diff --git a/sp_network_algebra_tutorial.ipynb b/sp_network_algebra_tutorial.ipynb
index 1e4887d..c36a1ab 100644
--- a/sp_network_algebra_tutorial.ipynb
+++ b/sp_network_algebra_tutorial.ipynb
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 82,
    "outputs": [],
    "source": [
     "from src.models import OuterKey, InnerKey, SubstitutionKey"
@@ -20,8 +20,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.906547Z",
-     "start_time": "2024-07-03T16:38:57.867931Z"
+     "end_time": "2024-07-03T17:15:30.365133Z",
+     "start_time": "2024-07-03T17:15:30.328857Z"
     }
    }
   },
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 83,
    "outputs": [],
    "source": [
     "height = 4\n",
@@ -49,8 +49,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.907029Z",
-     "start_time": "2024-07-03T16:38:57.872544Z"
+     "end_time": "2024-07-03T17:15:30.365712Z",
+     "start_time": "2024-07-03T17:15:30.332512Z"
     }
    }
   },
@@ -67,13 +67,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 84,
    "outputs": [
     {
      "data": {
-      "text/plain": "[[2, 0, 1], [0, 2, 1], [0, 2, 1], [1, 2, 0]]"
+      "text/plain": "[[1, 2, 0], [0, 1, 2], [2, 1, 0], [2, 0, 1]]"
      },
-     "execution_count": 37,
+     "execution_count": 84,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -88,8 +88,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.907507Z",
-     "start_time": "2024-07-03T16:38:57.876023Z"
+     "end_time": "2024-07-03T17:15:30.366169Z",
+     "start_time": "2024-07-03T17:15:30.335990Z"
     }
    }
   },
@@ -105,13 +105,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 85,
    "outputs": [
     {
      "data": {
-      "text/plain": "[[3, 2, 1, 0]]"
+      "text/plain": "[[1, 2, 3, 0]]"
      },
-     "execution_count": 38,
+     "execution_count": 85,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -126,8 +126,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.954081Z",
-     "start_time": "2024-07-03T16:38:57.880359Z"
+     "end_time": "2024-07-03T17:15:30.405313Z",
+     "start_time": "2024-07-03T17:15:30.341422Z"
     }
    }
   },
@@ -143,13 +143,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 106,
    "outputs": [
     {
      "data": {
-      "text/plain": "[[21, 62, 42], [151, 171, 33], [31, 131, 141], [100, 202, 161]]"
+      "text/plain": "[[237, 92, 1], [165, 114, 152], [38, 71, 114], [52, 116, 61]]"
      },
-     "execution_count": 39,
+     "execution_count": 106,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -157,13 +157,14 @@
    "source": [
     "a0 = SubstitutionKey.init_matrix(width, height)\n",
     "a1 = SubstitutionKey.init_matrix(width, height)\n",
+    "\n",
     "a0.matrix"
    ],
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.954770Z",
-     "start_time": "2024-07-03T16:38:57.884556Z"
+     "end_time": "2024-07-03T17:26:59.359984Z",
+     "start_time": "2024-07-03T17:26:59.355497Z"
     }
    }
   },
@@ -171,7 +172,8 @@
    "cell_type": "markdown",
    "source": [
     "## Operators Types\n",
-    "### ***<<*** Inner Permutation"
+    "### ***<*** Outer Permutation\n",
+    "#### Substitution Key < Outer Key"
    ],
    "metadata": {
     "collapsed": false
@@ -179,21 +181,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
-   "outputs": [],
-   "source": [],
+   "execution_count": 107,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1, 2, 3, 0]]\n",
+      "[[237, 92, 1], [165, 114, 152], [38, 71, 114], [52, 116, 61]]\n",
+      "[[165, 114, 152], [38, 71, 114], [52, 116, 61], [237, 92, 1]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "a0_o0 = a0 < o0\n",
+    "print(o0.matrix)\n",
+    "print(a0.matrix)\n",
+    "print(a0_o0.matrix)"
+   ],
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.955162Z",
-     "start_time": "2024-07-03T16:38:57.887640Z"
+     "end_time": "2024-07-03T17:27:00.733689Z",
+     "start_time": "2024-07-03T17:27:00.729585Z"
     }
    }
   },
   {
    "cell_type": "markdown",
    "source": [
-    "### ***<*** Outer Permutation"
+    "#### Inner Key < Outer Key"
    ],
    "metadata": {
     "collapsed": false
@@ -201,21 +218,37 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
-   "outputs": [],
-   "source": [],
+   "execution_count": 108,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1, 2, 3, 0]]\n",
+      "[[1, 2, 0], [0, 1, 2], [2, 1, 0], [2, 0, 1]]\n",
+      "[[0, 1, 2], [2, 1, 0], [2, 0, 1], [1, 2, 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "i0_o0 = i0 < o0\n",
+    "print(o0.matrix)\n",
+    "print(i0.matrix)\n",
+    "print(i0_o0.matrix)"
+   ],
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.955526Z",
-     "start_time": "2024-07-03T16:38:57.890158Z"
+     "end_time": "2024-07-03T17:27:04.433733Z",
+     "start_time": "2024-07-03T17:27:04.429380Z"
     }
    }
   },
   {
    "cell_type": "markdown",
    "source": [
-    "### ***^*** Substitution"
+    "### ***<<*** Inner Permutation\n",
+    "#### Outer Key << OuterKey"
    ],
    "metadata": {
     "collapsed": false
@@ -223,14 +256,143 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
-   "outputs": [],
-   "source": [],
+   "execution_count": 109,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[2, 1, 3, 0]]\n",
+      "[[1, 2, 3, 0]]\n",
+      "[[3, 2, 0, 1]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "o0_o1 = o0 << o1\n",
+    "print(o1.matrix)\n",
+    "print(o0.matrix)\n",
+    "print(o0_o1.matrix)"
+   ],
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.957721Z",
-     "start_time": "2024-07-03T16:38:57.892476Z"
+     "end_time": "2024-07-03T17:27:08.293098Z",
+     "start_time": "2024-07-03T17:27:08.288126Z"
+    }
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "#### Inner Key << Inner Key"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0, 1, 2], [0, 2, 1], [0, 1, 2], [2, 1, 0]]\n",
+      "[[1, 2, 0], [0, 1, 2], [2, 1, 0], [2, 0, 1]]\n",
+      "[[1, 2, 0], [0, 2, 1], [2, 1, 0], [1, 0, 2]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "i0_i1 = i0 << i1\n",
+    "print(i1.matrix)\n",
+    "print(i0.matrix)\n",
+    "print(i0_i1.matrix)"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T17:27:11.574355Z",
+     "start_time": "2024-07-03T17:27:11.568652Z"
+    }
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "#### Substitution Key << Inner Key"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1, 2, 0], [0, 1, 2], [2, 1, 0], [2, 0, 1]]\n",
+      "[[237, 92, 1], [165, 114, 152], [38, 71, 114], [52, 116, 61]]\n",
+      "[[92, 1, 237], [165, 114, 152], [114, 71, 38], [61, 52, 116]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "a0_i0 = a0 << i0\n",
+    "print(i0.matrix)\n",
+    "print(a0.matrix)\n",
+    "print(a0_i0.matrix)"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T17:27:14.277217Z",
+     "start_time": "2024-07-03T17:27:14.272132Z"
+    }
+   }
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "### ***^*** Substitution\n",
+    "#### Substitution Key ^ Substitution Key"
+   ],
+   "metadata": {
+    "collapsed": false
+   }
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[237, 92, 1], [165, 114, 152], [38, 71, 114], [52, 116, 61]]\n",
+      "[[184, 159, 115], [199, 221, 35], [158, 70, 86], [74, 43, 129]]\n",
+      "[[85, 195, 114], [98, 175, 187], [184, 1, 36], [126, 95, 188]]\n",
+      "85\n"
+     ]
+    }
+   ],
+   "source": [
+    "a0_a1 = a0 ^ a1\n",
+    "print(a0.matrix)\n",
+    "print(a1.matrix)\n",
+    "print(a0_a1.matrix)\n",
+    "print(a0.matrix[0][0] ^ a1.matrix[0][0])"
+   ],
+   "metadata": {
+    "collapsed": false,
+    "ExecuteTime": {
+     "end_time": "2024-07-03T17:29:15.922958Z",
+     "start_time": "2024-07-03T17:29:15.915126Z"
     }
    }
   },
@@ -245,13 +407,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 88,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 40,
+     "execution_count": 88,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -265,20 +427,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.957791Z",
-     "start_time": "2024-07-03T16:38:57.896696Z"
+     "end_time": "2024-07-03T17:15:30.408639Z",
+     "start_time": "2024-07-03T17:15:30.361902Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 89,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 41,
+     "execution_count": 89,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -291,20 +453,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.958249Z",
-     "start_time": "2024-07-03T16:38:57.900751Z"
+     "end_time": "2024-07-03T17:15:30.408838Z",
+     "start_time": "2024-07-03T17:15:30.365269Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 90,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 42,
+     "execution_count": 90,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -317,20 +479,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.958404Z",
-     "start_time": "2024-07-03T16:38:57.903708Z"
+     "end_time": "2024-07-03T17:15:30.408892Z",
+     "start_time": "2024-07-03T17:15:30.368768Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 91,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 50,
+     "execution_count": 91,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -341,20 +503,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:42:45.756613Z",
-     "start_time": "2024-07-03T16:42:45.746766Z"
+     "end_time": "2024-07-03T17:15:30.408977Z",
+     "start_time": "2024-07-03T17:15:30.371377Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 92,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 44,
+     "execution_count": 92,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -368,20 +530,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.958613Z",
-     "start_time": "2024-07-03T16:38:57.910939Z"
+     "end_time": "2024-07-03T17:15:30.409076Z",
+     "start_time": "2024-07-03T17:15:30.375604Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 93,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 49,
+     "execution_count": 93,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -392,20 +554,20 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:41:01.725294Z",
-     "start_time": "2024-07-03T16:41:01.718345Z"
+     "end_time": "2024-07-03T17:15:30.409139Z",
+     "start_time": "2024-07-03T17:15:30.378496Z"
     }
    }
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 94,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 46,
+     "execution_count": 94,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -421,8 +583,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.958859Z",
-     "start_time": "2024-07-03T16:38:57.915888Z"
+     "end_time": "2024-07-03T17:15:30.409210Z",
+     "start_time": "2024-07-03T17:15:30.381727Z"
     }
    }
   },
@@ -438,13 +600,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 95,
    "outputs": [
     {
      "data": {
       "text/plain": "True"
      },
-     "execution_count": 47,
+     "execution_count": 95,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -455,8 +617,8 @@
    "metadata": {
     "collapsed": false,
     "ExecuteTime": {
-     "end_time": "2024-07-03T16:38:57.958925Z",
-     "start_time": "2024-07-03T16:38:57.920831Z"
+     "end_time": "2024-07-03T17:15:30.409260Z",
+     "start_time": "2024-07-03T17:15:30.384147Z"
     }
    }
   }