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# Common tricks used in (T)FHE | ||
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As explained in the [Basics of FHE](../getting-started/fhe_basics.md), the challenge for developers | ||
is to adapt their code to fit FHE constraints. In this document we have collected some common examples | ||
to illustrate the kind of optimization one can do to get better performance. | ||
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{% hint style="info" %} | ||
All code snippets provided here are temporary workarounds. In future version of Concrete, some | ||
functions described here could be directly available in a more generic and efficient form. | ||
These code snippets are coming from support answers in our [community forum](https://community.zama.ai) | ||
{% endhint %} | ||
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## Minimum for Two values | ||
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In this first example, we compute a minimum by creating a difference between the two numbers `y` and `x` | ||
and conditionally remove this diff from `y` to either get `x` if `y>x` or `y` if `x>y`: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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@fhe.compiler({"x": "encrypted", "y": "encrypted"}) | ||
def min_two(x, y): | ||
diff = y - x | ||
min_x_y = y - np.maximum(y - x, 0) | ||
return min_x_y | ||
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inputset = [tuple(np.random.randint(0, 16, size=2)) for _ in range(50)] | ||
circuit = min_two.compile(inputset) | ||
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x, y = np.random.randint(0, 16, size=2) | ||
assert circuit.encrypt_run_decrypt(x, y) == min(x, y) | ||
``` | ||
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## Maximum for Two values | ||
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The companion example of above with the maximum value of two integers instead of the minimum: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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@fhe.compiler({"x": "encrypted", "y": "encrypted"}) | ||
def max_two(x, y): | ||
diff = y - x | ||
max_x_y = y - np.minimum(y - x, 0) | ||
return max_x_y | ||
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inputset = [tuple(np.random.randint(0, 16, size=2)) for _ in range(50)] | ||
circuit = max_two.compile(inputset) | ||
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x, y = np.random.randint(0, 16, size=2) | ||
assert circuit.encrypt_run_decrypt(x, y) == max(x, y) | ||
``` | ||
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## Minimum for several values | ||
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And an extension for more than two values: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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@fhe.compiler({"args": "encrypted"}) | ||
def fhe_min(args): | ||
remaining = list(args) | ||
while len(remaining) > 1: | ||
a = remaining.pop() | ||
b = remaining.pop() | ||
min_a_b = b - np.maximum(b - a, 0) | ||
remaining.insert(0, min_a_b) | ||
return remaining[0] | ||
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inputset = [np.random.randint(0, 16, size=5) for _ in range(50)] | ||
circuit = fhe_min.compile(inputset) | ||
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x1, x2, x3, x4, x5 = np.random.randint(0, 16, size=5) | ||
assert circuit.encrypt_run_decrypt([x1, x2, x3, x4, x5]) == min(x1, x2, x3, x4, x5) | ||
``` | ||
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## Retrieving a value within an encrypted array with an encrypted index | ||
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This example show how to deal with an array and an encrypted index. It will create a "selection" array filled with `0` except for the requested index that will be `1`, and sum the products of all array values by this selection array: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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@fhe.compiler({"array": "encrypted", "index": "encrypted"}) | ||
def indexed_value(array, index): | ||
all_indices = np.arange(array.size) | ||
index_selection = index == all_indices | ||
selection_and_zeros = array * index_selection | ||
selection = np.sum(selection_and_zeros) | ||
return selection | ||
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inputset = [(np.random.randint(0, 16, size=5), np.random.randint(0, 5)) for _ in range(50)] | ||
circuit = indexed_value.compile(inputset) | ||
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array = np.random.randint(0, 16, size=5) | ||
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index = np.random.randint(0, 5) | ||
assert circuit.encrypt_run_decrypt(array, index) == array[index] | ||
``` | ||
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## Filter an array with comparison (>) | ||
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This example filters an encrypted array with an encrypted condition, here a `greater than` with an encrypted value. | ||
It packs all values with a selection bit, resulting from the comparison that allow the unpacking of only the filtered values: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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@fhe.compiler({"numbers": "encrypted", "threshold": "encrypted"}) | ||
def filtering(numbers, threshold): | ||
is_greater = numbers > threshold | ||
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shifted_numbers = numbers * 2 # open space for a single bit at the end | ||
combined_numbers_and_is_greater = shifted_numbers + is_greater # put is_greater to that bit | ||
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def extract(combination): | ||
is_greater = (combination % 2) == 1 # extract is_greater back from packing | ||
if_true = combination // 2 # if is greater is true, we unpack the number and use it | ||
if_false = 0 # otherwise we set the element to zero | ||
return np.where(is_greater, if_true, if_false) # and apply the operation | ||
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return fhe.univariate(extract)(combined_numbers_and_is_greater) | ||
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inputset = [(np.random.randint(0, 16, size=5), np.random.randint(0, 16)) for _ in range(50)] | ||
circuit = filtering.compile(inputset) | ||
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numbers = np.random.randint(0, 16, size=5) | ||
threshold = np.random.randint(0, 16) | ||
assert np.array_equal(circuit.encrypt_run_decrypt(numbers, threshold), list(map(lambda x: x if x > threshold else 0, numbers))) | ||
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``` | ||
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## Matrix Row/Col means | ||
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In this example of Matrix operation, we are introducing a key concept when using Concrete: | ||
trying to maximize the parallelization. Here instead of sequentially sum all values to create a | ||
mean value, we split the values in sub-groups, and do the mean of the sub-groups means: | ||
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```python | ||
import numpy as np | ||
from concrete import fhe | ||
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def smallest_prime_divisor(n): | ||
if n % 2 == 0: | ||
return 2 | ||
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for i in range(3, int(np.sqrt(n)) + 1): | ||
if n % i == 0: | ||
return i | ||
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return n | ||
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def mean_of_vector(x): | ||
assert x.size != 0 | ||
if x.size == 1: | ||
return x[0] | ||
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group_size = smallest_prime_divisor(x.size) | ||
if x.size == group_size: | ||
return np.round(np.sum(x) / x.size).astype(np.int64) | ||
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groups = [] | ||
for i in range(x.size // group_size): | ||
start = i * group_size | ||
end = start + group_size | ||
groups.append(x[start:end]) | ||
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mean_of_groups = [] | ||
for group in groups: | ||
mean_of_groups.append(np.round(np.sum(group) / group_size).astype(np.int64)) | ||
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return mean_of_vector(fhe.array(mean_of_groups)) | ||
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@fhe.compiler(({"x": "encrypted"})) | ||
def mean_of_matrix(x): | ||
return mean_of_vector(x.flatten()) | ||
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@fhe.compiler(({"x": "encrypted"})) | ||
def mean_of_rows_of_matrix(x): | ||
means = [] | ||
for i in range(x.shape[0]): | ||
means.append(mean_of_vector(x[i])) | ||
return fhe.array(means) | ||
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@fhe.compiler(({"x": "encrypted"})) | ||
def mean_of_columns_of_matrix(x): | ||
means = [] | ||
for i in range(x.shape[1]): | ||
means.append(mean_of_vector(x[:, i])) | ||
return fhe.array(means) | ||
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inputset = [np.random.randint(0, 16, size=(5,5)) for _ in range(50)] | ||
matrix = np.random.randint(0, 16, size=(5, 5)) | ||
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circuit = mean_of_matrix.compile(inputset) | ||
assert circuit.encrypt_run_decrypt(matrix) == round(matrix.mean()) | ||
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circuit = mean_of_rows_of_matrix.compile(inputset) | ||
assert np.array_equal(circuit.encrypt_run_decrypt(matrix), [round(x) for x in matrix.mean(1)]) | ||
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circuit = mean_of_columns_of_matrix.compile(inputset) | ||
assert np.array_equal(circuit.encrypt_run_decrypt(matrix), [round(x) for x in matrix.mean(0)]) | ||
``` |