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Table Lookup
In this tutorial, we are going to go over the ways to perform direct table lookups in Concrete Numpy. Please read Compiling and Executing before reading further to see how you can compile the functions below.
Direct table lookup
Concrete Numpy provides a special class to allow direct table lookups. Here is how to use it:
import concrete.numpy as hnp
table = hnp.LookupTable([2, 1, 3, 0])
def f(x):
return table[x]
where
x = "encrypted"scalar
results in
circuit.run(0) == 2
circuit.run(1) == 1
circuit.run(2) == 3
circuit.run(3) == 0
Moreover, direct lookup tables can be used with tensors where the same table lookup is applied to each value in the tensor, so
x = "encrypted"tensor of shape(2, 3)
results in
input = np.array([[0, 1, 3], [2, 3, 1]], dtype=np.uint8)
circuit.run(input) == [[2, 1, 0], [3, 0, 1]]
Direct Multi Table Lookup
Sometimes you may want to apply a different lookup table to each value in a tensor. That's where direct multi lookup table becomes handy. Here is how to use it:
import concrete.numpy as hnp
squared = hnp.LookupTable([i ** 2 for i in range(4)])
cubed = hnp.LookupTable([i ** 3 for i in range(4)])
table = hnp.MultiLookupTable([
[squared, cubed],
[squared, cubed],
[squared, cubed],
])
def f(x):
return table[x]
where
x = "encrypted"tensor of shape(3, 2)
results in
input = np.array([[2, 3], [1, 2], [3, 0]], dtype=np.uint8)
circuit.run(input) == [[4, 27], [1, 8], [9, 0]]
Basically, we applied squared table to the first column and cubed to the second one.
Fused table lookup
Direct tables are tedious to prepare by hand. When possible, Concrete Numpy fuses the floating point operations into table lookups automatically. There are some limitations on fusing operations, which you can learn more about on the next tutorial, Working With Floating Points.
Here is an example function that results in fused table lookup:
def f(x):
return 127 - (50 * (np.sin(x) + 1)).astype(np.uint32) # astype is to go back to integer world
where
x = "encrypted"scalar
results in
circuit.run(0) == 77
circuit.run(1) == 35
circuit.run(2) == 32
circuit.run(3) == 70
circuit.run(4) == 115
circuit.run(5) == 125
circuit.run(6) == 91
circuit.run(7) == 45
Initially, the function is converted to this operation graph
and after floating point operations are fused, we get the following operation graph
Internally, it uses the following lookup table
table = hnp.LookupTable([50, 92, 95, 57, 12, 2, 36, 82])
which is calculated by:
[(50 * (np.sin(x) + 1)).astype(np.uint32) for x in range(2 ** 3)]