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final draft

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Donovan
2025-03-20 06:40:54 -05:00
parent 65f3559ef0
commit 9651455c1a
1 changed files with 216 additions and 227 deletions
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notebooks/nkode_tutorial.ipynb
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@@ -30,12 +30,12 @@
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@@ -121,30 +121,30 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Customer Position Key: [21284 3999 4057 48308 14680 46323]\n",
"Customer Position Key: [10895 31772 47823 53466 56263 49352]\n",
"Customer Properties Key:\n",
"[45633 21215 48438 45863 52540 14191]\n",
"[11907 4042 56372 63103 45179 58318]\n",
"[28909 48497 31171 15125 2886 9246]\n",
"[15651 10936 5595 16546 8096 13333]\n",
"[41923 43364 15227 43001 11056 62605]\n",
"[32913 31208 39571 1116 2737 19900]\n",
"[ 4026 23392 64571 25864 56877 34756]\n",
"[56837 8582 51951 34890 37611 61978]\n",
"[55074 11623 3931 21342 53702 21700]\n",
"[26922 1472 49420 42668 7254 41918]\n",
"Position to Properties Map:\n",
"21284: [45633 11907 28909 15651 41923]\n",
"3999: [21215 4042 48497 10936 43364]\n",
"4057: [48438 56372 31171 5595 15227]\n",
"48308: [45863 63103 15125 16546 43001]\n",
"14680: [52540 45179 2886 8096 11056]\n",
"46323: [14191 58318 9246 13333 62605]\n"
"10895: [32913 4026 56837 55074 26922]\n",
"31772: [31208 23392 8582 11623 1472]\n",
"47823: [39571 64571 51951 3931 49420]\n",
"53466: [ 1116 25864 34890 21342 42668]\n",
"56263: [ 2737 56877 37611 53702 7254]\n",
"49352: [19900 34756 61978 21700 41918]\n"
]
}
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@@ -161,16 +161,16 @@
"output_type": "stream",
"text": [
"Position Value to Icons Map:\n",
"21284: ['😀' '🥺' '🤔' '🐱' '🦄']\n",
"3999: ['😂' '😡' '🙃' '🐶' '🌟']\n",
"4057: ['🥳' '😱' '😇' '🦁' '⚡']\n",
"48308: ['😍' '🤯' '🤖' '🐻' '🔥']\n",
"14680: ['🤓' '🥰' '👽' '🐸' '🍕']\n",
"46323: ['😎' '😴' '👾' '🐙' '🎉']\n"
"10895: ['😀' '🥺' '🤔' '🐱' '🦄']\n",
"31772: ['😂' '😡' '🙃' '🐶' '🌟']\n",
"47823: ['🥳' '😱' '😇' '🦁' '⚡']\n",
"53466: ['😍' '🤯' '🤖' '🐻' '🔥']\n",
"56263: ['🤓' '🥰' '👽' '🐸' '🍕']\n",
"49352: ['😎' '😴' '👾' '🐙' '🎉']\n"
]
}
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@@ -194,8 +194,8 @@
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@@ -223,11 +223,11 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Key 0: ['🦄' '😂' '😇' '👽' '😴']\n",
"Key 1: ['🐱' '🌟' '😱' '🐸' '😎']\n",
"Key 2: ['🤔' '🙃' '🦁' '🥰' '🐙']\n",
"Key 3: ['😀' '😡' '⚡' '🍕' '👾']\n",
"Key 4: ['🥺' '🐶' '🥳' '🤓' '🎉']\n"
"Key 0: ['🐱' '🌟' '🤖' '🤓' '🎉']\n",
"Key 1: ['🥺' '🙃' '🔥' '🍕' '😎']\n",
"Key 2: ['🦄' '🐶' '🤯' '👽' '🐙']\n",
"Key 3: ['😀' '😂' '😍' '🥰' '😴']\n",
"Key 4: ['🤔' '😡' '🐻' '🐸' '👾']\n"
]
},
{
@@ -244,11 +244,11 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Key 0: [24 1 14 16 11]\n",
"Key 1: [18 25 8 22 5]\n",
"Key 2: [12 13 20 10 23]\n",
"Key 3: [ 0 7 26 28 17]\n",
"Key 4: [ 6 19 2 4 29]\n"
"Key 0: [18 25 15 4 29]\n",
"Key 1: [ 6 13 27 28 5]\n",
"Key 2: [24 19 9 16 23]\n",
"Key 3: [ 0 1 3 10 11]\n",
"Key 4: [12 7 21 22 17]\n"
]
},
{
@@ -265,15 +265,15 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Key 0: [41923 21215 31171 2886 58318]\n",
"Key 1: [15651 43364 56372 8096 14191]\n",
"Key 2: [28909 48497 5595 45179 13333]\n",
"Key 3: [45633 4042 15227 11056 9246]\n",
"Key 4: [11907 10936 48438 52540 62605]\n"
"Key 0: [55074 1472 34890 2737 41918]\n",
"Key 1: [ 4026 8582 42668 7254 19900]\n",
"Key 2: [26922 11623 25864 37611 21700]\n",
"Key 3: [32913 31208 1116 56877 34756]\n",
"Key 4: [56837 23392 21342 53702 61978]\n"
]
}
],
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@@ -286,8 +286,8 @@
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"cell_type": "code",
@@ -306,20 +306,20 @@
"name": "stdout",
"output_type": "stream",
"text": [
"User Passcode Indices: [19, 7, 10, 6]\n",
"User Passcode Icons: ['🐶' '😡' '🥰' '🥺']\n",
"User Passcode Server-side properties: [10936 4042 45179 11907]\n",
"Selected Keys: [4, 3, 2, 4]\n"
"User Passcode Indices: [28, 13, 9, 10]\n",
"User Passcode Icons: ['🍕' '🙃' '🤯' '🥰']\n",
"User Passcode Server-side properties: [ 7254 8582 25864 56877]\n",
"Selected Keys: [1, 1, 2, 3]\n"
]
}
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@@ -334,23 +334,23 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Key 0: [18 7 20 4 11]\n",
"Key 1: [12 1 26 22 29]\n",
"Key 2: [ 0 19 14 10 5]\n",
"Key 3: [24 25 2 28 23]\n",
"Key 4: [ 6 13 8 16 17]\n",
"Key 0: [ 6 7 3 4 23]\n",
"Key 1: [24 1 15 28 17]\n",
"Key 2: [12 25 27 16 11]\n",
"Key 3: [ 0 13 9 22 29]\n",
"Key 4: [18 19 21 10 5]\n",
"Selected Keys\n",
"[2, 0, 2, 4]\n"
"[1, 3, 3, 4]\n"
]
}
],
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"execution_count": 81
},
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@@ -360,7 +360,7 @@
"assert success"
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@@ -380,8 +380,8 @@
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@@ -391,13 +391,13 @@
"user_prop_key_keypad = user_cipher.property_key.reshape(-1, keypad_size.props_per_key)"
],
"outputs": [],
"execution_count": 35
"execution_count": 83
},
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@@ -408,21 +408,21 @@
"output_type": "stream",
"text": [
"Property Key:\n",
"[[43643 58945 45655 10493 17462 5635]\n",
" [42071 15680 60860 39600 15784 4102]\n",
" [60857 21300 14877 25869 12858 50934]\n",
" [55451 44486 22660 41758 36853 37697]\n",
" [24236 53340 57175 52425 5167 2017]]\n"
"[[53739 14349 64971 50952 51008 37461]\n",
" [45744 17444 29958 27397 60694 8069]\n",
" [43064 47943 49025 5623 3145 4890]\n",
" [ 1128 11012 53093 14232 26108 5391]\n",
" [59341 47378 48497 6840 34437 29587]]\n"
]
}
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"cell_type": "code",
@@ -432,17 +432,17 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Passcode Key: [31049 4633 40678 55986 14115 22499 3470 53359 20871 60539]\n"
"Passcode Key: [16245 48001 4534 55258 54613 15211 33171 56565 33961 50654]\n"
]
}
],
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"cell_type": "code",
@@ -452,17 +452,17 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Mask Key: [55361 38182 36656 63013 26815 17961 23911 65497 28524 60226]\n"
"Mask Key: [52084 24514 63626 6657 19669 39430 35626 25229 14824 63798]\n"
]
}
],
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"execution_count": 86
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@@ -472,17 +472,17 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Combined Position Key: [33934 3750 42586 25190 7504 35546]\n"
"Combined Position Key: [10235 12456 898 54650 50445 20719]\n"
]
}
],
"execution_count": 39
"execution_count": 87
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@@ -492,17 +492,17 @@
"name": "stdout",
"output_type": "stream",
"text": [
"User Position Key = combined_pos_key XOR customer_pos_key: [55210 313 43395 57042 9224 15913]\n"
"User Position Key = combined_pos_key XOR customer_pos_key: [ 3444 19636 47437 1440 7882 36903]\n"
]
}
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@@ -518,16 +518,16 @@
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"text": [
"Combined Position to Properties Map:\n",
"33934: [43643 42071 60857 55451 24236]\n",
"3750: [58945 15680 21300 44486 53340]\n",
"42586: [45655 60860 14877 22660 57175]\n",
"25190: [10493 39600 25869 41758 52425]\n",
"7504: [17462 15784 12858 36853 5167]\n",
"35546: [ 5635 4102 50934 37697 2017]\n"
"10235: [53739 45744 43064 1128 59341]\n",
"12456: [14349 17444 47943 11012 47378]\n",
"898: [64971 29958 49025 53093 48497]\n",
"54650: [50952 27397 5623 14232 6840]\n",
"50445: [51008 60694 3145 26108 34437]\n",
"20719: [37461 8069 4890 5391 29587]\n"
]
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"execution_count": 89
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@@ -544,8 +544,8 @@
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@@ -557,25 +557,25 @@
"encoded_mask = user_cipher.encode_base64_str(mask)"
],
"outputs": [],
"execution_count": 42
"execution_count": 90
},
{
"metadata": {},
"cell_type": "markdown",
"source": [
"#### Encipher Passcode\n",
"UserCipherKeys.encipher_salt_hash_code:\n",
"\n",
"- ciphered_customer_prop = alpha_key ^ customer_prop\n",
"- ciphered_passcode_i = pass_key_i ^ ciphered_customer_prop_i\n",
"- code = hash(ciphered_passcode, salt)"
"1. Compute `combined_property_key`\n",
"2. Recover `user_passcode = ordered_combined_proptery_key`; order by passcode_property_indices\n",
"3. Zero pad `user_pascode`\n",
"4. Encipher `user_passcode` with `user.cipher.pass_key`\n",
"5. Hash `ciphered_passcode`"
]
},
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@@ -583,48 +583,13 @@
"combined_prop_key = customer.cipher.property_key ^ user_cipher.property_key\n",
"user_passcode = combined_prop_key[passcode_property_indices]\n",
"pad_len = customer.nkode_policy.max_nkode_len - passcode_len\n",
"user_passcode_padded = np.concatenate((user_passcode, np.zeros(pad_len, dtype=user_passcode.dtype)))\n",
"ciphered_passcode = user_passcode_padded ^ user_cipher.pass_key\n",
"padded_passcode = np.concatenate((user_passcode, np.zeros(pad_len, dtype=user_passcode.dtype)))\n",
"ciphered_passcode = padded_passcode ^ user_cipher.pass_key\n",
"passcode_prehash = base64.b64encode(hashlib.sha256(ciphered_passcode.tobytes()).digest())\n",
"passcode_hash = bcrypt.hashpw(passcode_prehash, bcrypt.gensalt(rounds=12)).decode(\"utf-8\")"
],
"outputs": [],
"execution_count": 43
},
{
"metadata": {},
"cell_type": "markdown",
"source": [
"### Enciphered nKode\n",
"An encipher passcode has two parts:\n",
"1. Code: the enciphered and hashed passcode\n",
"2. Mask: the mask is used to recover the passcode sets. The mask and the users key select are used to recover the property values of the user's passcode\n",
"The method UserCipherKeys.encipher_nkode secures a users nKode in the database. This method is called in api.confirm_nkode\n",
"```\n",
"class EncipheredNKode(BaseModel):\n",
" code: str\n",
" mask: str\n",
"```\n"
]
},
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},
"cell_type": "code",
"source": [
"from src.models import EncipheredNKode\n",
"\n",
"enciphered_nkode = EncipheredNKode(\n",
" mask=encoded_mask,\n",
" code=passcode_hash,\n",
")"
],
"outputs": [],
"execution_count": 44
"execution_count": 91
},
{
"metadata": {},
@@ -632,14 +597,14 @@
"source": [
"### User Login\n",
"1. Get login keypad\n",
"2. Login\n"
"2. Select keys with passcode icons (in our case, passcode property indices)\n"
]
},
{
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"cell_type": "code",
@@ -657,29 +622,29 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Key 0: [24 1 14 27 16 11]\n",
"Key 1: [18 25 8 3 22 5]\n",
"Key 2: [12 13 20 21 10 23]\n",
"Key 3: [ 0 7 26 9 28 17]\n",
"Key 4: [ 6 19 2 15 4 29]\n",
"User Passcode: [19, 7, 10, 6]\n",
"Key 0: [18 25 14 15 4 29]\n",
"Key 1: [ 6 13 20 27 28 5]\n",
"Key 2: [24 19 26 9 16 23]\n",
"Key 3: [ 0 1 8 3 10 11]\n",
"Key 4: [12 7 2 21 22 17]\n",
"User Passcode: [28, 13, 9, 10]\n",
"\n",
"Selected Keys:\n",
" [4, 3, 2, 4]\n",
" [1, 1, 2, 3]\n",
"\n"
]
}
],
"execution_count": 45
"execution_count": 92
},
{
"metadata": {},
"cell_type": "markdown",
"source": [
"## Validate Login Key Entry\n",
"- decipher user mask and recover nkode set values\n",
"- get presumed properties from key selection and set values\n",
"- encipher, salt and hash presumed properties values and compare it to the users hashed code"
"- decipher user mask and recover nkode position values\n",
"- get presumed properties from key selection and position values\n",
"- compare with hash"
]
},
{
@@ -687,22 +652,18 @@
"cell_type": "markdown",
"source": [
"### Decipher Mask\n",
"Recall:\n",
"- combined_set_key = user_set_key ^ customer_set_key\n",
"- mask = mask_key ^ ordered_user_set_key\n",
"\n",
"Recover nKode set values: \n",
"Recover nKode position values:\n",
"- decode mask from base64 to int\n",
"- ordered_user_set_key = mask ^ mask_key\n",
"- ordered_combined_set_key = ordered_customer_set_key ^ ordered_user_set_key\n",
"- ordered_user_position_key = mask ^ mask_key\n",
"- user_position_key = user.cipher.co\n",
"- deduce the set indices"
]
},
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"start_time": "2025-03-20T10:38:45.567396Z"
}
},
"cell_type": "code",
@@ -711,34 +672,51 @@
"selected_keys_login = select_keys_with_passcode_values(passcode_property_indices, login_keypad, keypad_size.props_per_key)\n",
"user = api.customers[customer_id].users[username]\n",
"mask = user.cipher.decode_base64_str(user.enciphered_passcode.mask)\n",
"deciphered_mask = mask ^ user.cipher.mask_key\n",
"set_key = customer.cipher.position_key ^ user.cipher.combined_position_key\n",
"passcode_set_index = [int(np.where(set_key == set_cipher)[0][0]) for set_cipher in deciphered_mask[:passcode_len]]\n",
"presumed_selected_properties_idx = customer.users[username].user_keypad.get_prop_idxs_by_keynumb_setidx(selected_keys_login, passcode_set_index)\n",
"assert passcode_property_indices == presumed_selected_properties_idx\n"
"ordered_user_position_key = mask ^ user.cipher.mask_key\n",
"user_position_key = customer.cipher.position_key ^ user.cipher.combined_position_key\n"
],
"outputs": [],
"execution_count": 46
"execution_count": 93
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Compare Enciphered Passcodes"
"source": [
"#### Get Presumed Properties\n",
"- Get the passcode position indices (within the keys)\n",
"- Get the presumed property indices from the key and position within the key"
]
},
{
"metadata": {},
"cell_type": "code",
"outputs": [],
"execution_count": null,
"source": [
"passcode_position_indices = [int(np.where(user_position_key == pos)[0][0]) for pos in ordered_user_position_key[:passcode_len]]\n",
"presumed_property_indices = customer.users[username].user_keypad.get_prop_idxs_by_keynumb_setidx(selected_keys_login, passcode_position_indices)\n",
"assert passcode_property_indices == presumed_property_indices\n"
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Compare Enciphered Passcodes\n"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2025-03-20T08:32:09.526068Z",
"start_time": "2025-03-20T08:32:09.295445Z"
"end_time": "2025-03-20T10:38:45.809575Z",
"start_time": "2025-03-20T10:38:45.576610Z"
}
},
"cell_type": "code",
"source": [
"valid_nkode = user.cipher.compare_nkode(presumed_selected_properties_idx, customer.cipher, user.enciphered_passcode.code)\n",
"assert valid_nkode\n"
"valid_nkode = user.cipher.compare_nkode(presumed_property_indices, customer.cipher, user.enciphered_passcode.code)\n",
"assert valid_nkode"
],
"outputs": [],
"execution_count": 47
"execution_count": 94
},
{
"metadata": {},
@@ -754,8 +732,8 @@
{
"metadata": {
"ExecuteTime": {
"end_time": "2025-03-20T08:32:09.996256Z",
"start_time": "2025-03-20T08:32:09.529950Z"
"end_time": "2025-03-20T10:38:46.286081Z",
"start_time": "2025-03-20T10:38:45.816688Z"
}
},
"cell_type": "code",
@@ -765,110 +743,121 @@
" code = api.customers[customer_id].users[username].enciphered_passcode.code\n",
" print(f\"mask: {mask}, code: {code}\\n\")\n",
"\n",
"print_user_enciphered_code() \n",
"api.renew_keys(customer_id)\n",
"print(\"Old User Cipher and Mask\")\n",
"print_user_enciphered_code()\n",
"\n",
"api.renew_keys(customer_id) # Steps 1 and 2\n",
"login_keypad = api.get_login_keypad(username, customer_id)\n",
"selected_keys_login = select_keys_with_passcode_values(passcode_property_indices, login_keypad, keypad_size.props_per_key)\n",
"success = api.login(customer_id, username, selected_keys_login)\n",
"assert success\n",
"print_user_enciphered_code()"
"success = api.login(customer_id, username, selected_keys_login) # Step 3\n",
"print(\"New User Cipher and Mask\")\n",
"print_user_enciphered_code()\n",
"assert success"
],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mask: cz9m1OunYlEK42X0jRrGAzKvheg=, code: $2b$12$Z.N7qwUTMgSVJFQC9hKgjeQ8owBpZMm5Aa14RQdiJH7C8l61QJENS\n",
"Old User Cipher and Mask\n",
"mask: y8aMd+5qYcPVLETTcs2aHqx2hhk=, code: $2b$12$wMi7WGmlch8kWMYJ2v.FHOne1.YSQPqKU/itpBuycwSFyasryF/2u\n",
"\n",
"mask: cz9m1OunYlEK42X0jRrGAzKvheg=, code: $2b$12$Z.N7qwUTMgSVJFQC9hKgjeQ8owBpZMm5Aa14RQdiJH7C8l61QJENS\n",
"\n",
"mask: e+RtDYeB1G1RfuTOjCna6K9xLUU=, code: $2b$12$DHdD52jbBdVoXYArhWCm7eABlnch.tNhO/1Eipygj8fpoUFuPzyEC\n",
"New User Cipher and Mask\n",
"mask: aln5Su79utoVmqQXNCjYiUdwVYw=, code: $2b$12$gQf3UVa3cWMBy0CO0sBLyuJzdXGzg3qpNFMTD6MvycuR6N3gLFdgC\n",
"\n"
]
}
],
"execution_count": 48
"execution_count": 95
},
{
"metadata": {},
"cell_type": "markdown",
"source": [
"#### Renew Customer Keys\n",
"- Get old properties and sets\n",
"- Replace properties and sets"
"### Renew Customer Keys\n",
"The customer cipher keys are replaced."
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2025-03-20T08:32:10.012897Z",
"start_time": "2025-03-20T08:32:10.009292Z"
"end_time": "2025-03-20T10:38:46.296985Z",
"start_time": "2025-03-20T10:38:46.293584Z"
}
},
"cell_type": "code",
"source": [
"old_props = customer.cipher.property_key.copy()\n",
"old_sets = customer.cipher.position_key.copy()\n",
"customer.cipher.renew()\n",
"old_pos = customer.cipher.position_key.copy()\n",
"customer.cipher.property_key = np.random.choice(2 ** 16, size=keypad_size.total_props, replace=False)\n",
"customer.cipher.position_key = np.random.choice(2 ** 16, size=keypad_size.props_per_key, replace=False)\n",
"new_props = customer.cipher.property_key\n",
"new_sets = customer.cipher.position_key"
"new_pos = customer.cipher.position_key"
],
"outputs": [],
"execution_count": 49
"execution_count": 96
},
{
"metadata": {},
"cell_type": "markdown",
"source": [
"### Renew User\n",
"\n"
"User property and position keys go through an intermediate phase.\n",
"#### user.cipher.combined_position_key\n",
"- user_combined_position_key = user_combined_position_key XOR pos_xor\n",
"- user_combined_position_key = (user_position_key XOR old_customer_position_key) XOR (old_customer_position_key XOR new_customer_position_key)\n",
"- user_combined_position_key = user_position_key XOR new_customer_position_key\n",
"#### user.cipher.combined_position_key\n",
"- user_property_key = user_property_key XOR props_xor\n",
"- user_property_key = user_property_key XOR old_customer_property_key XOR new_customer_property_key\n"
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2025-03-20T08:32:10.019285Z",
"start_time": "2025-03-20T08:32:10.017224Z"
"end_time": "2025-03-20T10:38:46.312031Z",
"start_time": "2025-03-20T10:38:46.310019Z"
}
},
"cell_type": "code",
"source": [
"props_xor = np.bitwise_xor(new_props, old_props)\n",
"sets_xor = np.bitwise_xor(new_sets, old_sets)\n",
"props_xor = new_props ^ old_props\n",
"pos_xor = new_pos ^ old_pos\n",
"for user in customer.users.values():\n",
" user.renew = True\n",
" user.cipher.combined_position_key = np.bitwise_xor(user.cipher.combined_position_key, sets_xor)\n",
" user.cipher.property_key = np.bitwise_xor(user.cipher.property_key, props_xor)"
" user.cipher.combined_position_key = user.cipher.combined_position_key ^ pos_xor\n",
" user.cipher.property_key = user.cipher.property_key ^ props_xor"
],
"outputs": [],
"execution_count": 50
"execution_count": 97
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Refresh User Keys"
"source": [
"### Refresh User Keys\n",
"After a user's first successful login, the renew flag is checked. If it's true, the user's cipher is replaced with a new cipher."
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2025-03-20T08:32:10.260051Z",
"start_time": "2025-03-20T08:32:10.026503Z"
"end_time": "2025-03-20T10:38:46.553807Z",
"start_time": "2025-03-20T10:38:46.318482Z"
}
},
"cell_type": "code",
"source": [
"user.cipher = UserCipher.create(\n",
" customer.cipher.keypad_size,\n",
" customer.cipher.position_key,\n",
" user.cipher.max_nkode_len\n",
")\n",
"user.enciphered_passcode = user.cipher.encipher_nkode(presumed_selected_properties_idx, customer.cipher)\n",
"user.renew = False"
"if user.renew:\n",
" user.cipher = UserCipher.create(\n",
" customer.cipher.keypad_size,\n",
" customer.cipher.position_key,\n",
" user.cipher.max_nkode_len\n",
" )\n",
" user.enciphered_passcode = user.cipher.encipher_nkode(presumed_property_indices, customer.cipher)\n",
" user.renew = False"
],
"outputs": [],
"execution_count": 51
"execution_count": 98
}
],
"metadata": {