SPAIC_Project14.ipynb

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      "name": "SPAIC_Project14.ipynb",
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      "name": "python3",
      "display_name": "Python 3"
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    "accelerator": "GPU"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/agatagruza/private-ai/blob/master/SPAIC_Project14.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yh7_EEujIbqK",
        "colab_type": "text"
      },
      "source": [
        "# Project 14: Encrypted Deep Learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HYWcqdeaLbJU",
        "colab_type": "text"
      },
      "source": [
        "##Reviewing Additive Secret Sharing\n",
        "For more info about SMPC protocols like this one, visit https://mortendahl.github.io (Below example was pulled with Morten's permission from above website).\n",
        "**Encode/Decode** - takes a decimal number and encode them using fixed precision. \n",
        "**Encrypt** - takes a decrype number and converst it into three hares specifically. \n",
        "**Decrypt** does the opposite to encrypt."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IXRUdtRmIVRS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pip install syft"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rMr-ehLZJ6GY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        },
        "outputId": "4dd969ed-f366-4267-ec92-f99f06ddab8c"
      },
      "source": [
        "import torch as th\n",
        "import numpy as np\n",
        "import random\n",
        "import syft as sy"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING: Logging before flag parsing goes to stderr.\n",
            "W0729 00:51:21.629671 139883854743424 secure_random.py:26] Falling back to insecure randomness since the required custom op could not be found for the installed version of TensorFlow. Fix this by compiling custom ops. Missing file was '/usr/local/lib/python3.6/dist-packages/tf_encrypted/operations/secure_random/secure_random_module_tf_1.14.0.so'\n",
            "W0729 00:51:21.646487 139883854743424 deprecation_wrapper.py:119] From /usr/local/lib/python3.6/dist-packages/tf_encrypted/session.py:26: The name tf.Session is deprecated. Please use tf.compat.v1.Session instead.\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_u6EUnWSJ6JH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "BASE = 10\n",
        "INT_PRECISION = 8\n",
        "FRACTIONAL_PRECISION = 8\n",
        "Q = 293973345475167247070445277780365744413"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bMUft4E4J6PE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "PRECISION = INT_PRECISION + FRACTIONAL_PRECISION\n",
        "assert(Q > BASE**PRECISION)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hg7fVw8pJ6Ro",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def encode(rational):\n",
        "    upscaled = int(rational * BASE**FRACTIONAL_PRECISION)\n",
        "    field_element = upscaled % Q\n",
        "    return field_element"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WeGqe4vPJ6TX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def decode(field_element):\n",
        "    upscaled = field_element if field_element <= Q/2 else field_element - Q\n",
        "    rational = upscaled / BASE**FRACTIONAL_PRECISION\n",
        "    return rational"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z8RjKg1oJ6Wz",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def encrypt(secret):\n",
        "  first = random.randrange(Q)\n",
        "  second = random.randrange(Q)\n",
        "  third = (secret - first - second) % Q\n",
        "  return [first, second, third]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RBV8-2afJ6Yy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def decrypt(sharing):\n",
        "  return sum(sharing) % Q"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1t_0IcXyJ6cl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def add(a, b):\n",
        "    c = list()\n",
        "    for i in range(len(a)):\n",
        "        c.append((a[i] + b[i]) % Q)\n",
        "    return tuple(c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "egnRgvmCJ6eT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "4b7092c7-c3fe-4a3f-e8d2-9e8769e44a35"
      },
      "source": [
        "x = encrypt(encode(6.5))\n",
        "x"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[139302545989461104869649037927381149848,\n",
              " 168956177393360569247802030954103594063,\n",
              " 279687967567512820023439486679896744915]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KxGjk8gvJ6hy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "a627274c-32a1-40e9-ae34-f848ec978d68"
      },
      "source": [
        "y = encrypt(encode(6.5))\n",
        "y"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[101257153225568791149931919691097707704,\n",
              " 183295898122160688367087536885261547207,\n",
              " 9420294127437767553425821204656489502]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t_R1lEnDJ6kc",
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          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "4ca0548f-4daa-4003-a23a-de53517a2902"
      },
      "source": [
        "z = add(x, y)\n",
        "z"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(240559699215029896019580957618478857552,\n",
              " 58278730040354010544444290058999396857,\n",
              " 289108261694950587576865307884553234417)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sir3ESYuRaRc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e029659b-3bdd-4620-b52a-a8efa65c3427"
      },
      "source": [
        "decrypt(z)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1300000000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZlByy5hcJ6nn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "37b8a832-77f4-4885-8f5e-c322978dfb07"
      },
      "source": [
        "decode(decrypt(z))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "13.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZlCqkfrmJ6pT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9bbe9d14-7dcf-412b-c02e-10e446af1a86"
      },
      "source": [
        "25 % BASE"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p-Z4qmk0UrzH",
        "colab_type": "text"
      },
      "source": [
        "##Encrypted Subtraction and Public/Scalar Multiplication"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6UvWfz7fWDzq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sub(a, b):\n",
        "    c = list()\n",
        "    for i in range(len(a)):\n",
        "        c.append((a[i] - b[i]) % Q)\n",
        "    return tuple(c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g8jtvD9uJ7Sf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "field = 23740629843760239486723"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PV72i6kvJ7Wb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = 5\n",
        "\n",
        "bob_x_share = 2372385723 # random number\n",
        "alices_x_share = field - bob_x_share + x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pu7ySep2J7Zm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "39394ba1-955f-4e29-a108-bd9f309ab041"
      },
      "source": [
        "(bob_x_share + alices_x_share) % field"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fWUw_LUDJ7fU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "field = 10\n",
        "\n",
        "x = 5\n",
        "\n",
        "bob_x_share = 8\n",
        "alice_x_share = field - bob_x_share + x\n",
        "\n",
        "y = 1\n",
        "\n",
        "bob_y_share = 9\n",
        "alice_y_share = field - bob_y_share + y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yhqyocppW2EA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9e04d3e8-edac-47a1-9e6f-9d81b296e5ac"
      },
      "source": [
        "bob_x_share + alice_x_share"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "15"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "23rnPXIuXDdn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b6924ee1-bdb0-4b74-fcf8-45d398d426cc"
      },
      "source": [
        "bob_y_share + alice_y_share"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "11"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tzU_Y2HiXKUi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bd945003-ebce-4224-bf70-016e5086682c"
      },
      "source": [
        "15 + 11"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "26"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qVfrT0cSXOCR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "74f05a53-2ade-4caf-80e3-cb665ad622bc"
      },
      "source": [
        "15 - 11"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o8vWdZ4HJ7hm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a264abc4-78f5-423d-cdbb-879cdb7ffc41"
      },
      "source": [
        "((bob_x_share + alice_x_share) - (bob_y_share + alice_y_share)) % field"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1A3vERktJ7mV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7dc0fc78-5ec7-4382-df8f-93dee9c5caa4"
      },
      "source": [
        "((bob_x_share - bob_y_share) + (alice_x_share - alice_y_share)) % field"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0lkqUFDSJ7o5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "76e0d7c8-e7c2-46e6-adfb-9825ec78a8a9"
      },
      "source": [
        "bob_x_share + alice_x_share + bob_y_share + alice_y_share"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "26"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6PkxtY3SJ7j8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "bob_z_share = (bob_x_share - bob_y_share)\n",
        "alice_z_share = (alice_x_share - alice_y_share)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T2Bk5pmHJ7ec",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2a4aa86c-4790-4203-9d06-3b076f334415"
      },
      "source": [
        "(bob_z_share + alice_z_share) % field"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GlEcwOUiJ7Rd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "field = 10\n",
        "\n",
        "x = 5\n",
        "\n",
        "bob_x_share = 8\n",
        "alice_x_share = field - bob_x_share + x\n",
        "\n",
        "y = 6\n",
        "\n",
        "bob_y_share = 9\n",
        "alice_y_share = field - bob_y_share + y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NyUidcKQJ7Qn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2d5cab93-a280-41e5-89ab-715c645e3891"
      },
      "source": [
        "z = bob_x_share + alice_x_share + bob_y_share + alice_y_share\n",
        "z"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "26"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o2nb2YD_J7Ol",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e8077ff0-f897-4959-d7e9-176572b9e990"
      },
      "source": [
        "z % BASE"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BqCo_PfxJ7Nn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y = 6\n",
        "\n",
        "bob_y_share = 9\n",
        "alice_y_share = field - bob_y_share + y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QoSpWu5xJ7Mz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "af45b14f-52e4-4f76-fa8d-00118630535d"
      },
      "source": [
        "z = bob_x_share + alice_x_share + bob_y_share + alice_y_share\n",
        "z"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "31"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "10tqcLNTJ7L7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2ef7eb26-cb10-41d3-d472-dd3884c8b671"
      },
      "source": [
        "z % BASE"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zvbz5_ewJ7KR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = encrypt(25)\n",
        "y = encrypt(11)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LSMR6LStJ7Jb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9108baec-9fb5-4ba9-a807-9b428842f190"
      },
      "source": [
        "decrypt(sub(x, y))"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "14"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gosHxPdKJ7Io",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1f03770a-1111-471b-8e8f-0d5e56cc29ef"
      },
      "source": [
        "((bob_y_share * 3) + (alice_y_share * 3)) % field"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tDg_A2dsJ7H2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def imul(a, scalar):\n",
        "    \n",
        "    # logic here which can multiply by a public scalar\n",
        "    \n",
        "    c = list()\n",
        "    \n",
        "    for i in range(len(a)):\n",
        "        c.append((a[i] * scalar) % Q)\n",
        "        \n",
        "    return tuple(c)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X1S2Bd7tJ7HF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "783d7915-2948-4015-8eab-b7bf4102c353"
      },
      "source": [
        "x = encrypt(encode(5.5))\n",
        "x"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[46949748933161072485910754975423127558,\n",
              " 242120101164703670671564514268939352770,\n",
              " 4903495377302503912970008536553264085]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3haQDNcPJ7GN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "z = imul(x, 3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4krproTxJ7Fb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6c48fa00-0b46-41d2-addb-1b0307a2cbf8"
      },
      "source": [
        "decode(decrypt(z))"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "16.5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    }
  ]
}