "stream",

  48.      "text": [

  49.       "\u001b[4;37m       Running the Attack      \u001b[0m\n",

  50.       "1\n"

  51.      ]

  52.     },

  53.     {

  54.      "ename": "ValueError",

  55.      "evalue": "Float type 'ld' not understood.",

  56.      "output_type": "error",

  57.      "traceback": [

  58.       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",

  59.       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",

  60.       "\u001b[0;32m<ipython-input-14-b4e7e86f62fe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msecret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",

  61.       "\u001b[0;32m<string>\u001b[0m in \u001b[0;36mattack\u001b[0;34m(self, beta_max, beta_pre, randomize, tours)\u001b[0m\n",

  62.       "\u001b[0;32msrc/fpylll/fplll/gso.pyx\u001b[0m in \u001b[0;36mfpylll.fplll.gso.MatGSO.__init__\u001b[0;34m()\u001b[0m\n",

  63.       "\u001b[0;31mValueError\u001b[0m: Float type 'ld' not understood."

  64.      ]

  65.     }

  66.    ],

  67.    "source": [

  68.     "secret = dbdd.attack()"

  69.    ]

  70.   },

  71.   {

  72.    "cell_type": "code",

  73.    "execution_count": 3,

  74.    "metadata": {},

  75.    "outputs": [

  76.     {

  77.      "data": {

  78.       "text/plain": [

  79.        "(17, -12, 9, -15)"

  80.       ]

  81.      },

  82.      "execution_count": 3,

  83.      "metadata": {},

  84.      "output_type": "execute_result"

  85.     }

  86.    ],

  87.    "source": [

  88.     "# Simulating perfect hints\n",

  89.     "v0 = vec([randint(0, 1) for i in range(m + n)])\n",

  90.     "v1 = vec([randint(0, 1) for i in range(m + n)])\n",

  91.     "v2 = vec([randint(0, 1) for i in range(m + n)])\n",

  92.     "v3 = vec([randint(0, 1) for i in range(m + n)]) \n",

  93.     "# Computing l = <vi, s>\n",

  94.     "dbdd.leak(v0), dbdd.leak(v1), dbdd.leak(v2), dbdd.leak(v3)"

  95.    ]

  96.   },

  97.   {

  98.    "cell_type": "code",

  99.    "execution_count": 4,

  100.    "metadata": {},

  101.    "outputs": [

  102.     {

  103.      "name": "stdout",

  104.      "output_type": "stream",

  105.      "text": [

  106.       "\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=140, δ=1.01252495, β=41.94 \u001b[0m\n",

  107.       "\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=139, δ=1.01275154, β=38.44 \u001b[0m\n",

  108.       "\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=138, δ=1.01293762, β=34.79 \u001b[0m\n",

  109.       "\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01314871, β=30.92 \u001b[0m\n"

  110.      ]

  111.     }

  112.    ],

  113.    "source": [

  114.     "_ = dbdd.integrate_perfect_hint(v0, 25) \n",

  115.     "_ = dbdd.integrate_perfect_hint(v1, 12) \n",

  116.     "_ = dbdd.integrate_perfect_hint(v2, -14) \n",

  117.     "_ = dbdd.integrate_perfect_hint(v3, -3)"

  118.    ]

  119.   },

  120.   {

  121.    "cell_type": "code",

  122.    "execution_count": 5,

  123.    "metadata": {},

  124.    "outputs": [

  125.     {

  126.      "data": {

  127.       "text/plain": [

  128.        "(1, 1, 0, 3)"

  129.       ]

  130.      },

  131.      "execution_count": 5,

  132.      "metadata": {},

  133.      "output_type": "execute_result"

  134.     }

  135.    ],

  136.    "source": [

  137.     "# Simulating modular hints\n",

  138.     "v0 = vec([randint(0, 1) for i in range(m + n)])\n",

  139.     "v1 = vec([randint(0, 1) for i in range(m + n)])\n",

  140.     "v2 = vec([randint(0, 1) for i in range(m + n)])\n",

  141.     "v3 = vec([randint(0, 1) for i in range(m + n)]) \n",

  142.     "# Computing l = <vi, s> mod k\n",

  143.     "dbdd.leak(v0)%2, dbdd.leak(v1)%3, dbdd.leak(v2)%4, dbdd.leak(v3)%5"

  144.    ]

  145.   },

  146.   {

  147.    "cell_type": "code",

  148.    "execution_count": 6,

  149.    "metadata": {},

  150.    "outputs": [

  151.     {

  152.      "name": "stdout",

  153.      "output_type": "stream",

  154.      "text": [

  155.       "\u001b[1;37m integrate modular hint \u001b[0m \u001b[0m (smooth) \u001b[0m "

  156.      ]

  157.     },

  158.     {

  159.      "ename": "NotImplementedError",

  160.      "evalue": "",

  161.      "output_type": "error",

  162.      "traceback": [

  163.       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",

  164.       "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",

  165.       "\u001b[0;32m<ipython-input-6-0bba940b5cde>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Integrate modular hints\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",

  166.       "\u001b[0;32m<string>\u001b[0m in \u001b[0;36mdecorated\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n",

  167.       "\u001b[0;32m<string>\u001b[0m in \u001b[0;36mdecorated\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n",

  168.       "\u001b[0;32m<string>\u001b[0m in \u001b[0;36mintegrate_modular_hint\u001b[0;34m(self, v, l, k, smooth)\u001b[0m\n",

  169.       "\u001b[0;31mNotImplementedError\u001b[0m: "

  170.      ]

  171.     }

  172.    ],

  173.    "source": [

  174.     "# Integrate modular hints\n",

  175.     "_ = dbdd.integrate_modular_hint(v0, 1, 2, False) \n",

  176.     "_ = dbdd.integrate_modular_hint(v1, 1, 3, True)\n",

  177.     "_ = dbdd.integrate_modular_hint(v2, 0, 4, True) \n",

  178.     "_ = dbdd.integrate_modular_hint(v3, 3, 5, True)"

  179.    ]

  180.   },

  181.   {

  182.    "cell_type": "code",

  183.    "execution_count": 19,

  184.    "metadata": {},

  185.    "outputs": [

  186.     {

  187.      "data": {

  188.       "text/plain": [

  189.        "(-5, 24, 9, 54)"

  190.       ]

  191.      },

  192.      "execution_count": 19,

  193.      "metadata": {},

  194.      "output_type": "execute_result"

  195.     }

  196.    ],

  197.    "source": [

  198.     "# Simulating approximate hints\n",

  199.     "v0 = vec([randint(0, 1) for i in range(m + n)])\n",

  200.     "v1 = vec([randint(0, 1) for i in range(m + n)])\n",

  201.     "v2 = vec([randint(0, 1) for i in range(m + n)])\n",

  202.     "v3 = vec([randint(0, 1) for i in range(m + n)]) \n",

  203.     "# Computing l = <vi, s> + noise\n",

  204.     "dbdd.leak(v0) + 2, dbdd.leak(v1) + 1, dbdd.leak(v2) - 1, dbdd.leak(v3)"

  205.    ]

  206.   },

  207.   {

  208.    "cell_type": "code",

  209.    "execution_count": 20,

  210.    "metadata": {},

  211.    "outputs": [

  212.     {

  213.      "name": "stdout",

  214.      "output_type": "stream",

  215.      "text": [

  216.       "\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01334785, β=26.99 \u001b[0m\n",

  217.       "\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01342129, β=25.49 \u001b[0m\n",

  218.       "\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01350341, β=24.44 \u001b[0m\n",

  219.       "\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01362755, β=23.65 \u001b[0m\n"

  220.      ]

  221.     }

  222.    ],

  223.    "source": [

  224.     "# Integrate approximate hints\n",

  225.     "var = 10\n",

  226.     "_ = dbdd.integrate_approx_hint(v0, -5, var, aposteriori=False) \n",

  227.     "_ = dbdd.integrate_approx_hint(v1, 24, var, aposteriori=False) \n",

  228.     "_ = dbdd.integrate_approx_hint(v2, 9, var, aposteriori=False) \n",

  229.     "_ = dbdd.integrate_approx_hint(v3, 54, var, aposteriori=False)"

  230.    ]

  231.   },

  232.   {

  233.    "cell_type": "code",

  234.    "execution_count": 21,

  235.    "metadata": {},

  236.    "outputs": [

  237.     {

  238.      "name": "stdout",

  239.      "output_type": "stream",

  240.      "text": [

  241.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  242.       "\u001b[1;33m dim=137 \t δ=1.013628 \t β=23.65  \u001b[0m\n",

  243.       "\u001b[0m  \u001b[0m\n",

  244.       "\u001b[4;37m       Running the Attack      \u001b[0m\n",

  245.       "1\n"

  246.      ]

  247.     },

  248.     {

  249.      "ename": "ValueError",

  250.      "evalue": "Float type 'ld' not understood.",

  251.      "output_type": "error",

  252.      "traceback": [

  253.       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",

  254.       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",

  255.       "\u001b[0;32m<ipython-input-21-7c2ddea6b769>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdelta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_attack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0msecret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",

  256.       "\u001b[0;32m<string>\u001b[0m in \u001b[0;36mattack\u001b[0;34m(self, beta_max, beta_pre, randomize, tours)\u001b[0m\n",

  257.       "\u001b[0;32msrc/fpylll/fplll/gso.pyx\u001b[0m in \u001b[0;36mfpylll.fplll.gso.MatGSO.__init__\u001b[0;34m()\u001b[0m\n",

  258.       "\u001b[0;31mValueError\u001b[0m: Float type 'ld' not understood."

  259.      ]

  260.     }

  261.    ],

  262.    "source": [

  263.     "beta, delta = dbdd.estimate_attack()\n",

  264.     "secret = dbdd.attack()"

  265.    ]

  266.   },

  267.   {

  268.    "cell_type": "code",

  269.    "execution_count": 23,

  270.    "metadata": {},

  271.    "outputs": [

  272.     {

  273.      "name": "stdout",

  274.      "output_type": "stream",

  275.      "text": [

  276.       "\u001b[0m --- Demonstration mode (no averaging) --- \u001b[0m\n",

  277.       "\u001b[0m Set of parameters: CCS1 \u001b[0m\n",

  278.       "\u001b[4;37m Attack without hints:  268.83 bikz \u001b[0m\n",

  279.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  280.       "\u001b[1;33m n=352 \t m=352 \t q=2048 \u001b[0m\n",

  281.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = -1.047495308214138 + χ(σ²=0.074) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00520912, β=268.64 \u001b[0m\n",

  282.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00533686, β=258.80 \u001b[0m\n",

  283.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -1.047495308214138 + χ(σ²=0.074) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00547581, β=248.73 \u001b[0m\n",

  284.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00560729, β=239.71 \u001b[0m\n",

  285.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00573966, β=231.20 \u001b[0m\n",

  286.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00587017, β=223.15 \u001b[0m\n",

  287.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00600691, β=214.98 \u001b[0m\n",

  288.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00613813, β=207.71 \u001b[0m\n",

  289.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u351 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00614016, β=207.61 \u001b[0m\n",

  290.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  291.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c703 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=704, δ=1.00614274, β=207.50 \u001b[0m\n",

  292.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c653 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=654, δ=1.00623802, β=202.43 \u001b[0m\n",

  293.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c603 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=604, δ=1.00629226, β=199.59 \u001b[0m\n",

  294.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  295.       "\u001b[3;34m ln(dvol)=2229.2964391 \t ln(Bvol)=1761.2869858 \t ln(Svol)=-936.0189067 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  296.       "\u001b[1;33m dim=584 \t δ=1.006299 \t β=199.30  \u001b[0m\n",

  297.       "\u001b[0m  \u001b[0m\n",

  298.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  299.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=517 \t delta=1.007041 \t beta=165.65 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.784776775862473 \u001b[0m\n",

  300.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=449 \t delta=1.008001 \t beta=132.43 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.615874587933098 \u001b[0m\n",

  301.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=374 \t delta=1.009401 \t beta=96.94 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.227714429544019 \u001b[0m\n",

  302.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=295 \t delta=1.011563 \t beta=58.46 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.0417737457149379 \u001b[0m\n",

  303.       "\u001b[0m Set of parameters: CCS2 \u001b[0m\n",

  304.       "\u001b[4;37m Attack without hints:  447.85 bikz \u001b[0m\n",

  305.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  306.       "\u001b[1;33m n=592 \t m=592 \t q=4096 \u001b[0m\n",

  307.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00368084, β=447.74 \u001b[0m\n",

  308.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.146460874616214 + χ(σ²=0.127) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00376168, β=434.18 \u001b[0m\n",

  309.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00383428, β=422.44 \u001b[0m\n",

  310.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00391176, β=410.48 \u001b[0m\n",

  311.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00398557, β=399.57 \u001b[0m\n",

  312.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00406105, β=388.84 \u001b[0m\n",

  313.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00412447, β=380.28 \u001b[0m\n",

  314.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00419601, β=370.82 \u001b[0m\n",

  315.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00426402, β=362.29 \u001b[0m\n",

  316.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00433281, β=353.83 \u001b[0m\n",

  317.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.146460874616214 + χ(σ²=0.127) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00440385, β=345.52 \u001b[0m\n",

  318.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00447868, β=337.11 \u001b[0m\n",

  319.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u591 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00453370, β=331.08 \u001b[0m\n",

  320.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  321.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1183 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1184, δ=1.00453416, β=330.92 \u001b[0m\n",

  322.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1133 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1134, δ=1.00460786, β=323.20 \u001b[0m\n",

  323.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1083 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1084, δ=1.00467681, β=316.15 \u001b[0m\n",

  324.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1033 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1034, δ=1.00473859, β=309.91 \u001b[0m\n",

  325.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c983 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=984, δ=1.00479311, β=304.69 \u001b[0m\n",

  326.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c933 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=934, δ=1.00483487, β=300.74 \u001b[0m\n",

  327.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c883 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=884, δ=1.00485996, β=298.46 \u001b[0m\n",

  328.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  329.       "\u001b[3;34m ln(dvol)=3529.6911796 \t ln(Bvol)=2195.8902680 \t ln(Svol)=-2667.6018232 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  330.       "\u001b[1;33m dim=857 \t δ=1.004864 \t β=298.11  \u001b[0m\n",

  331.       "\u001b[0m  \u001b[0m\n",

  332.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  333.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=804 \t delta=1.005161 \t beta=272.46 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.986359509012097 \u001b[0m\n",

  334.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=750 \t delta=1.005502 \t beta=247.03 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.972905081018585 \u001b[0m\n",

  335.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=696 \t delta=1.005890 \t beta=221.82 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.959634178028866 \u001b[0m\n",

  336.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=642 \t delta=1.006345 \t beta=196.85 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.946544296671780 \u001b[0m\n",

  337.       "\u001b[0m Set of parameters: CCS3 \u001b[0m\n",

  338.       "\u001b[4;37m Attack without hints:  491.98 bikz \u001b[0m\n"

  339.      ]

  340.     },

  341.     {

  342.      "name": "stdout",

  343.      "output_type": "stream",

  344.      "text": [

  345.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  346.       "\u001b[1;33m n=752 \t m=752 \t q=32768 \u001b[0m\n",

  347.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = -2.187046263345110 + χ(σ²=0.163) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1505, δ=1.00344395, β=491.89 \u001b[0m\n",

  348.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1505, δ=1.00349544, β=481.73 \u001b[0m\n",

  349.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00354986, β=471.38 \u001b[0m\n",

  350.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00359717, β=462.61 \u001b[0m\n",

  351.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00363783, β=455.33 \u001b[0m\n",

  352.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00369078, β=445.99 \u001b[0m\n",

  353.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 1.604094165813716 + χ(σ²=0.242) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00373686, β=438.27 \u001b[0m\n",

  354.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00378107, β=430.89 \u001b[0m\n",

  355.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00382418, β=424.06 \u001b[0m\n",

  356.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00386791, β=417.19 \u001b[0m\n",

  357.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00392265, β=408.79 \u001b[0m\n",

  358.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00396794, β=402.16 \u001b[0m\n",

  359.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00401167, β=395.78 \u001b[0m\n",

  360.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u650 = 2.998692810457516 + χ(σ²=0.003) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00406457, β=388.40 \u001b[0m\n",

  361.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00411096, β=382.00 \u001b[0m\n",

  362.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00416366, β=374.99 \u001b[0m\n",

  363.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u751 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00416457, β=374.89 \u001b[0m\n",

  364.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  365.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1503 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1502, δ=1.00416557, β=374.77 \u001b[0m\n",

  366.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1453 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1452, δ=1.00420958, β=369.15 \u001b[0m\n",

  367.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1403 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1402, δ=1.00424963, β=364.09 \u001b[0m\n",

  368.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1353 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1352, δ=1.00428447, β=359.71 \u001b[0m\n",

  369.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1303 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1302, δ=1.00431461, β=356.11 \u001b[0m\n",

  370.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1253 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1252, δ=1.00433620, β=353.47 \u001b[0m\n",

  371.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1203 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1202, δ=1.00434902, β=352.01 \u001b[0m\n",

  372.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  373.       "\u001b[3;34m ln(dvol)=5873.7705379 \t ln(Bvol)=4429.2104838 \t ln(Svol)=-2889.1201083 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  374.       "\u001b[1;33m dim=1177 \t δ=1.004350 \t β=351.81  \u001b[0m\n",

  375.       "\u001b[0m  \u001b[0m\n",

  376.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  377.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1122 \t delta=1.004547 \t beta=329.58 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.997189039098024 \u001b[0m\n",

  378.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1068 \t delta=1.004764 \t beta=307.51 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.994385979697240 \u001b[0m\n",

  379.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1013 \t delta=1.005004 \t beta=285.60 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.991590799586837 \u001b[0m\n",

  380.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=959 \t delta=1.005270 \t beta=263.86 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.988803476618439 \u001b[0m\n",

  381.       "\u001b[0m Set of parameters: CCS4 \u001b[0m\n",

  382.       "\u001b[4;37m Attack without hints:  584.09 bikz \u001b[0m\n",

  383.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  384.       "\u001b[1;33m n=864 \t m=864 \t q=32768 \u001b[0m\n",

  385.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u0 = 3.00000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1728, δ=1.00304787, β=583.29 \u001b[0m\n",

  386.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u50 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1712, δ=1.00311466, β=566.08 \u001b[0m\n",

  387.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 4.03571428571429 + χ(σ²=0.066) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1698, δ=1.00317667, β=550.73 \u001b[0m\n",

  388.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u150 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1686, δ=1.00323493, β=536.95 \u001b[0m\n",

  389.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u200 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1671, δ=1.00330361, β=521.49 \u001b[0m\n",

  390.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 1.635097971811619 + χ(σ²=0.234) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1649, δ=1.00339599, β=501.70 \u001b[0m\n",

  391.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1632, δ=1.00347647, β=485.47 \u001b[0m\n",

  392.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1613, δ=1.00356554, β=468.44 \u001b[0m\n",

  393.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1602, δ=1.00362960, β=456.74 \u001b[0m\n",

  394.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1585, δ=1.00371670, β=441.61 \u001b[0m\n",

  395.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u500 = 3.00000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1567, δ=1.00381197, β=425.91 \u001b[0m\n",

  396.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1554, δ=1.00389208, β=413.45 \u001b[0m\n",

  397.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u600 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1535, δ=1.00399725, β=397.84 \u001b[0m\n",

  398.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u650 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1518, δ=1.00409770, β=383.81 \u001b[0m\n",

  399.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00419478, β=371.06 \u001b[0m\n",

  400.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1490, δ=1.00428223, β=359.95 \u001b[0m\n",

  401.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u800 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1475, δ=1.00438267, β=347.93 \u001b[0m\n",

  402.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u850 = 1.635097971811619 + χ(σ²=0.234) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1459, δ=1.00449591, β=335.17 \u001b[0m\n",

  403.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u863 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1455, δ=1.00452419, β=332.09 \u001b[0m\n",

  404.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  405.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1727 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1454, δ=1.00452460, β=331.95 \u001b[0m\n",

  406.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1677 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1404, δ=1.00458760, β=325.29 \u001b[0m\n",

  407.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1627 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1354, δ=1.00464808, β=319.05 \u001b[0m\n",

  408.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1577 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1304, δ=1.00470490, β=313.30 \u001b[0m\n",

  409.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1527 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1254, δ=1.00475783, β=308.13 \u001b[0m\n",

  410.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1477 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1204, δ=1.00480390, β=303.65 \u001b[0m\n",

  411.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1427 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1154, δ=1.00484348, β=300.02 \u001b[0m\n",

  412.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1377 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1104, δ=1.00487098, β=297.43 \u001b[0m\n",

  413.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1327 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1054, δ=1.00488544, β=296.15 \u001b[0m\n",

  414.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  415.       "\u001b[3;34m ln(dvol)=5223.8138965 \t ln(Bvol)=4657.9490534 \t ln(Svol)=-1131.7296863 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  416.       "\u001b[1;33m dim=1039 \t δ=1.004886 \t β=296.07  \u001b[0m\n",

  417.       "\u001b[0m  \u001b[0m\n",

  418.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  419.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=963 \t delta=1.005249 \t beta=265.50 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.818477853233848 \u001b[0m\n",

  420.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=886 \t delta=1.005675 \t beta=235.28 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.669905996234288 \u001b[0m\n",

  421.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=808 \t delta=1.006181 \t beta=205.45 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.548303221666322 \u001b[0m\n",

  422.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=729 \t delta=1.006800 \t beta=175.62 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.256443378603881 \u001b[0m\n",

  423.       "\u001b[0m Set of parameters: NIST1 \u001b[0m\n",

  424.       "\u001b[4;37m Attack without hints:  487.00 bikz \u001b[0m\n",

  425.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  426.       "\u001b[1;33m n=640 \t m=640 \t q=32768 \u001b[0m\n",

  427.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 3.069447793585725 + χ(σ²=0.444) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1281, δ=1.00346927, β=486.85 \u001b[0m\n",

  428.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1271, δ=1.00354851, β=471.62 \u001b[0m\n",

  429.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 1.755049101352603 + χ(σ²=0.765) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1266, δ=1.00360481, β=461.28 \u001b[0m\n",

  430.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -4.57717926440819 + χ(σ²=1.097) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1262, δ=1.00365626, β=451.99 \u001b[0m\n",

  431.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 4.090359168241965 + χ(σ²=0.159) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1253, δ=1.00373273, β=438.88 \u001b[0m\n",

  432.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = -2.41906805640610 + χ(σ²=0.436) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1243, δ=1.00381626, β=425.31 \u001b[0m\n",

  433.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -2.661084529507207 + χ(σ²=0.837) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1235, δ=1.00389158, β=413.53 \u001b[0m\n",

  434.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = -2.41906805640610 + χ(σ²=0.436) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1230, δ=1.00395482, β=404.11 \u001b[0m\n",

  435.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1223, δ=1.00403038, β=393.22 \u001b[0m\n",

  436.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -2.661084529507207 + χ(σ²=0.837) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1216, δ=1.00410464, β=382.87 \u001b[0m\n",

  437.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1211, δ=1.00417085, β=374.17 \u001b[0m\n",

  438.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 4.090359168241965 + χ(σ²=0.159) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1206, δ=1.00423643, β=365.69 \u001b[0m\n",

  439.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = 1.755049101352603 + χ(σ²=0.765) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1194, δ=1.00434773, β=352.15 \u001b[0m\n",

  440.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u639 = -1.515323025952966 + χ(σ²=1.992) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1189, δ=1.00441030, β=344.75 \u001b[0m\n",

  441.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  442.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1279 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1188, δ=1.00441100, β=344.68 \u001b[0m\n",

  443.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1229 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1138, δ=1.00443703, β=341.70 \u001b[0m\n",

  444.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1179 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1088, δ=1.00445220, β=340.08 \u001b[0m\n",

  445.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  446.       "\u001b[3;34m ln(dvol)=4931.2206559 \t ln(Bvol)=5364.9591775 \t ln(Svol)=867.4770433 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  447.       "\u001b[1;33m dim=1065 \t δ=1.004453 \t β=339.89  \u001b[0m\n",

  448.       "\u001b[0m  \u001b[0m\n",

  449.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  450.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=978 \t delta=1.004823 \t beta=301.82 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.333906700218510 \u001b[0m\n",

  451.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=884 \t delta=1.005297 \t beta=261.80 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.00102495772223270 \u001b[0m\n",

  452.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=787 \t delta=1.005904 \t beta=221.11 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 1.17943929438748e-6 \u001b[0m\n",

  453.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=691 \t delta=1.006660 \t beta=181.81 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 7.67683727015403e-12 \u001b[0m\n",

  454.       "\u001b[0m Set of parameters: NIST2 \u001b[0m\n",

  455.       "\u001b[4;37m Attack without hints:  708.06 bikz \u001b[0m\n",

  456.       "\u001b[4;37m      Build DBDD from LWE      \u001b[0m\n",

  457.       "\u001b[1;33m n=976 \t m=976 \t q=65536 \u001b[0m\n",

  458.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1953, δ=1.00264550, β=707.92 \u001b[0m\n"

  459.      ]

  460.     },

  461.     {

  462.      "name": "stdout",

  463.      "output_type": "stream",

  464.      "text": [

  465.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1950, δ=1.00267055, β=699.04 \u001b[0m\n",

  466.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1942, δ=1.00270492, β=686.89 \u001b[0m\n",

  467.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = 5.235337243401759 + χ(σ²=0.243) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1932, δ=1.00274506, β=673.32 \u001b[0m\n",

  468.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1923, δ=1.00278259, β=660.89 \u001b[0m\n",

  469.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1917, δ=1.00281478, β=650.62 \u001b[0m\n",

  470.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1907, δ=1.00285614, β=637.75 \u001b[0m\n",

  471.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u350 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1895, δ=1.00290400, β=623.42 \u001b[0m\n",

  472.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u400 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1884, δ=1.00295046, β=610.02 \u001b[0m\n",

  473.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1875, δ=1.00299260, β=598.21 \u001b[0m\n",

  474.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u500 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1862, δ=1.00304489, β=583.99 \u001b[0m\n",

  475.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1851, δ=1.00309357, β=571.39 \u001b[0m\n",

  476.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1845, δ=1.00312943, β=562.34 \u001b[0m\n",

  477.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u650 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1840, δ=1.00316311, β=553.98 \u001b[0m\n",

  478.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1832, δ=1.00320516, β=543.91 \u001b[0m\n",

  479.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1824, δ=1.00324807, β=533.92 \u001b[0m\n",

  480.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u800 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1814, δ=1.00329760, β=522.78 \u001b[0m\n",

  481.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u850 = -1.089403973506705 + χ(σ²=0.393) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1808, δ=1.00333637, β=514.35 \u001b[0m\n",

  482.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u900 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1801, δ=1.00337834, β=505.41 \u001b[0m\n",

  483.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u950 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1792, δ=1.00342669, β=495.42 \u001b[0m\n",

  484.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u975 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1789, δ=1.00344645, β=491.43 \u001b[0m\n",

  485.       "\u001b[4;37m       Integrating q-vectors      \u001b[0m\n",

  486.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1951 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1788, δ=1.00344701, β=491.33 \u001b[0m\n",

  487.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1901 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1738, δ=1.00347079, β=486.57 \u001b[0m\n",

  488.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1851 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1688, δ=1.00349212, β=482.41 \u001b[0m\n",

  489.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1801 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1638, δ=1.00350973, β=478.94 \u001b[0m\n",

  490.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1751 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1588, δ=1.00352409, β=476.27 \u001b[0m\n",

  491.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1701 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1538, δ=1.00353300, β=474.54 \u001b[0m\n",

  492.       "\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1651 ∈ Λ \u001b[0m \u001b[3;31m \t Unworthy hint, Rejected. \u001b[0m\n",

  493.       "\u001b[4;37m       Attack Estimation      \u001b[0m\n",

  494.       "\u001b[3;34m ln(dvol)=7436.1356246 \t ln(Bvol)=7497.0799049 \t ln(Svol)=121.8885608 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",

  495.       "\u001b[1;33m dim=1489 \t δ=1.003536 \t β=473.94  \u001b[0m\n",

  496.       "\u001b[0m  \u001b[0m\n",

  497.       "\u001b[4;37m      Hybrid attack estimation      \u001b[0m\n",

  498.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1405 \t delta=1.003735 \t beta=438.59 \t guesses=  50 \u001b[0m \u001b[1;33m Proba success = 0.802156595500351 \u001b[0m\n",

  499.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1324 \t delta=1.003948 \t beta=405.08 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.603232864940319 \u001b[0m\n",

  500.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1240 \t delta=1.004199 \t beta=370.52 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.265895477646676 \u001b[0m\n",

  501.       "\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1152 \t delta=1.004501 \t beta=334.55 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.0905624388817529 \u001b[0m\n"

  502.      ]

  503.     }

  504.    ],

  505.    "source": [

  506.     "load('exploiting_SCA_from_Bos_et_al.sage')"

  507.    ]

  508.   },

  509.   {

  510.    "cell_type": "code",

  511.    "execution_count": 25,

  512.    "metadata": {},

  513.    "outputs": [

  514.     {

  515.      "ename": "TypeError",

  516.      "evalue": "version() takes 0 positional arguments but 1 was given",

  517.      "output_type": "error",

  518.      "traceback": [

  519.       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",

  520.       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",

  521.       "\u001b[0;32m<ipython-input-25-576b6e31d0fc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mfpylll\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mversion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfpylll\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",

  522.       "\u001b[0;31mTypeError\u001b[0m: version() takes 0 positional arguments but 1 was given"

  523.      ]

  524.     }

  525.    ],

  526.    "source": [

  527.     "import fpylll\n",

  528.     "version(fpylll)"

  529.    ]

  530.   },

  531.   {

  532.    "cell_type": "code",

  533.    "execution_count": null,

  534.    "metadata": {},

  535.    "outputs": [],

  536.    "source": []

  537.   }

  538.  ],

  539.  "metadata": {

  540.   "kernelspec": {

  541.    "display_name": "SageMath 9.0",

  542.    "language": "sage",

  543.    "name": "sagemath"

  544.   },

  545.   "language_info": {

  546.    "codemirror_mode": {

  547.     "name": "ipython",

  548.     "version": 3

  549.    },

  550.    "file_extension": ".py",

  551.    "mimetype": "text/x-python",

  552.    "name": "python",

  553.    "nbconvert_exporter": "python",

  554.    "pygments_lexer": "ipython3",

  555.    "version": "3.7.3"

  556.   }

  557.  },

  558.  "nbformat": 4,

  559.  "nbformat_minor": 2

  560. }