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docs(frontend): adding the URL-filtering example
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bcm-at-zama committed Sep 13, 2024
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76 changes: 45 additions & 31 deletions frontends/concrete-python/examples/pir/PIR.ipynb
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Expand Up @@ -7,7 +7,7 @@
"source": [
"# Private information retrieval\n",
"\n",
"This notebook explains how to do PIR with Concrete, in a simple way, with an application to blocking phone numbers. The principle of PIR is that there is a large database on the server side, which we can't move to the client side for some reasons, like it's too big or we don't want to for privacy reasons or it's updated too often. With PIR, we let the user query the database, and the query (input and output) is not seen in the clear by the server."
"This notebook explains how to do PIR with Concrete, in a simple way, with applications to blocking spam phone numbers or bad URLs. The principle of PIR is that there is a non-encrypted large database on the server side, which we can't move to the client side for some reasons, like it's too big or we don't want to for privacy reasons or it's updated too often. With PIR, we let the user query the database, and the query (input and output) is not seen in the clear by the server."
]
},
{
Expand Down Expand Up @@ -193,7 +193,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"FHE computation done in 2.2 milliseconds -- database is 8 (2**3) elements of 5 bits\n"
"FHE computation done in 1.6 milliseconds -- database is 8 (2**3) elements of 5 bits\n"
]
}
],
Expand Down Expand Up @@ -258,18 +258,18 @@
"name": "stdout",
"output_type": "stream",
"text": [
"For a database of 2** 4 elements of 8 bits, average execution time is 1.0 milliseconds\n",
"For a database of 2** 4 elements of 16 bits, average execution time is 1.1 milliseconds\n",
"For a database of 2** 8 elements of 8 bits, average execution time is 3.2 milliseconds\n",
"For a database of 2** 8 elements of 16 bits, average execution time is 4.3 milliseconds\n",
"For a database of 2** 9 elements of 8 bits, average execution time is 5.8 milliseconds\n",
"For a database of 2** 9 elements of 16 bits, average execution time is 8.3 milliseconds\n",
"For a database of 2**10 elements of 4 bits, average execution time is 8.1 milliseconds\n",
"For a database of 2**10 elements of 8 bits, average execution time is 9.0 milliseconds\n",
"For a database of 2**12 elements of 4 bits, average execution time is 30.8 milliseconds\n",
"For a database of 2**12 elements of 8 bits, average execution time is 42.6 milliseconds\n",
"For a database of 2**14 elements of 4 bits, average execution time is 139.2 milliseconds\n",
"For a database of 2**14 elements of 8 bits, average execution time is 199.6 milliseconds\n"
"For a database of 2** 4 elements of 8 bits, average execution time is 1.2 milliseconds\n",
"For a database of 2** 4 elements of 16 bits, average execution time is 1.2 milliseconds\n",
"For a database of 2** 8 elements of 8 bits, average execution time is 3.4 milliseconds\n",
"For a database of 2** 8 elements of 16 bits, average execution time is 5.6 milliseconds\n",
"For a database of 2** 9 elements of 8 bits, average execution time is 6.3 milliseconds\n",
"For a database of 2** 9 elements of 16 bits, average execution time is 9.7 milliseconds\n",
"For a database of 2**10 elements of 4 bits, average execution time is 8.4 milliseconds\n",
"For a database of 2**10 elements of 8 bits, average execution time is 10.3 milliseconds\n",
"For a database of 2**12 elements of 4 bits, average execution time is 34.5 milliseconds\n",
"For a database of 2**12 elements of 8 bits, average execution time is 53.6 milliseconds\n",
"For a database of 2**14 elements of 4 bits, average execution time is 184.2 milliseconds\n",
"For a database of 2**14 elements of 8 bits, average execution time is 198.4 milliseconds\n"
]
}
],
Expand Down Expand Up @@ -323,7 +323,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"For a database of 2**14 elements of 32 bits with 4 sub-databases, average execution time is 256.2 milliseconds\n"
"For a database of 2**14 elements of 32 bits with 4 sub-databases, average execution time is 256.6 milliseconds\n"
]
}
],
Expand Down Expand Up @@ -447,7 +447,7 @@
"id": "76855d6d-a65d-442c-b428-f1a077c07570",
"metadata": {},
"source": [
"## Use-cases\n",
"## Use-cases for phone spamming\n",
"\n",
"Now, let see where PIR could be used. Let's imagine we want to build a spam database. In France, there are 10 ** 9 ~ 2 ** 30 phone numbers, we could have a database T[i] for i an integer of 30 bits, returning a boolean stating if the phone number is a known spam number. The database would be server side, and often updated. Phones could query the database on an number, and if the result is positive, filter the call as a spam. All of this would be done without the server knowing the calling numbers.\n",
"\n",
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"name": "stdout",
"output_type": "stream",
"text": [
"Estimated time would be 8764.0 seconds for 8388608 DBs of (4, 8)\n",
"Estimated time would be 4608.0 seconds for 4194304 DBs of (4, 16)\n",
"Estimated time would be 1673.0 seconds for 524288 DBs of (8, 8)\n",
"Estimated time would be 1124.0 seconds for 262144 DBs of (8, 16)\n",
"Estimated time would be 1523.0 seconds for 262144 DBs of (9, 8)\n",
"Estimated time would be 1086.0 seconds for 131072 DBs of (9, 16)\n",
"Estimated time would be 2127.0 seconds for 262144 DBs of (10, 4)\n",
"Estimated time would be 1182.0 seconds for 131072 DBs of (10, 8)\n",
"Estimated time would be 2022.0 seconds for 65536 DBs of (12, 4)\n",
"Estimated time would be 1397.0 seconds for 32768 DBs of (12, 8)\n",
"Estimated time would be 2280.0 seconds for 16384 DBs of (14, 4)\n",
"Estimated time would be 1636.0 seconds for 8192 DBs of (14, 8)\n",
"Estimated time would be 9669.0 seconds for 8388608 DBs of (4, 8)\n",
"Estimated time would be 5054.0 seconds for 4194304 DBs of (4, 16)\n",
"Estimated time would be 1774.0 seconds for 524288 DBs of (8, 8)\n",
"Estimated time would be 1474.0 seconds for 262144 DBs of (8, 16)\n",
"Estimated time would be 1648.0 seconds for 262144 DBs of (9, 8)\n",
"Estimated time would be 1277.0 seconds for 131072 DBs of (9, 16)\n",
"Estimated time would be 2203.0 seconds for 262144 DBs of (10, 4)\n",
"Estimated time would be 1344.0 seconds for 131072 DBs of (10, 8)\n",
"Estimated time would be 2260.0 seconds for 65536 DBs of (12, 4)\n",
"Estimated time would be 1757.0 seconds for 32768 DBs of (12, 8)\n",
"Estimated time would be 3018.0 seconds for 16384 DBs of (14, 4)\n",
"Estimated time would be 1626.0 seconds for 8192 DBs of (14, 8)\n",
"\n",
"Best combination: 1086.0 seconds for a DB of 30 bits\n",
"Best combination: 1277.0 seconds for a DB of 30 bits\n",
"\n",
"Estimated time would be 9.0 seconds for 8192 DBs of (4, 8)\n",
"Estimated time would be 10.0 seconds for 8192 DBs of (4, 8)\n",
"Estimated time would be 5.0 seconds for 4096 DBs of (4, 16)\n",
"Estimated time would be 2.0 seconds for 512 DBs of (8, 8)\n",
"Estimated time would be 2.0 seconds for 256 DBs of (8, 16)\n",
"Estimated time would be 2.0 seconds for 256 DBs of (9, 8)\n",
"Estimated time would be 2.0 seconds for 128 DBs of (9, 16)\n",
"Estimated time would be 3.0 seconds for 256 DBs of (10, 4)\n",
"Estimated time would be 2.0 seconds for 128 DBs of (10, 8)\n",
"Estimated time would be 2.0 seconds for 64 DBs of (12, 4)\n",
"Estimated time would be 3.0 seconds for 64 DBs of (12, 4)\n",
"Estimated time would be 2.0 seconds for 32 DBs of (12, 8)\n",
"Estimated time would be 3.0 seconds for 16 DBs of (14, 4)\n",
"Estimated time would be 2.0 seconds for 8 DBs of (14, 8)\n",
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"find_best_combination(30)\n",
"find_best_combination(20)"
]
},
{
"cell_type": "markdown",
"id": "ff578b6f-98b9-4073-8427-ec32aff5437a",
"metadata": {},
"source": [
"## Another use-case for URL checking\n",
"\n",
"It might also be tempting to keep (and refresh very often) a list of bad URL on the server side, and to use them to protect user to click on bad links. Of course, there will be too many URLs to keep with the previous system: fortunately we have an hash-based solution for this. \n",
"\n",
"The principle will be to use a small non-cryptographic hash function, which maps strings to small integers, let say 20-bit integers. Then, any time the server would see a bad URL `u`, it would hash it to `h` and would store `T[h] = 1` to set that this hash is potentially dangerous. Then, with our system, the user can use privacy-preserving PIR to know if a given URL `u'` is dangerous, by having it to `h'` and checking if `T[h'] == 1`. \n",
"\n",
"As we know with such-a-small hash function, there will be collisions, which means that sometimes, the user will receive false positives: having `T[h] == 1` doesn't mean that this given URL is dangerous, but that there exists an URL with same hash which is dangerous. These collisions is not a problem per se, the user may just see a \"Warning, this URL is potentially dangerous\" but still access if he is confident. Or, we could use several different hash functions and different tables `T_i`, and we would check if all `T_i` return 1 to define if an URL is a spam, to highly reduce the probability of collisions. "
]
}
],
"metadata": {
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10 changes: 5 additions & 5 deletions frontends/concrete-python/examples/pir/pir_utils.py
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Expand Up @@ -2,9 +2,12 @@

from concrete import fhe


@fhe.compiler({"one_hot_vector": "encrypted", "database": "clear"})
def get_ith_element_of_database(one_hot_vector: np.ndarray, database: np.ndarray) -> int:
return np.dot(one_hot_vector, database)


def make_one_hot_vector(index: int, size: int) -> np.ndarray:

answer = np.zeros(shape=(size,), dtype=np.int8)
Expand All @@ -14,9 +17,7 @@ def make_one_hot_vector(index: int, size: int) -> np.ndarray:

def compile_function(database, show_mlir=False, show_graph=False):

@fhe.compiler({"one_hot_vector": "encrypted", "database": "clear"})
def get_ith_element_of_database(one_hot_vector: np.ndarray, database: np.ndarray) -> int:
return np.dot(one_hot_vector, database)
get_ith_element_of_database.reset()

database_length = database.shape[0]
inputset_length = 100
Expand All @@ -30,11 +31,10 @@ def get_ith_element_of_database(one_hot_vector: np.ndarray, database: np.ndarray
return circuit


def test_encrypted_queries(database, circuit, how_many_tests=1, verbose=True):
def test_encrypted_queries(database, circuit, how_many_tests=1):

for _ in range(how_many_tests):
database_length = database.shape[0]
log_database_length = np.ceil(np.log2(database_length)).astype(np.int32)

# Random index in the database
random_index = np.random.randint(database_length)
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