tinymt.ipynb

{
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mat1 = 0x8f7011ee\n",
    "mat2 = 0xfc78ff1f\n",
    "tmat = 0x3793fdff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "F2 = GF(2)\n",
    "\n",
    "def int_to_f2(x):\n",
    "    return vector([F2((x >> i) & 1) for i in range(32)])\n",
    "\n",
    "def ints_to_f2(xs):\n",
    "    return vector([F2((xs[floor(i / 32)] >> (i % 32)) & 1) for i in range(32*len(xs))])\n",
    "\n",
    "def f2_to_int(vec):\n",
    "    x = 0\n",
    "    for i in range(32):\n",
    "        x |= Integer(vec[i]) << i\n",
    "    return x\n",
    "\n",
    "def f2_to_ints(vec):\n",
    "    return [f2_to_int(vec[i*32:i*32+32]) for i in range(floor(len(vec) / 32))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def join_matrix_yoko(mats):\n",
    "    m = mats[0].nrows()\n",
    "    n = mats[0].ncols()\n",
    "    return matrix([[mats[floor(j / n)][i, j % n] for j in range(n*len(mats))] for i in range(m)])\n",
    "\n",
    "def join_matrix_tate(mats):\n",
    "    m = mats[0].nrows()\n",
    "    n = mats[0].ncols()\n",
    "    return matrix([[mats[floor(i / m)][i % m, j] for j in range(n)] for i in range(m*len(mats))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def elem_matrix(i):\n",
    "    mats = [Mat(GF(2), 32, 32).zero() for j in range(4)]\n",
    "    mats[i] = Mat(GF(2), 32, 32).identity_matrix()\n",
    "    return join_matrix_yoko(mats)\n",
    "\n",
    "def xi(x):\n",
    "    if x:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "def rshift_matrix(k):\n",
    "    return matrix([[F2(xi(j - i == k)) for j in range(32)] for i in range(32)])\n",
    "\n",
    "def lshift_matrix(k):\n",
    "    return rshift_matrix(-k)\n",
    "\n",
    "def get_0bit_matrix():\n",
    "    return matrix([[F2(xi(j == 0)) for j in range(32)]])\n",
    "\n",
    "get_0bit = get_0bit_matrix()\n",
    "\n",
    "def vect_to_matrix(vec):\n",
    "    return matrix([[vec[i]] for i in range(len(vec))])\n",
    "\n",
    "def mask_matrix(a):\n",
    "    return matrix([[F2(a[i] * xi(i == j)) for j in range(32)] for i in range(32)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def temper_matrix():\n",
    "    t0 = elem_matrix(3)\n",
    "    t1 = elem_matrix(0) + rshift_matrix(8) * elem_matrix(2)\n",
    "    return t0 + t1 + vect_to_matrix(int_to_f2(tmat)) * get_0bit * t1\n",
    "\n",
    "temper = temper_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def next_state_matrix():\n",
    "    y = elem_matrix(3)\n",
    "    x = mask_matrix(int_to_f2(0x7fffffff)) * elem_matrix(0) + elem_matrix(1) + elem_matrix(2)\n",
    "    x += lshift_matrix(1) * x\n",
    "    y += rshift_matrix(1) * y + x\n",
    "    st0 = elem_matrix(1)\n",
    "    st1 = elem_matrix(2) + vect_to_matrix(int_to_f2(mat1)) * get_0bit * y\n",
    "    st2 = x + lshift_matrix(10) * y + vect_to_matrix(int_to_f2(mat2)) * get_0bit * y\n",
    "    st3 = y\n",
    "    return join_matrix_tate([st0, st1, st2, st3])\n",
    "\n",
    "next_state = next_state_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def from_128bit_to_127bit_matrix():\n",
    "    m = [[F2(0) for j in range(128)] for i in range(127)]\n",
    "    for i in range(31):\n",
    "        m[i][i] = F2(1)\n",
    "    for i in range(31, 127):\n",
    "        m[i][i+1] = F2(1)\n",
    "    return matrix(m)\n",
    "\n",
    "def from_127bit_to_128bit_matrix():\n",
    "    m = [[F2(0) for j in range(127)] for i in range(128)]\n",
    "    for i in range(31):\n",
    "        m[i][i] = F2(1)\n",
    "    for i in range(31, 127):\n",
    "        m[i+1][i] = F2(1)\n",
    "    return matrix(m)\n",
    "\n",
    "from_128bit_to_127bit = from_128bit_to_127bit_matrix()\n",
    "from_127bit_to_128bit = from_127bit_to_128bit_matrix()\n",
    "\n",
    "next_state_127 = from_128bit_to_127bit * next_state * from_127bit_to_128bit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def from_state_to_random_stream_matrix():\n",
    "    mats = [None for i in range(127)]\n",
    "    step = Mat(GF(2), 127, 127).identity_matrix()\n",
    "    A = get_0bit * temper * from_127bit_to_128bit\n",
    "    for i in range(127):\n",
    "        mats[i] = A * step\n",
    "        step *= next_state_127\n",
    "    return join_matrix_tate(mats)\n",
    "\n",
    "from_state_to_random_stream = from_state_to_random_stream_matrix()\n",
    "\n",
    "from_random_stream_to_state = from_state_to_random_stream.inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1aa43aaa', '61d7401', '7e68dffd', '34d0c803']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec = [F2(0) for i in range(127)]\n",
    "vec[0] = 1\n",
    "state = from_127bit_to_128bit * from_random_stream_to_state * vector(vec)\n",
    "[x.str(16) for x in f2_to_ints(state)]"
   ]
  }
 ],
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